# Robust all-electrical topological valley filtering using monolayer 2D-Xenes

Koustav Jana  Bhaskaran Muralidharan  Department of Electrical Engineering,
Indian Institute of Technology Bombay, Powai, Mumbai-400076, India

(August 27, 2024)

###### Abstract

We propose a realizable device design for an all-electrical robust valley
filter that utilizes spin protected topological interface states hosted on
monolayer group-IV 2D-Xene materials with large intrinsic spin-orbit coupling.
In contrast with conventional quantum spin-Hall edge states localized around
the $X$-points, the interface states appearing at the domain wall between
topologically distinct phases are either from the $K$ or $K\textquoteright$
points, making them suitable prospects for serving as valley-polarized
channels. We show that the presence of a large band-gap quantum spin Hall
effect enables the spatial separation of the spin-valley locked helical
interface states with the valley states being protected by spin conservation,
leading to a robustness against short-range non-magnetic disorder. By adopting
the scattering matrix formalism on a suitably designed device structure,
valley-resolved transport in the presence of non-magnetic short-range disorder
for different 2D-Xene materials is also analyzed in detail. Our numerical
simulations confirm the role of spin-orbit coupling in achieving an improved
valley filter performance with a perfect quantum of conductance attributed to
the topologically protected interface states. Our analysis further elaborates
clearly the right choice of material, device geometry and other factors that
need to be considered while designing an optimized valleytronic filter device.

##  I Introduction

Two-dimensional (2D) materials beyond graphene [1] featuring honeycomb
lattices, such as MoS2 and other transition metal di-chalcogenides (TMDCs)
[2], group-IV 2D-Xenes such as silicene, germanene, stanene [3, 4] etc., have
enjoyed significant research activity targeting a wide range of applications.
The uniqueness of these materials lies in their bandstructure having energy
minimas far apart in the momentum space, endowing the low-energy carriers a
valley degree of freedom that can be exploited for information manipulation.
This has paved the way for the field of valleytronics [5, 6, 7, 8, 9, 10, 11,
12, 13, 14], in which the valley filter [12] is a primary device paradigm that
facilitates the generation of spatially separated valley-polarized carriers.
There have been several proposals for valley filtering that include utilizing
nanoconstrictions [12], optical pumping [10, 8, 11, 13, 15], the valley Hall
effect [13, 6, 7, 14, 9], strain engineering [16, 17], the valley polarized
quantum anomalous Hall (QAH) phase [18, 19, 20], and domain walls between
materials with broken inversion symmetry [21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34]. Two indices critical for a valley filter performance are
the valley polarization and the total transmission, and their immunity against
backscattering [18].
Interface states at domain walls in monolayer 2D materials created using line
junctions or defects which have been considered in previous works have
different levels of topological robustness [21, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 35, 36, 34]. Interface states formed along the zero mass
lines, where the effective mass reverses sign, are valley-momentum locked and
hence serve as perfectly valley polarized channels. In buckled honeycomb
lattices [37] of 2D-Xenes and bilayer materials such as bilayer graphene (BLG)
[23, 24, 25, 9] and bilayer MoS2 [38], it is possible to break the inversion
symmetry and control the band gap by the application of a perpendicular
electric field using electrical gating, in order to possibly facilitate an
all-electrical valley filter. Previous proposals and experimental realizations
of domain wall-based valley filters in monolayer [33, 34] and bi-layer
structures [24, 23] suffer from a serious deterioration in the transmission
and valley polarization due to back-scattering and bulk-assisted inter-valley
scattering from strong short-range disorder [25, 24, 32].
In this paper, we utilize the spin protection to the valley states through
spin-valley locking [27], to demonstrate a realizable device design for robust
valley filtering via the spatial separation of spin-valley locked interface
states. This is, in general possible in materials with strong spin-orbit (SO)
coupling featuring a broken inversion symmetry, typical examples being
monolayer MoS2 and related materials [39], as well as group-IV 2D-Xenes under
a perpendicular electric field [40, 41]. Despite naturally possessing broken
inversion symmetry, the band gap in monolayer TMDCs cannot be controlled via
electrical gating [38]. Hence, we center the proposal on monolayer group-IV
2D-Xenes with buckled lattice structures [42, 43, 44, 37, 45, 46, 47, 48] to
design and realize topologically robust valley filtering.
Our device design is inspired by the following ideas. Buckled 2D-Xene
materials, in the absence of an electric field possess a topologically non-
trivial bandstructure with quantum spin Hall (QSH) edge states and continue to
do so until a critical field beyond which they transition to a topologically
trivial band insulator phase also known as quantum valley Hall (QVH) phase
[41]. Adopting the experimentally well-established dual-split gate structure
[24, 23] as depicted in Fig. 1(a), with the side and top views as shown in
Fig. 1(b), we demonstrate that it is also possible to achieve QVH-QSH-QVH
domain walls in contrast with the QVH-QVH domain walls of the earlier
proposals. The QVH-QVH domain wall as illustrated in Fig. 1(c) hosts valley-
momentum locked states, for both the spins, operating as valley-polarized
channels. On the other hand, with the QVH-QSH-QVH domain walls illustrated in
Fig. 1(d), we can obtain spatially separated valley-polarized channels
protected by spin conservation through spin-valley locking, provided time
reversal symmetry (TRS) is preserved. This introduces the desired spin
protection to the valley states via spin-valley locking in each of the two
domain walls. Given the two domain walls are spatially well separated, we
expect our valley filter to be robust, even against short-range disorder that
can cause large momentum transfer, given the disorder is non-magnetic and does
not break TRS. This demands a QSH region that has a large gap, i.e., a large
intrinsic SO coupling.

Figure 1: Device schematics: a) Proposed dual-split-gated device where red
denotes the positive plate and blue denotes the negative plate. A monolayer 2D
Xene nanoribbon with a buckling height $2l$ is sandwiched between the gates.
This configuration helps us achieve opposite electrical field $E_{z}$ on
either sides with a line junction in between where $E_{z}$ transitions from
positive to negative or vice-versa. b) Side and top view of the device
structure. Sublattice $A$ sites are marked in yellow and sublattice $B$ sites
in green. The width of the line junction is determined by the spacing $W_{j}$
between the adjacent gates. The location of the Fermi level of the line
junction can be controlled by $U$ whereas $E_{z}$ can be controlled by V. The
left lead, the right lead and the channel region are denoted by $L$,$R$ and
$C$ respectively. c) Earlier proposals feature domain walls between the QVH
phases with reversed inversion asymmetry, giving rise to valley-momentum
locked interface states for both the spins. d) Our proposal features domain
walls between the QSH and the QVH phases spatially separated from each other,
such that, each one hosts spin-valley locked interface states and hence the
valley-polarized conducting electrons are spin-protected when TRS is
preserved. The yellow (dark blue) line denotes $K$ ($K^{\prime}$) valley
whereas the solid (dotted) line denotes the up(down) spin states.

We also demonstrate this high degree of robustness by subjecting our channel
to short-range non-magnetic disorder of varying strength and examining the
effect of SO coupling and line junction width on the valley filter
performance. Based on our findings we conclude the superiority of our QVH-QSH-
QVH structure compared to other existing proposals. This implies the
preservation of unity transmission and a mild degradation of the valley
polarization with increase in disorder, guaranteeing a large enough valley
polarized current. To support our claims, we also present the local density of
states (LDOS) calculations over the entire channel region. Apart from
demonstrating the role of SO coupling and line junction width in achieving
improved valley filtering, we also present a strategy to optimize the
performance of the valley filter to tap into the full potential of our design.

##  II Results and Discussions

###  II.1 Device set up

In our proposed valley filter device sketched in Figs. 1(a) and 1(b), we
consider the channel as well as the leads to be made of monolayer 2D-Xene. The
tight binding Hamiltonian, based on the Kane-Mele model [49], for a typical
monolayer 2D-Xene having a honeycomb lattice structure reads [41, 40]

$\hat{H}=-t\sum_{\langle
i,j\rangle\alpha}c_{i\alpha}^{\dagger}c_{j\alpha}+i\frac{\lambda_{SO}}{3\sqrt{3}}\sum_{\langle\langle
i,j\rangle\rangle\alpha}\alpha\nu_{ij}c_{i\alpha}^{\dagger}c_{j\alpha}\\\
+\sum_{i\alpha}\mu_{i}\Delta_{z}c_{i\alpha}^{\dagger}c_{i\alpha},$ (1)

where $c_{i\alpha}^{(\dagger)}$ represents the annihilation (creation)
operator of an electron on site $i$ with a spin $\alpha$, and $\langle
i,j\rangle$ and $\langle\langle i,j\rangle\rangle$ run over all the nearest
and next-nearest neighbour hopping sites respectively. The spin index $\alpha$
can be $\uparrow/\downarrow$, represented with corresponding values $+1/-1$
respectively. The first term in (1) corresponds to the usual nearest neighbour
hopping term with a hopping strength $t$. The second term represents the
intrinsic SO coupling with strength $\lambda_{SO}$, where $\nu_{ij}=+1(-1)$
for anti-clockwise(clockwise) next-nearest neighbour hopping with respect to
the positive $z$-axis. The third term denotes the staggered sublattice
potential due to $\Delta_{z}$, with $\mu_{i}=+1(-1)$, when $i$ belongs to
sublattice A(B). Here, $\Delta_{z}$ is site dependent even though the $i$
index has been dropped. This term can be easily realized in buckled lattices
through the application of a perpendicular electric field $E_{z}$, giving
$\Delta_{z}=lE_{z}$ where $2l$ is the buckling height.There are additional
Rashba SO coupling terms which have been neglected because they either are
negligible in value for group-IV Xenes or have negligible effect on the states
around the $K$/$K^{\prime}$ points [41, 40, 31, 50, 22].

Table 1: The parameters corresponding to graphene, silicene, germanene and stanene. $t$ is the hopping parameer, $a$ is the lattice constant, $\lambda_{SO}$ is the intrinsic SO coupling, $l$ is half the buckling height [41] |  | $t(eV)$ |  |  $a$(Å) |  | $\lambda_{SO}(meV)$ |  |  $l$(Å)
---|---|---|---|---|---|---|---|---
Graphene |  | 2.8 |  | 2.46 |  | $10^{-3}$ |  | 0
Silicene |  | 1.6 |  | 3.86 |  | 3.9 |  | 0.23
Germanene |  | 1.3 |  | 4.02 |  | 43 |  | 0.33
Stanene |  | 1.3 |  | 4.7 |  | 100 |  | 0.4
Table 2: Chern numbers ($\mathcal{C}^{\eta}_{s}$) corresponding to the spin ($s$) and valley ($\eta$) degrees of freedom, along with the spin ($\mathcal{C}_{s}$) and valley ($\mathcal{C}_{v}$) Chern numbers, for the QSH, QVH-I and QVH-II phases [41, 40, 27, 31, 32, 28] |  | $\mathcal{C}^{K}_{\uparrow}$ |  | $\mathcal{C}^{K}_{\downarrow}$ |  | $\mathcal{C}^{K^{\prime}}_{\uparrow}$ |  | $\mathcal{C}^{K^{\prime}}_{\downarrow}$ |  | $2\mathcal{C}_{s}$ |  | $\mathcal{C}_{v}$
---|---|---|---|---|---|---|---|---|---|---|---|---
QVH-I |  | 1/2 |  | 1/2 |  | -1/2 |  | -1/2 |  | 0 |  | 2
QSH |  | 1/2 |  | -1/2 |  | 1/2 |  | -1/2 |  | 2 |  | 0
QVH-II |  | -1/2 |  | -1/2 |  | 1/2 |  | 1/2 |  | 0 |  | -2

Choice of the material. Typical values of the parameters involved in (1) for
the candidate materials [41] have been summarized in Tab. 1. Graphene does not
have a buckled structure ($l=0$) and hence electrical gating cannot be an
option to introduce the $\Delta_{z}$ term in it. Also both graphene and
silicene have very small $\lambda_{SO}$ values of $10^{-3}meV$ and $3.9meV$
respectively, thus not making them suitable candidates to exploit the
topological robustness of the QSH phase that we intend to do in order to
design an efficient valley filter. It is worth mentioning that theoretical
possibilities of engineering QSH and QVH states in strained graphene exist
[16], even in the absence of SO coupling, but such proposals rely on complex
quantum pumping processes.
Stanene with an intrinsic SO coupling of $\approx 0.1eV$, seems to be a
promising candidate for our valley filter [41, 51] proposal. Apart from this,
functionalized germanene [52] and stanene [53, 54] have shown sizable band
gaps of around $0.3eV$ along with a record band gap of around $1.34eV$ in
chemically decorated monolayer plumbene [55]. Also the above materials show a
large enough buckling height [55, 54], with $l$ ranging from $0.4-0.7$Å and
hence the possibility of achieving a large gap QVH state as well. Thus the
possibility of large band gap QSH and QVH phases in germanene and stanene
makes them the ideal choice of materials to serve our purpose.
Having $l=0.4$ Å would require an electrical field ($E_{z}$) of $5V/nm$ to
achieve $\Delta_{z}=0.2eV$, which is practically quite achievable [56, 37].
Based on this discussion, we choose the parameters involved in our model to be
the following: $t=1.3eV$, $l=0.4$Å and $a=4$Å. We then vary $\lambda_{SO}$ and
$\Delta_{z}$ within the practically realizable limits, in order to optimize
the valley filter performance.

Figure 2: a) Phase diagram depicting the effect of the sublattice potential,
$\Delta_{z}$ on the Dirac mass, $|\Delta_{s}^{\eta}|$ (see text). Topological
phase transitions at $\Delta_{z}=\pm\lambda_{SO}$. At
$\Delta_{z}=-\lambda_{SO}$, the gap closes for $(\uparrow,K\textquoteright)$
and $(\downarrow,K)$ and we have a QVH-I/QSH transition. Similarly at
$\Delta_{z}=\lambda_{SO}$, gap closes for $(\uparrow,K)$ and
$(\downarrow,K^{\prime})$ and we have a QVH-II/QSH transition. b) The
staggered sublattice potential, $\mu_{i}\Delta_{z}$ variation along the
y-direction in the sublattices(solid line for sublattice A and dashed line for
sublattice B) when $W_{j}=6.25nm$, which is small enough such that the width
of the region having $\Delta_{z}=0$ is negligible. $\Delta_{zo}$ is the
maximum value of $\Delta_{z}$, which is varied as per our band gap
requirements. c) $\mu_{i}\Delta_{z}$ variation when $W_{j}=20.8nm$, which
ensures that the width of the region having $\Delta_{z}=0$ is large enough.

Topological Phases. Based on the low energy Dirac Hamiltonian [40], the gap of
the energy spectrum corresponding to a spin $s$ and valley $\eta$, is given by
$2|\Delta^{\eta}_{s}|$, where $\Delta^{\eta}_{s}=\Delta_{z}-\eta
s\lambda_{SO}$ is the Dirac mass term [41, 40]. We define the point
$(4\pi/3a,0)$ as the $K$ valley and $(2\pi/3a,0)$ as the $K\textquoteright$
valley. On varying $\Delta_{z}$, $\Delta^{\eta}_{s}$ reverses its sign when
$\Delta_{z}=\eta s\lambda_{SO}$ signalling a topological phase transition.
The above phase transitions can be better understood by an analysis of the
Berry curvature and the Chern number. It is well known that the Berry
curvature of the given Hamiltonian (1) is strictly localized around the $K$
and $K\textquoteright$ points, allowing us to associate each valley with a
Chern number $\mathcal{C}^{\eta}_{s}$, where spin index
$s=\uparrow,\downarrow$ and valley index $\eta=\pm$. The Chern number
$\mathcal{C}^{\eta}_{s}$ can be obtained using the Dirac Hamiltonian and is
given by $\mathcal{C}^{\eta}_{s}=-\frac{\eta}{2}sgn(\Delta^{\eta}_{s})$ [41,
40, 27, 31, 32, 28]. Figure 2(a) shows the variation of $|\Delta^{\eta}_{s}|$
with $\Delta_{z}$ for all four pairs of $(s,\eta)$ values and the
corresponding Chern numbers have been listed in Tab. 2.
Here it is important to further introduce the spin Chern number
$\mathcal{C}_{s}$ and the valley Chern number $\mathcal{C}_{v}$ as:

$\displaystyle\mathcal{C}_{s}=\frac{1}{2}(\mathcal{C}^{K}_{\uparrow}+\mathcal{C}^{K\textquoteright}_{\uparrow}-\mathcal{C}^{K}_{\downarrow}-\mathcal{C}^{K\textquoteright}_{\downarrow})$
(2)
$\displaystyle\mathcal{C}_{v}=\mathcal{C}^{K}_{\uparrow}-\mathcal{C}^{K\textquoteright}_{\uparrow}+\mathcal{C}^{K}_{\downarrow}-\mathcal{C}^{K\textquoteright}_{\downarrow}.$
(3)

Based on $\mathcal{C}_{s}$ and $\mathcal{C}_{v}$, we can now label the various
topological phases, namely the QSH phase and the QVH phases by varying
$\Delta_{z}$. For $-\lambda_{SO}<\Delta_{z}<\lambda_{SO}$, the material exists
in the QSH phase, characterized by $2\mathcal{C}_{s}=+2$ (given
$\lambda_{SO}>0$) and $\mathcal{C}_{v}=0$. On the other hand, for
$\Delta_{z}<-\lambda_{SO}$ $(\Delta_{z}>\lambda_{SO})$, the material is in the
QVH-I (QVH-II) phase having $2\mathcal{C}_{s}=0$ and $\mathcal{C}_{v}=+2(-2)$.
Topological Domain Walls. We now move on to investigate the interface states
at the topological domain walls between different phases [32, 27, 31, 28, 29,
24, 30]. At the QVH-I/QSH interface, $\Delta\mathcal{C}^{\eta}_{s}$ is non-
zero only for the $(\uparrow,K\textquoteright)$ and $(\downarrow,K)$ states
and has opposite signs, thus yielding a pair of counter-propagating helical
interface states. Hence at the domain wall between the QVH-I and QSH phases,
we have spin-valley-momentum locked interface states,
$(\uparrow,K\textquoteright)$ and $(\downarrow,K)$ propagating in opposite
directions. A similar analysis of the domain wall between the QVH-II and QSH
phases yields counter-propagating $(\uparrow,K)$ and
$(\downarrow,K\textquoteright)$ interface states. There is a third possible
scenario that arises when $\lambda_{SO}=0$, that is, no QSH phase exists and
we will have a domain wall between the QVH-I and QVH-II phases. In this case
$\Delta\mathcal{C}^{\eta}_{s}$ is non-zero for all the four possible states
with opposite signs for the $K$ and $K\textquoteright$ valley states. Thus we
expect four interface states with the $K$ valley states propagating in one
direction and the $K\textquoteright$ states in the opposite direction. One
special feature of these interface states which makes them an attractive
option for valley filtering is that the counter-propagating states are
localised at the $K$ and $K\textquoteright$ points and are immune to any back-
scattering due to long range disorder [32, 25, 24].
Device structure. The domain walls discussed above can be easily realized by
creating a line junction between oppositely gated regions using a dual-split-
gate structure shown in Figs. 1(a) and 1(b). The given configuration of
voltage sources ensures that a voltage of $U\pm V$ is applied to the gates,
where $V$ is responsible for modulating $E_{z}$ and $U$ allows us to control
the channel electrochemical potential. Thus the channel has an additional on-
site potential $U$ on every site realized via the addition of the Hamiltonian
term $\hat{H}_{U}=\sum_{i\alpha}Uc_{i\alpha}^{\dagger}c_{i\alpha}$. For the
leads, we consider both $\lambda_{SO}$ and $\Delta_{z}$ to be zero.
Given the width of the nanoribbon is $W_{o}$, we consider its y-coordinates to
be in the range $\left[-\frac{W_{o}}{2},\frac{W_{o}}{2}\right]$. The dual-
split-gates have a spacing of $W_{j}$, with the adjacent edges located at
$y=\pm\frac{W_{j}}{2}$. We have modelled the spatial dependence of $E_{z}$
using the following analytical expression:

$E_{z}(y)=\frac{E_{zo}}{2}\left({\bf{tanh}}\left(\frac{y-\frac{W_{j}}{2}}{\frac{W_{f}}{2}}\right)+{\bf{tanh}}\left(\frac{y+\frac{W_{j}}{2}}{\frac{W_{f}}{2}}\right)\right),$
(4)

where $E_{zo}$ is the maximum magnitude of the perpendicular electric field
applied and $W_{f}$ is the fringing width of the electric field at the gate
edges. In an actual setup $W_{f}$ has a direct dependence on the perpendicular
spacing between the gates, which we assume to be $3.125nm$. Figures 2(b) and
2(c) illustrate the potential variation ($\mu_{i}\Delta_{z}$) along
sublattices $A$ and $B$ for the two cases: $W_{j}=6.25nm$ (small $W_{j}$) and
$W_{j}=20.8nm$ (large $W_{j}$) respectively. The above two cases differ in the
fact that in the former case, the width of the region having $\Delta_{z}=0$ is
negligible, whereas in the latter this width is large enough. Interestingly,
exploiting the above potential variations, it is possible to have different
cases of domain walls as depicted in Figs. 1(c) and 1(d), a deeper discussion
of which will follow in the upcoming section.

Figure 3: Gate voltage configuration, corresponding band structure and valley
polarization of our proposed valley filter: $W_{j}=6.25nm$ and
$\lambda_{SO}=0.1eV$ a) "$+-$" configuration gives a $K$-valley polarized
filter for transmission from the left ($L$) to the right ($R$) lead, given the
channel electrochemical potential lies within the band gap, where as suggested
by the band structure, all the $K$-valley electrons are right-going and all
$K^{\prime}$-valley electrons are left-going. b) The "$-+$" configuration
makes it a $K^{\prime}$-valley polarized filter as the interface states
reverse their direction of propagation and now the $K$-valley electrons are
left-going whereas the $K^{\prime}$-valley electrons are right-going.

In all our calculations, we consider a zig-zag nanoribbon which is $180$ atoms
wide, corresponding to a width $W_{o}=62.5nm$. The channel region $C$ as well
as the leads $L$ and $R$ have the same width $W_{o}$, with the length $L_{o}$
of the channel region being 40nm i.e., $100$ atoms long, which is long enough
such that the out-going carriers are completely valley polarized in the clean
limit. The electrochemical potential of the leads ($E$) is fixed at $E=t/3$,
corresponding to precisely seventy eight propagating modes, and that of the
channel ($E-U$) is controlled by varying $U$. For all the numerical results
that follow, unless explicitly mentioned, the width of the nanoribbon, length
of the channel region $C$ and the electrochemical potential of the leads are
fixed.
Depicted in Fig. 3 is the operation of our valley filter in the absence of any
form of disorder, i.e., the clean limit. The electrochemical potential of both
the leads is fixed at $E$. For this case: $W_{j}=6.25nm$, $E=t/3$,
$\lambda_{SO}=0.1eV$ and $\Delta_{zo}=lE_{zo}=0.2eV$(max. value of
$\Delta_{z}$), thus creating a gap of
$2\left(\Delta_{zo}-\lambda_{SO}\right)=0.2eV$. The gap defined above
corresponds to the gap of the QVH regions, given that the QSH region gap is
independent of $\Delta_{zo}$ and depends only on $\lambda_{SO}$. Both Fig.
3(a) and Fig. 3(b) corresponding to opposite gate configurations, show close
to perfect valley polarization in the gap range $\left[-0.1eV,0.1eV\right]$.
Since the valley polarization plotted is for transmission from $L$ to $R$,
whenever the $K$-valley electrons are right going, our filter is $K$-valley
polarized as in Fig. 3(a) and similarly $K\textquoteright$-valley polarization
in Fig. 3(b). The fact that the valley polarization of the filter can be
reversed by just reversing the signs of the gate voltages, makes this valley
filter design quite convenient for practical purposes.

###  II.2 Results

Figure 4: Spatial variation of local band gap and electronic band structure
for different cases of $\lambda_{SO}$ and $W_{j}$ considered. a1, a2)
$W_{j}=6.25nm$ and $\lambda_{SO}=0eV$ b1, b2) $W_{j}=6.25nm$ and
$\lambda_{SO}=0.04eV$ c1, c2) $W_{j}=6.25nm$ and $\lambda_{SO}=0.1eV$ d1, d2)
$W_{j}=20.8nm$ and $\lambda_{SO}=0eV$ e1, e2) $W_{j}=20.8nm$ and
$\lambda_{SO}=0.04eV$ f1, f2) $W_{j}=20.8nm$ and $\lambda_{SO}=0.1eV$

To ensure a fair comparison across all the cases, we assume the band gap of
the bulk states in the QVH regions to be $0.2eV$, i.e., a gap range of
$\left[-0.1eV,0.1eV\right]$, demanding $\Delta_{zo}=0.1+\lambda_{SO}$, which
implies that as $\lambda_{SO}$ is varied, the applied gate voltage $V$ also
needs to be varied accordingly. Figure 4(a1-f1) shows the spatial variation of
local band gap along the nanoribbon width for six different combinations of
$\lambda_{SO}$ and $W_{j}$ along with the corresponding band structures in
Figure 4(a2-f2). As indicated by the blue bands in Fig. 4(a1-f1), localized
interface states appear at the locations where the band gap closes. The total
transmission $T$ and valley polarization $Pv$ are plotted in Fig. 5, in two
different ways: a) Disorder strength $W$ varied, for $E-U=0$, with $E=t/3$, as
shown in Fig. 5(a-d) b) $E-U$ varied over the gap range
$\left[-0.1eV,0.1eV\right]$ for $W=2eV$, as in Fig. 5(e-h). In the clean
limit, within the gap range, we expect $Pv$ to be close to unity, and $T=2$,
corresponding to two interface states, one for each spin.
However for disorder strength $W=2eV$, $Pv$ deteriorates significantly,
suggesting an increased inter-valley scattering between the helical interface
states and hence a suppressed transmission due to increased backscattering.
This does hold true for $E-U$ around zero, but when $E-U$ approaches the band
edge, an enhancement in $T$ is observed indicating the bulk state assistance
in inter-valley scattering, similar to what has been reported in [25]. Thus
the inter-valley mixing that is detrimental to the efficiency of our valley
filter can happen either directly via backscattering between the helical
interface states or indirectly assisted by the bulk states. The former is
dominant when the electrochemical potential lies in the middle of the band gap
and the latter takes over as the electrochemical potential approaches the band
edge.
Although there is no clear way to get rid of the bulk-assisted inter-valley
scattering other than having a larger band gap, the direct one can be evaded
by introducing a spatial separation between interface states of the same spin.
The results in Figs. 5(c) and 5(g) indeed confirm this. Unlike the other
cases, as suggested by Fig. 5(c), $T$ remains unchanged when
$\lambda_{SO}=0.1eV$ and $W_{j}=20.8nm$, even in the presence of very strong
disorder ($W=2.4eV$) and does not degrade with $W$ as seen in other cases.
Figure 5(g) shows that $T$ remains perfectly quantized when the
electrochemical potential lies around the mid-gap before getting affected by
the bulk states as we move closer to the band edge. Despite showing a mild
degradation in $Pv$ with $W$ like the others, it still has the best valley
polarization in the presence of strong disorder.
The obtained results make more sense once the local band gap profiles in Fig.
4 are analyzed. Since the interface states appear at the locations where the
gap closes, for the $W_{j}=6.25nm$ case, the four interface states co-exist
and overlap with one another (Fig. 4(a1-c1)). On the other hand when
$W_{j}=20.8nm$, the interface states can now be hosted with spatial
separation. However that alone is not enough to ensure spatial separation
without any overlap. For example, in the case of $\lambda_{SO}=0eV$, the
central line junction region is semi-metallic and gapless thus leading to the
interface states spreading out uniformly over the entire central region
instead of being localized as depicted in Fig. 4(d1).
A wide semi-metallic region also leads to bulk states, thus decreasing the
available band gap as suggested by Fig. 4(d2). This has a detrimental effect
on the valley filter performance, with the device now not only having a
diminished operational energy range, but also a degrading valley polarization
within this range, as confirmed by Fig. 5(h), thus highlighting the role of
bulk-assisted inter-valley scattering in deteriorating the filtering
efficiency. Similarly when $\lambda_{SO}=0.04eV$ there exists a low band gap
QSH region in the line junction. Although the interface states are hosted at
different locations as depicted in Fig. 4(e1), they can still interact with
one another via tunneling through the low band gap central region, thus
leading to inevitable back-scattering. Even in this case, some bulk states
enter the band gap as shown in Fig. 4(e2) and further deteriorate the valley
filter performance.
However, when $\lambda_{SO}=0.1eV$, the gap is free from bulk states as the
QSH region has a gap equal to that of the QVH regions and any possible
tunneling between the interface states is suppressed owing to the larger
bandgap central region. Thus the back-scattering is strongly suppressed even
in presence of strong disorder and we get a perfectly quantized transmission
$T=2$ around the mid-gap. However the bulk-assisted inter-valley scattering
still persists and hence the degradation of $Pv$ with $W$.

Figure 5:  Numerical results for different combinations of $W_{j}=6.25nm$,
$20.8nm$ and $\lambda_{SO}=0eV$, $0.04eV$, $0.1eV$. In (a)-(d), the results
are plotted versus varying disorder strength $W$ for channel electrochemical
potential, $E-U=0$. In (e)-(h), the results are plotted versus varying $E-U$
over the band gap for $W=2eV$. The case having $W_{j}=20.8nm$ and
$\lambda_{SO}=0.1eV$ clearly outperforms the rest. Figure 6: LDOS profile for
different cases of $\lambda_{SO}$ and $W_{j}$ considered. The channel
electrochemical potential $E-U=0$ and disorder strength $W=0$ a)
$W_{j}=6.25nm$ and $\lambda_{SO}=0eV$ b) $W_{j}=6.25nm$ and
$\lambda_{SO}=0.04eV$ c) $W_{j}=6.25nm$ and $\lambda_{SO}=0.1meV$ d)
$W_{j}=20.8nm$ and $\lambda_{SO}=0eV$ e) $W_{j}=20.8nm$ and
$\lambda_{SO}=0.04eV$ f) $W_{j}=20.8nm$ and $\lambda_{SO}=0.1eV$

To further validate the arguments made above, the LDOS in the absence of
disorder, for $E-U=0$, has been plotted for all the cases in Fig. 6. The
spatial variation of the interface states is illustrated for varied
$\lambda_{SO}$, when $W_{j}$ is small, in Fig. 6(a-c) and similarly in Fig.
6(d-f) for large $W_{j}$. The LDOS plots confirm our previous claims of the
interface states being spatially separated only for the case with
$\lambda_{SO}=0.1eV$ and $W_{j}=20.8nm$ (Fig. 6(f)). Thus our simulation
results shed light on the possibility of achieving an improved valley filter
performance, with a perfectly quantized $T$, by spatially separating the
interface states with the same spin through a suitable chosen gate
configuration. We now look into the important aspect of optimizing the
proposed valley filter device.

###  II.3 Device Optimization

As mentioned before, a good electrical valley filter should have a large
valley polarization along with a large enough total current in order to
achieve a large valley current. In other words, perfect valley polarization
with a very small amount of current is of no practical utility to any of the
valleytronic applications. Thus exploiting the topological robustness and
dissipation-less nature of spatially separated interface states with the
introduction of intrinsic SO coupling is the key to achieve improved valley
filtering.
Our valley filter can be optimized by considering the following two crucial
requirements: Firstly, the QSH region should be well-gapped and wide enough to
ensure that the spatially separated interface states do not overlap with each
other. This is necessary to ensure that backscattering is negligible and $T$
is perfectly quantized even in the presence of strong non-magnetic disorder.
Secondly, the QVH regions also need to be well-gapped and wide enough to
ensure that the interface states do not spread out to the nanoribbon edges.
Ensuring this is critical to maintain the valley-polarized character of the
interface states so that the valley filter produces significant valley
polarization.
Optimal $\bf{\lambda_{SO}}$. So far, the comparison between the different
cases was made after considering the same bulk band gap of the QVH region and
this requires different perpendicular fields $E_{zo}$ for different values of
$\lambda_{SO}$. In Fig. 5, we notice that when $\lambda_{SO}=0eV$, the valley
filter performs the best when the adjacent gates are as close as possible,
whereas for $\lambda_{SO}=0.1eV$ the valley filter efficiency is enhanced when
the adjacent gates are far apart to ensure spatial separation of interface
states. Hence for $\lambda_{SO}=0eV$ we consider $W_{j}=6.25nm$ whereas when
$\lambda_{SO}=0.1eV$ we increase $W_{j}$ to 20.8nm to have the best possible
valley filter. Similar to Fig. 4, we consider $\Delta=0.1eV$ for
$\lambda_{SO}=0.1eV$ case and this requires $E_{zo}=5V/nm$ given $l=0.4$Å,
which is practically achievable. For the same $E_{z}$ and $l$, in the
$\lambda_{SO}=0eV$ case we can achieve $\Delta=0.2eV$.
The transmission plots in Fig. 7(a,b) clearly show the superiority of
$\lambda_{SO}=0.1eV$ case in its robustness to back-scattering. However, as
suggested by Fig. 7(c,d), $Pv$ degrades a bit in this case compared to the
$\lambda_{SO}=0eV$ case because of a smaller band gap leading to increased
bulk-assisted inter-valley scattering. Thus when the same gate voltage is
applied, addition of SO coupling to host spatially separated interface states
helps us achieve a perfectly quantized $T$ but at the cost of a reduced $Pv$.
In the above comparison, we considered $E_{zo}=5V/nm$ where for the
$\lambda_{SO}=0.1eV$ case we had $\Delta=0.1eV$ and hence we achieved
reasonably good valley filtering whereas for a lower $E_{zo}$ say, $3V/nm$,
the performance degrades due to a very small $\Delta$ of $0.02eV$. The bare
minimum one needs to ensure is that $\lambda_{SO}<E_{zo}/l$, in order to
assure the existence of the QSH/QVH domain walls, and hence the interface
states. Hence the best case would be when the QSH as well as the QVH regions
have the same gap implying $\lambda_{SO}=lE_{zo}/2$ for a given $E_{zo}$. Thus
for $E_{zo}=5V/nm$ and $l=0.4$Å, $\lambda_{SO}=lE_{zo}/2=0.1eV$ is the optimal
one to get the best yields as valley filter given the interface states are
well separated after choosing a suitable $W_{j}$.
Optimal $\bf{W_{j}}$. One might expect that a larger $W_{j}$ should ensure a
greater degree of robustness for the interface states. However, since we have
considered a fixed width for the nanoribbon ($W_{o}=62.5nm$), invariably
increasing $W_{j}$ implies that the widths of the QVH regions keep decreasing
and the interface states move closer to the nanoribbon edges. As a
consequence, the interface states start resembling the conventional QSH edge
states as shown in Fig. 7(e), in which $W_{j}\approx 60nm$, which then results
in diminishing $Pv$ as they move towards the $X$-point of the Brillouin zone.
On the other hand, decreasing $W_{j}$ also brings the interface states closer
from which they interact with each other via tunneling, thus further degrading
$T$ via back-scattering. Thus $W_{j}$ needs to be chosen such that the
interface states are neither too close to each other nor too far apart that
they come in the vicinity of the nanoribbon edges.

Figure 7: Comparison of valley filtering efficiency for the cases with
($\lambda_{SO}=0.1eV$) and without ($\lambda_{SO}=0eV$) SO coupling when
subjected to the same dual gate voltage. a,c) $T$ and $Pv$ versus $E-U$ for
$W=2eV$ b,d) $T$ and $Pv$ versus $W$ for $E-U=0eV$ e) Band structure for
$W_{j}\approx 60nm$, the interface states move towards the $X$-point of the
Brillouin zone f) Variation of $T$ and $Pv$ w.r.t $W_{j}$ for $W=2eV$ and
$E-U=0eV$. $T$ shows droop at low $W_{j}$ because of increased tunneling
between the interface states whereas $Pv$ shows droop at high $W_{j}$ as the
interface states move away from the $K$ and $K^{\prime}$ points. g,h)
Variation of $T$ and $Pv$ w.r.t $E-U$ for different values of $W_{j}$ as
depicted by the color bar and $W=2eV$. For intermediate values of $W_{j}$ we
expect the best performance in terms of both $T$ and $Pv$.

To quantify the above arguments, we consider the spatial extent of the
interface states on either side of the domain wall given by the damping
length, $\zeta=\hbar v_{f}/2\Delta=\sqrt{(}3)at/4\Delta$ [32, 57]. One thing
to note is that this expression is valid for an abrupt topological phase
transition. However, in our case, it is rather smooth over a fringing width of
$W_{f}=3.125nm$. Hence the actual $\zeta$ would be slightly larger than what
we estimate. It is clear that $\zeta$ is inversely proportional to $\Delta$,
thus maintaining our earlier conclusion that $\Delta$ needs to be large enough
for all the QSH as well as QVH regions, so that the interface states are well
confined. For the electric field we consider ($E_{zo}=5V/nm$) the
corresponding optimal $\lambda_{SO}$ was $0.1eV$, thus $\Delta=0.1eV$ for the
QSH as well as QVH regions. The $\zeta$ calculated for our case comes out to
be $2.25nm$ which is in fact smaller than $W_{f}=3.125nm$ and hence we choose
$\zeta=3.125nm$. Considering exponential variation of the wavefunction along
the $y$\- direction on either sides of the domain wall, 96% of the
wavefunction remains confined within a distance i.e., three times the damping
length $\zeta$, for our case $3\zeta\approx 9.5nm$.
Based on the above calculations, we can conclude for the spatially separated
interface states to be decoupled from each other, we require $W_{j}>2\times
9.5=19nm$ and to ensure that they do not spread out all the way into the
nanoribbon edges $W_{j}<W_{o}-2\times 9.5=43.5nm$ is required. Hence choosing
$19nm<W_{j}<43.5nm$, ensures the desirable valley filtering performance both
in terms of $T$ and $Pv$.
Our analytical calculations are also validated by the simulation results in
Fig. 7(f), where $T$ and $Pv$ are plotted against varying $W_{j}$ for $E-U=0$
and $W=2eV$. The total transmission $T$ remains constant at $2$, as we lower
$W_{j}$ before declining rapidly as $W_{j}$ goes below $20nm$. On the other
hand, the valley polarization $Pv$ decreases steadily as we increase $W_{j}$,
before showing a sudden droop once $W_{j}$ goes past $40nm$. Thus our choice
of $W_{j}=20.8nm$ when $E_{zo}=5V/nm$ and $\lambda_{SO}=0.1eV$, as suggested
by both our analytical calculations and simulation results, is optimal in
terms of both $T$ and $Pv$. The variation of $T$ and $Pv$ over the entire band
gap, for different values of $W_{j}$, is illustrated in Fig. 7(g,h). One
important thing to note is that in our above optimization strategy, we were
constrained by the maximum electric field $E_{zo}$ we can apply and the
nanoribbon width $W_{o}$, unconstrained by which, we can further enhance the
valley filter performance.

##  III Conclusion

In conclusion, we proposed a design for an all-electrical robust valley filter
that utilizes topological interface states hosted on monolayer group-IV
2D-Xene materials with large intrinsic spin-orbit coupling. In contrast with
conventional QSH edge states localized around the $X$-points, the interface
states appearing at the domain wall between topologically distinct phases are
either from the $K$ or $K\textquoteright$ points, making them suitable
prospects for serving as valley-polarized channels. We showed that the
presence of a large band-gap quantum spin Hall effect facilitates the spatial
separation of the spin-valley locked helical interface states with the valley
states being protected by spin conservation, leading to robustness against
short-range non-magnetic disorder. By adopting the scattering matrix formalism
on a suitably designed device structure, valley-resolved transport in the
presence of non-magnetic short-range disorder for different 2D-Xene materials
was analyzed in detail. Our numerical simulations confirm the role of spin-
orbit coupling in achieving an improved valley filter performance with a
perfect quantum of conductance attributed to the topologically protected
interface states. Our analysis further elaborated clearly the right choice of
material, device geometry and other factors that need to be considered while
designing an optimized valleytronic filter device. We believe that our work
opens the door for researching the utility of the 1D topological conducting
channels hosted in the monolayer 2D-Xene bulk for possible applications in
valleytronics and spintronics.

##  IV Methods

We use the software package "KWANT" [58] for calculating the transfer matrix
$\tau$, which gives us the transmission amplitude $\tau_{k_{2},k_{1}}$ from
the $k_{1}$ state of lead $L$ to the $k_{2}$ state of lead $R$. The inter-
valley($T_{KK\textquoteright}$ and $T_{K\textquoteright K}$) and intra-
valley($T_{KK}$ and $T_{K\textquoteright K\textquoteright}$), transmission
coefficients can be calculated using the following formula [18, 12]:

$T_{K_{2}K_{1}}=\sum_{k_{1}\in K_{1}}\sum_{k_{2}\in
K_{2}}|\tau_{k_{2},k_{1}}|^{2}$ (5)

Now the transmission coefficient corresponding to scattering into the
$K$-valley in lead $R$ is given by $T_{K}=T_{KK}+T_{KK\textquoteright}$ and
similarly $T_{K\textquoteright}=T_{K\textquoteright K}+T_{K\textquoteright
K\textquoteright}$. Once we have the valley-resolved transmission
coefficients($T_{K}$ and $T_{K\textquoteright}$), we can now calculate the
valley polarization $Pv$ and the total transmission $T$ [18, 12], the two
important metrics to evaluate the performance of a valley filter.

$Pv=\frac{T_{K}-T_{K\textquoteright}}{T_{K}+T_{K\textquoteright}}$ (6)
$T=T_{K}+T_{K\textquoteright}.$ (7)

To evaluate the performance of our valley filter in actual experimental
conditions, we subject it to short-range Anderson non-magnetic disorder which
does not break TRS and this can be done by introducing random on-site
potential for each site. Despite the Anderson disorder not reflecting all the
potential valley-mixing mechanisms in experimental samples, it does provide a
computationally efficient means to model the inter-valley scattering and
allows us to examine the effect of varying parameters such as $\lambda_{SO}$
and $W_{j}$ on the valley filter performance. This is achieved by adding the
term $\hat{H}_{W}=\sum_{i\alpha}\epsilon_{i}c_{i\alpha}^{\dagger}c_{i\alpha}$
to the channel Hamitonian, with $\epsilon_{i}$ being randomly distributed in
the interval $\left[-\frac{W}{2},\frac{W}{2}\right]$ where $W$ is the disorder
strength [18, 25, 24]. For each value of $W$, fifty different random disorder
configurations are considered and the results are averaged over all the
configurations.
We must remark at this stage that only static impurities inside the channel
are considered within the above approach. An unexplored frontier in terms of
understanding the stability of topological edge/interface states is the
inclusion of momentum relaxing dephasing [59, 60, 61, 62, 63] phase breaking
processes [64, 65, 66] and ultimately inelastic scattering processes [67, 68],
that can be well facilitated by using the Keldysh non-equilibrium Green’s
function approach [69].

## Data Availability

The data generated from this work is available from the authors upon request.

###### Acknowledgements.

The research and development work undertaken in the project under the
Visvesvaraya Ph.D Scheme of the Ministry of Electronics and Information
Technology (MEITY), Government of India, is implemented by Digital India
Corporation (formerly Media Lab Asia). This work is also supported by the
Science and Engineering Research Board (SERB), Government of India, Grant No.
Grant No. STR/2019/000030, the Ministry of Human Resource Development (MHRD),
Government of India, Grant No. STARS/APR2019/NS/226/FS under the STARS scheme.

## Author Contributions

BM and KJ conceived the idea. KJ performed all numerical simulations. All
authors contributed in analyzing the results and writing the paper.

## Competing Interests

The authors declare that there are no competing interests.

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Further author information: (Send correspondence to J.L.)
J.L.: E-mail<EMAIL_ADDRESS>Telephone: 1 808 934 5949

# AO3k at Subaru: First on-sky results of the facility extreme-AO

Julien Lozi  Subaru Telescope, National Astronomical Observatory of Japan,
National Institutes of Natural Sciences (NINS), 650 North A‘ohōkū Place, Hilo,
HI 96720, United States  Kyohoon Ahn  Korea Astronomy and Space Science
Institute Daedeokdae-ro 776, Yuseong-gu Daejeon 34055, Republic of Korea
Hannah Blue  Subaru Telescope, National Astronomical Observatory of Japan,
National Institutes of Natural Sciences (NINS), 650 North A‘ohōkū Place, Hilo,
HI 96720, United States  Alicia Chun  University of Chicago, 5801 S. Ellis
Ave., Chicago, IL 60637, United States  Christophe Clergeon  Gemini
International Observatory, a program of NSF’s NOIRlab, 670 North A‘ohōkū
Place, Hilo, HI 96720, United States  Vincent Deo  Subaru Telescope, National
Astronomical Observatory of Japan, National Institutes of Natural Sciences
(NINS), 650 North A‘ohōkū Place, Hilo, HI 96720, United States  Olivier Guyon
Subaru Telescope, National Astronomical Observatory of Japan, National
Institutes of Natural Sciences (NINS), 650 North A‘ohōkū Place, Hilo, HI
96720, United States  Steward Observatory, University of Arizona, Tucson, AZ
87521, United States  College of Optical Sciences, University of Arizona,
Tucson, AZ 87521, United States  Astrobiology Center of NINS, 2 Chome-21-1,
Osawa, Mitaka, Tokyo, 181-8588, Japan  Takashi Hattori  Subaru Telescope,
National Astronomical Observatory of Japan, National Institutes of Natural
Sciences (NINS), 650 North A‘ohōkū Place, Hilo, HI 96720, United States
Yosuke Minowa  Subaru Telescope, National Astronomical Observatory of Japan,
National Institutes of Natural Sciences (NINS), 650 North A‘ohōkū Place, Hilo,
HI 96720, United States  Shogo Nishiyama  Miyagi University of Education, 149,
Aramaki-aza-Aoba, Aobaku, Sendai  Yoshito Ono  Subaru Telescope, National
Astronomical Observatory of Japan, National Institutes of Natural Sciences
(NINS), 650 North A‘ohōkū Place, Hilo, HI 96720, United States  Shin Oya
Subaru Telescope, National Astronomical Observatory of Japan, National
Institutes of Natural Sciences (NINS), 650 North A‘ohōkū Place, Hilo, HI
96720, United States  Yuhei Takagi  Subaru Telescope, National Astronomical
Observatory of Japan, National Institutes of Natural Sciences (NINS), 650
North A‘ohōkū Place, Hilo, HI 96720, United States  Sébastien Vievard  Subaru
Telescope, National Astronomical Observatory of Japan, National Institutes of
Natural Sciences (NINS), 650 North A‘ohōkū Place, Hilo, HI 96720, United
States  Astrobiology Center of NINS, 2 Chome-21-1, Osawa, Mitaka, Tokyo,
181-8588, Japan  Maria Vincent  University of Hawai‘i Institute for Astronomy,
2680 Woodlawn Dr, Honolulu, HI 96822, United States

###### Abstract

The facility adaptive optics of the Subaru Telescope AO188 recently received
some long-awaited upgrades: a new 3224-actuator deformable mirror (DM) from
ALPAO (hence the name change to AO3000 or AO3k), an upgraded GPU-based real-
time computer, a visible nonlinear curvature wavefront sensor and a near-
infrared wavefront sensor (NIR WFS), closing the loop at up to 2 kHz. The
wavefront sensors were added in 2023, while the DM will be installed at the
beginning of 2024. With these new features, AO3k will provide extreme-AO level
of correction to all the instruments on the IR Nasmyth platform: The NIR-MIR
camera and spectrograph IRCS, the high-resolution Doppler spectrograph IRD,
and the high-contrast instrument SCExAO. AO3k will also support laser
tomography (LTAO), delivering high Strehl ratio imaging with large sky
coverage.

The NIR WFS, using part of the light from y- to H-band, is dramatically
increasing the number of reachable targets for high-contrast imaging (HCI),
for exoplanets characterization, as well as AGNs or the galactic center. It
has two modes that can be used to drive the new DM: A double roof-prism
pyramid WFS, and a focal plane WFS for faint targets.

The high Strehl will especially benefit SCExAO for high-contrast imaging, both
in infrared and visible. The second stage extreme AO will no longer have to
chase large residual atmospheric turbulence, and will focus on truly high-
contrast techniques to create and stabilize dark holes, as well as coherent
differential imaging techniques. We will finally be able to leverage the
several high performance coronagraphs tested in SCExAO, even in the visible.

AO3k will answer crucial questions as a precursor for future adaptive optics
systems for ELTs, especially as a technology demonstrator for the HCI
Planetary Systems Imager on the Thirty Meter Telescope. A lot of questions are
still unanswered on the on-sky behavior of high actuator counts DMs, NIR
wavefront sensing, the effect of rolling shutters or persistence.

We present here the first on-sky results of AO3k, before the system gets fully
offered to the observers in the second half of 2024. These results give us
some insight on the great scientific results we hope to achieve in the future.

###### keywords:

extreme adaptive optics, pyramid wavefront sensor, focal plane wavefront
sensor, near infrared wavefront sensor, deformable mirror, nonlinear curvature
wavefront sensor

##  1 INTRODUCTION

The first generations of adaptive optics (AO) and extreme AO (XAO) are getting
upgraded with a larger number of actuators, faster low-noise detectors, more
sensitive wavefront sensors (WFS) and even new near-infrared WFS (NIR WFS).

At the Subaru Telescope, following the success of the first AO system AO36,
AO188 was developed and installed in 2006[1], including a laser guide star[2].
With 188 actuators in the pupil, AO188 can provide Strehl ratios of $\sim
20$–40% in H-band in median seeing[3]. Three instruments are using the output
of AO188:

  * •

The facility instrument IRCS (Infrared Camera and Spectrograph), providing
both imaging (y- to M’-bands) and spectroscopy (zJ- to L-band) capabilities.

  * •

The PI XAO platform SCExAO (Subaru Coronagraphic Extreme Adaptive Optics),
feeding several science modules in visible (R- and i-band) and NIR (y- to
K-band), including the integral field spectrograph CHARIS, the MKID Exoplanet
Camera (MEC) and the newly-upgraded visible differential polarimetric imager
VAMPIRES[4, 5, 6].

  * •

the PI instrument IRD (Infrared Doppler spectrograph), a NIR (y- to H-band)
fiber-fed high resolution spectrograph. IRD can be fed directly with multi-
mode fibers from AO188, or with single-mode fibers from SCExAO (REACH
module)[7].

In the broader context of Subaru 2111Subaru 2 website:
https://subarutelescope.org/jp/subaru2/, aiming at enhancing Subaru’s
functionalities in key aspects, such as wide-field, high-resolution
observations and infrared astronomy, we want to push for better and faster
wavefront control by upgrading components of AO188, SCExAO, and the whole
instrument architecture of the infrared Nasmyth platform of Subaru. Finally,
we want to test technologies necessary to prepare for the next generation of
giant segmented telescopes like the Thirty Meter Telescope (TMT)[8]. The first
steps aim at upgrading AO188 into AO3k,an XAO platform combining ALPAO’s
3224-actuator deformable mirror (later referred as DM3k), a near infrared
wavefront sensor (NIR WFS) using a double roof-prism pyramid already
commissioned on-sky[9, 10] and a non-linear curvature wavefront sensor
(nlCWFS)[11].

In this paper, we will first present the steps envisioned to upgrade the
facility adaptive optics and the instrument configuration (Sec. 2). Then we
will detail journey to get the DM3k, its laboratory characterization and
installation inside the instrument (Sec. 3). We will show the first on-sky
results obtained with the new DM3k combined with the NIR WFS, as well as the
first demonstration of two XAO systems, AO3k and SCExAO, running at the same
time (Sec. 4). Finally, we will conclude and give some perspective to the work
ahead of us.

##  2 AO3k: AN UPGRADE OF AO188 IN PHASES

The current facility adaptive optics of the Subaru Telescope AO188 is composed
of a 188-actuator bimorph DM from Cilas (named after DM188), coupled with a
visible curvature wavefront sensor (CWFS) using avalanche photo-diodes (APDs).
A vibrating membrane modulate the signal at 2 kHz, So the loop runs at 1 kHz.
It provides Strehl ratios between 20 and 40% in H-band in median seeing.

Higher performances are now becoming essential to improve the scientific
output of the instruments using AO, by reaching deeper contrasts for high-
contrast imagers, reaching fainter targets for imaging and spectroscopy, and
reaching redder targets (M-type stars, stars embedded in dust, e.g. with
protoplanetary rings, or around the galactic center)

The goal is to upgrade the facility adaptive optics in phases, with minimal
impact on the observing schedule and current functionalities.

  * •

Phase Ia: Addition of a NIR WFS.

The goal of this phase was to add a NIR WFS inside the existing enclosure,
without affecting the current AO188 performances and functionalities. It was
integrated inside AO188 for the first time in May 2022, and tested on-sky
during some engineering time in May 2022 and May 2023. In 2022, we only
operated the NIR WFS in a passive way, while closing the loop with the current
visible CWFS. In 2023, we performed the first closed-loop tests using the
188-actuator bimorph DM. At the same time, a new real-time controller (RTC)
was developed to be able to control the NIR WFS, as well as the older
hardware, e.g. the DM188 and the APDs.

---
Figure 1: (a) H-band Strehl ratio measurements obtained with SCExAO’s Palila
camera, over a few seconds, for targets with various magnitudes. Each image is
2x2”. (b) All Strehl ratio measurements taken with Palila in y-, J- and
H-band.

Figure 1 (a) presents a sample of H-band images taken with SCExAO’s Palila
camera (First Light Imaging C-RED2, named after a critically endangered
Hawaiian honeycreeper found on the slopes of Maunakea) during the May 2023
engineering run, to measure the Strehl ratio, for several targets with various
magnitudes. The targets were chosen in the same part of the sky to have
similar atmospheric conditions for each of them. The airmass was between 1 and
1.4 for all of them, although the seeing was variable.

Figure 1 (b) shows a compilation of all the Strehl ratio measurements taken
with Palila in y-, J- and H-band during the engineering run. This includes
times where we were tuning various parameters, so some Strehl values can be
much lower than optimal. The higher values for each magnitude would represent
the performance of the loop in normal conditions. The Strehl ratio is over 40%
until magnitude 9, then decreases.

During the engineering time, we demonstrated we could use the NIR WFS with the
DM188 and achieve similar and even better performance than with the CWFS.
Thanks to these on-sky tests, the NIR WFS is now available for open-use
observations since S24A, and Phase Ia is completed.

  * •

Phase Ib: Replacement of the original 188-actuator DM (DM188) with ALPAO’s
64x64 DM (DM3k).

In this phase, the number of available actuators in the pupil will increase
from 188 to $\sim 3000$. Therefore, AO1888 will be re-branded as AO3k. Once
the DM is replaced, the priority is to demonstrate that we can maintain the
current performance of AO188 by down-sampling the DM and using the current
APDs for wavefront control. It ensures that we do not need to suspend Open-Use
observations and do a full characterization of the system before offering it
for science. We can do this characterization over time, once all the elements
are in place. The XAO performance of AO3k is achieved using the NIR WFS added
in Phase Ia and is the main focus of this paper.

The new DM3k is a drop-in replacement of the original one, although the DM188
was also mounted in a fast tip/tilt mount (TTM) (100 Hz) where offloads of
these modes are sent. To maintain this offload capability in this phase, the
fast TTM is equipped with a flat mirror and moved to the fold mirror right
before the DM (AOM2 mirror). Since the tip/tilt motion will not be in a pupil
plane anymore, the largest offsets are offloaded to the telescope pointing
more regularly than before (typically every tens of seconds instead of every
tens of minutes).

In parallel, we developed a non-linear CWFS to replace the original CWFS, this
time using a sCMOS camera and imaging simultaneously four out-of-focus pupil
images. This new nlCWFS is capable of controlling all the modes offered by the
DM3k and will provide the full XAO performances of AO3k in the future. This
new wavefront sensor will be tested on-sky with the DM3k in August 2024.[11]

  * •

Phase II: Installation of a NasIR beam switcher for up to 4 instruments.

A Nasmyth IR beam switcher (NBS) was designed to switch rapidly between up to
4 instruments without requiring craning as it is currently done behind
AO188/AO3k.[12] The light can potentially be split between 2 instruments (e.g.
SCExAO and IRCS) with a dichroic beamsplitter.

In this phase, the NIR WFS will move out of AO3k, on a common platform with
the laser tomography AO (LTAO) currently in development[13], a precursor of
the future MCAO ULTIMATE-SUBARU. The NBS is in its integration phase, and will
be added behind AO3k early 2025.

Two new instruments will be added thanks to the NBS: SPIDERS[14], a high-
contrast high-resolution spectro-imaging test platform, and NINJA[15], a
multi-purpose visible-NIR slit spectrograph.

##  3 ALPAO’S DM3k: A JOURNEY

###  3.1 There and Back Again

ALPAO built a first 3224-actuator DM for ESO in 2018, as a demonstrator for
larger versions for ELT[16]. The same design was the perfect size as a
replacement for the DM188, so we started its procurement between 2019 and
2021, after securing the funding through various grants. Due to the time
between the manufacture of two DMs, ALPAO struggled to meet our specs, and for
contractual reasons, delivered a product with known issues in March 2022. Even
if this first version did not performed as we hoped (missing actuators, rest
shape that could not be flatten with the stroke), we still kept it for a few
months, to develop our testbed in Hilo, Hawai‘i, and our testing software. The
first version was sent back to France in August 2022.

The ALPAO team ended up rebuilding the DM head several times and found similar
issues, leading them to change their fabrication process and quality control.
In addition, post-covid supply chain issues compounded on the delays.

Towards the end of 2023, the final version was successfully built and tested.
It was completed in December, and delivered in January 2024. When we plugged
it the first time, we noticed what looked like a bad actuator that was not
present before shipping. After investigation, we found out more issues, most
notably a strong gradient in the gain map and 5-6x less stroke than expected.
After some back-and-forth with the ALPAO team, on-site repairs were scheduled
in March 2024.

The ALPAO engineers concluded that all the issues were linked to the same root
cause, the shifting of an internal reference plate during shipping. They
successfully completed the repairs on March 17, and we started the
characterization right after.

###  3.2 Laboratory Characterization

The characterization of the DM3k was perform in Subaru’s base facility in
Hilo, Hawai‘i, on a crunched timeline due to all the delays, since the on-sky
engineering schedule, planned months in advance, did not change.

In a clean booth, we tested the DM3k on its mount, facing a Zygo
interferometer. Most of the characterization was done with the Zygo, although
we did some dynamical tests with the nlCWFS in parallel[11].

---
Figure 2: (a) Flatness of the DM after several flattening iterations with the
Zygo. The RMS value is 31 nm, although the edge of the DM is cropped here. (b)
Gain map for every actuator, using the Zygo. A small up/down gradient is
observed, as well as some weaker actuators close to the center. The small
circle represents the central obscuration, masking most of the weak actuators.
(c) and (d) AO3k logo and Olivier’s picture applied to the DM and measured
with the Zygo, showing the resolution and the DM.

The Zygo was used to flatten the DM iteratively. Figure 2 (a) presents the
result of such a process. The residual wavefront error measured here is 31 nm,
although we managed to go down below 20 nm on other occasions. The edges of
the mirror were cropped in this measurement, because they curl in such a way
that is not measurable by the Zygo. This effect impacts slightly the final
pupil edge, and we will discuss this later.

A gain map was also computed by poking each actuator individually. The result
is presented in Figure 2 (b). Once again, edge actuators are omitted because
they could not be measured. The final gain map shows a slight up/down
gradient, and a region with smaller gain (named the ”lazy” actuators), close
to the center. The circle at the center represents the obscuration of the
telescope M2 mirror, which masks most of the lazy region. So they should not
impact the final performance. The stroke was measured to be up to specs, to
about 40 ¯m (wavefront) for a 3x3 region.

Figure 2 (c) & (d) are patterns that were applied to the DM (the AO3k logo and
SCExAO’s PI Olivier Guyon respectively), showcasing that even if the influence
function blurs the image a little bit, the actuator density is impressive.

---
Figure 3: (a) Linearity and hysteresis measurement for one actuator. The
linearity is good and hysteresis in the order of a few percents. All actuators
have very similar profiles. (b) Measurement of the settling time (or creep)
for different regions. The DM will take approx. 30 minutes to settle to its
final amplitude, when the command is static. It is proportional to the
amplitude.

We also looked at the linearity and hysteresis, by applying a ramp of commands
on individual actuators and repeating the process several times. An example is
presented in Figure 3 (a), although all the actuators tested have an almost
identical profile. Both linearity and hysteresis are shown to be on the order
of a few percents, and the repeatability is at least an order of magnitude
better.

From the results of the first 3224-actuator DM[16], we know that the DM3k has
a ”warm-up” period, i.e. actuators will continue to drift for a while after a
command is applied. This behavior is shown in Fig. 3 (b), where several 5x5
regions on the DM were poked positively, then back to zero after 30 minutes,
then negatively after 30 minutes, then poked negatively after another 30
minutes, and finally back to zero again. We can see that every time, the
motion takes about 30 minutes to settle, and drifts for about 20% of the
original amplitude independently of the poke amplitude. In a dynamic closed-
loop environment such as an AO system correcting atmospheric turbulence, this
behavior is not an issue, since we are constantly adjusting the shape of the
mirror. But it will play a role in a more static configuration, for example if
we want to apply a flat map. For example, the flat map calculated for Fig. 2
(a) will drift and not provide a flat wavefront for very long. This would be a
”cold” flat map, to be used right away after being applied. It is possible to
compute a ”warm” flat map though, that would take into account this drift. In
that case, the DM would not be flat at first, but would slowly drift to a flat
wavefront after 30 minutes.

After these tests, the DM3k was deemed up to specs, and we were authorized to
go ahead with the upgrade of the instrument. Some contingency plans to roll
back to the original configuration were still put in place if the installation
was unsuccessful before the next science observation.

###  3.3 Installation at the Telescope and Preliminary Testing

The installation at the summit started on May 3, 2024, and was completed after
10 days. We started by removing the DM188 from the TTM, and measured the TTM
response for increasing mass simulators (700 g to 1.4 kg), since the AOM2
mirror is about 2 times heavier than the DM188. The response did not change
significantly from the DM188, so we proceeded with the installation of the
AOM2 mirror and the migration of the mount in the location of AOM2. Then the
DM3k was installed in place of the DM188 and aligned. Figure 4 (a) shows the
inside of AO3k after installation. The new DM3k with its cables can be seen in
the foreground, and the TTM with AOM2 can be seen in the background. The new
RTC and the 8 DM electronics are populating a rack located right next to the
instrument (Figure 4 (b). Right now, the heat from the rack (approx. 3 kW) is
just dumped on the Nasmyth platform and managed by the air conditioning, but
we are considering upgrading to a liquid-cooled rack in the future.

---
Figure 4: (a) The DM3k installed inside AO3k (foreground). The fast TTM of the
original DM of AO188 was moved to the flat mirror AOM2 right before the DM in
the optical path (background, the mount with red and yellow tapes). (b) The DM
electronics and the new RTC are populating a full rack located next to the
instrument, due to DM cable lengths.
---
Figure 5: NIR WFS near-pupil images (top row) and modulated PyWFS images
(bottom row) of: (a) & (b) the DM in its rest shape, (c) & (d) the flat map
calculated in the lab with the Zygo, (e) & (f) a bullseye pattern used for
alignment, (g) & (h) the AO3k logo applied to the DM.

Once the DM3k was in place and aligned, we performed the first tests using the
internal lasers (633 nm and 1550 nm) and the wavefront sensors (visible CWFS
and NIR WFS). We first checked that the DM was responding as well as in the
lab, and that it was not damaged by the transport to the summit. Figure 5
presents an example of tests that were performed. Here we applied various
patterns and looked at the result on the NIR WFS. Two modes were used: a near-
pupil plane imaging mode (top row), and the modulated PyWFS mode (bottom row).
Four patterns are presented on this figure, the rest shape (voltage zero), the
flat map calculated with the Zygo in the lab, a bullseye pattern (added to the
flat map) for alignment of the DM surface with the beam, and the AO3k logo
(added to the flat map again). Since the lab flat map is working well, we
confirmed that the DM was working as expected and we did not have last minute
surprises.

Once noticeable thing though is the fuzziness of the edge especially in pupil
plane imaging mode. We can see that the curliness of the surface at the edge
is affecting the pupil. Indeed, the reflective surface is 96.5 mm in diameter,
while the beam is 90x94 mm due to the incidence angle of $16^{o}$. This effect
is less pronounced in visible, probably due to the shorter wavelength. One
side is more affected than the other, which led us to translating the DM
vertically in relationship to the beam. This is possible because we do not
need a perfect registration of the actuators in relationship with the WFS
pixels, since it is calibrated with the response matrix.

The new RTC used to control the DM3k uses CACAO[17, 18]. The RTC can also
control the original DM, the TTM, as well as the wavefront sensors: The APDs
of the CWFS, the new nlCWFS, and the NIR WFS. It is also equipped with a pass-
through mode, designed to allow us to keep using the original RTC (deployed in
2006), and keep all the original functionalities (e.g. the LGS mode) without
forcing us the develop updated versions all at once.

---
Figure 6: Measurement of the hardware latency with CACAO, using the NIRWFS as
the wavefront sensor. The orange triangular profile is the ideal case, with
the rising time corresponding to the exposure time of the WFS, and the halfway
rising point the hardware latency, independent of the loop frequency. The
trailing end corresponds to mechanical resonances of the DM surfaces settling
in about 10 ms.

One of the functionalities of CACAO is to calculate with high precision the
hardware latency for any control loop (the ”mlat” function). Figure 6 presents
a measurement, using the NIR WFS at 2 kHz, and the DM3k. The orange triangular
shape is the ideal output. The rising time of the triangle corresponds to the
integration time of the WFS, while the half-way point of that same rising
slope corresponds to the hardware latency. This latency is independent from
the loop frequency, and only take into account the reaction time of the DM,
the communication delays, and the readout time of the WFS. This latency is
measured at 0.45 ms in this case. The trailing end is due to mechanical
resonances on the DM surface that create ripples when the DM is poked. It
takes about 10 ms for these ripples to settle. This behavior was known since
the first DM was tested. This will probably have an impact on the final
performance of the AO system, but this DM behaves way better than the DM188 in
this regard (see latency measurement at 2 kHz in [10]).

The operation of the AO system was validated with the new system and the
internal source, and we proceeded with the first on-sky tests with two half
nights on May 23 and 24, 2024, with SCExAO behind AO3k, and one full night on
May 26 with IRCS. Here we present results with SCExAO, since it can provide
the most telemetry. The seeing during these nights were good to excellent
(0.6” down to 0.25”!).

##  4 FIRST ON-SKY RESULTS OF AO3k

###  4.1 Validation of AO188 Mode for Uninterrupted Open-Use Observations

---
Figure 7: AO188 mode performance validation with H-band Strehl ratio
measurements. They were obtained with SCExAO’s Palila camera, over a few
seconds, on the target (a) $\delta$ Her and (b) Pira‘etea/Hawaiki (Deneb).

The highest priority was to make sure that the performance with in the AO188
mode (i.e. using the original CWFS) were not impacted by the change of DM.
This was paramount, since regular science observations were continuing a few
weeks later, on June 14. Therefore we tested the control of the DM3k using the
orignal CWFS, both in pass-through mode (using the original RTC), and with the
new RTC.

Figure 7 presents two examples of Strehl ratio measurements using SCExAO’s
Palila camera, in H-band. In these examples, only the AO188 loop is used,
while SCExAO is used passively to image the Point Spread Function (PSF).
Figure 7 (a) presents a Strehl measurement of 40% on the star $\delta$ Her,
while Fig. 7 (b) shows a Strehl of 53% on Pira‘etea or Hawaiki (respectively a
traditional name of the star Deneb in the Society Islands, French Polynesia,
and a modern Hawaiian name for the same star). Thanks to a more stable DM, we
can achieve better performance with the same wavefront sensor than before with
AO188.

These results confirmed that changing the DM will have no negative impact on
the AO correction for the rest of the scheduled science nights.

###  4.2 First Results of Two XAO Loops Running Together

For the first time ever, two XAO systems, AO3k —with the NIR WFS using the
First Light Imaging C-RED ONE running at 1 kHz, and ALPAO’s DM3k— and SCExAO
—with the visible PyWFS using the First Light Imaging OCAM2k running at 2 kHz,
and Boston Micromachines Corporation (BMC) MEMS 2k DM— were used at the same
time to correct the atmospheric turbulence. with such a number of actuators
and such speeds, it was sometimes hard to distinguish what we were seeing from
laboratory PSFs with the calibration source.

---
Figure 8: Still frames during the first on-sky closed loop demonstration of
two XAO loops running at the same time: AO3k (with the NIR WFS @ 1 kHz and
ALPAO’s DM3k) and SCExAO (with the visible PyWFS and BMC’s MEMS 2k DM), on the
target Hōkūle‘a (Arcturus). (a) AO3k’s PyWFS image (‘I‘iwi) in H-band. (b)
SCExAO’s PyWFS image (Pueo) in I-band. (c) DM3k command applied by the NIR WFS
(‘Elepaio). (d) Saturated H-band PSF on SCExAO’s Palila. The control region of
the SCExAO loop (diameter 45 $\lambda/D$) is visible. (e) Coronagraphic PSF
using a Lyot coronagraph. The control region is again visible, as well as the
25 nm astrometric speckle grid at 15 $\lambda/D$.

Figure 8 presents still frames of the various streams that were recorded
during the night with CACAO, on the target Hōkūle‘a (Arcturus), the ”star of
gladness”, used by Polynesian navigators as the zenith star indicating the
latitude of Hawai‘i:

  * •

(a) The PyWFS mode of the NIR WFS using the C-RED ONE camera and its mascot
the ‘I‘iwi, a vulnerable endemic species of Hawaiian honeycreeper. It uses 50%
of the H-band light in this example.

  * •

(b) The PyWFS mode of SCExAO using the OCAM2k and its mascot the Pueo, the
endangered species of Hawaiian Owls.

  * •

(c) The DM command computed by the new RTC and sent to the DM3k, with its
mascot the Hawai‘i ‘Elepaio, an endangered species of monarch flycatcher.

  * •

(d) and (e) Respectively a saturated image and coronagraphic image of the
H-band PSF with the Palila camera (C-RED 2). In both images, the ”dark hole”
or control region of the SCExAO DM, with a diameter of 45 $\lambda/D$ is
visible. The coronagraph used in (e) is a Lyot coronagraph with an inner
working angle of 116 mas. An astrometric grid of speckles at 15.9 $\lambda/D$
is also visible here.

Not pictured here is the command sent to the SCExAO DM, and its mascot the
Nēnē, a vulnerable species of Hawaiian goose and Hawai‘i’s state bird.

Pretty much right away, we demonstrated excellent corrections with both loops,
although some improvements need to be addressed. The AO3k loop was correcting
2000 modes, while the SCExAO loop was correcting 1200 modes. We can
potentially increase these numbers a little. Also, the NIR PyWFS would lock
into petal modes that split the PSF into two to four lobes, depending on the
profile of the modal gain used. Petal modes are known to be difficult for
PyWFSs to control, but we are working on several options to address this
issue.

---
Figure 9: Analysis of tip/tilt residuals using 5 seconds of unsaturated Palila
data (1.5 kHz). (a) Comparison of the on-sky PSF with the reference PSF used
to calculate the Strehl ratio, with an averaged PSF and a tip/tilt corrected
averaged PSF. (b) temporal measurement of the position of the PSF over the
sequence. (c) PSD of the measured position. (d) Cumulative integral of the PSD
of each axis. The steps show which vibrations are the most significant.

Figure 9 presents the analysis of a 5 s sequence of unsaturated images taken
with Palila at 1.5 kHz, on the star $\epsilon$ Boo. Figure 9 (a) shows the
reference PSF computed for the Strehl calculation, the simple temporal average
of the data cube, and the average after shifting each frame to correct for
tip/tilt residuals. The Strehl ratio go from 88.3% to 89.4%, showing a
marginal improvement of only 1%. The final PSF is mostly dominated by some
small low-order non-common path errors that we could not offset that night. On
Fig. 9 (b), we can see the temporal measurement of the PSF position in X and
Y. The RMS residual is only 3.5 and 3.3 mas for each axis respectively. We saw
residual tip/tilt between 2 and 4 mas on that night, both in IR and in visible
with VAMPIRES. Figure 9 (c) shows the power spectrum density (PSD) of the same
data. Mechanical resonances are seen on both axes on a wide range of
frequencies, especially around 5 Hz, 60 Hz, 120 Hz and 500 Hz. The peak around
5 Hz is known to originate from the telescope, while the other ones are
probably coming from the instrument itself. Figure 9 (d) shows the cumulative
integral of the PSD on both axes, telling us which vibrations contribute the
most to the measured residual: the higher the step, the stronger the vibration
is. In this case, vibrations are not a huge contributor, but we can still
notice the telescope vibration around 5 Hz, and the 60 Hz vibration. A
predictive control can be used to help correct for these, and improve even
more the tip/tilt stability.

More on-sky time is needed to characterize the double-XAO correction,
especially the contrast stability in coronagraphic mode, that most of SCExAO’s
users are interested in.

###  4.3 AO3k Providing High-Strehl With the NIR WFS

During the engineering nights, we also took time to characterize the AO3k
system by itself, using SCExAO passively to record the telemetry. The integral
field spectrograph CHARIS was also used to record the PSF in the range 1.1 to
2.4 ¯m (J, H and K-band).

---
Figure 10: (a) Strehl measurement on the target HD 172449 using CHARIS, in J,
H and K-band, by co-adding the slices of the spectro-imager over each band.
(b) Radial profile of the three PSFs compared to simulated ideal PSFs.

Even with AO3k alone, we achieved excellent Strehl ratios at all wavelengths,
like on the example presented in Fig. 10 (a). Here, the slices were co-added
to create a image for each band. As expected, the Strehl ratio gets better at
longer wavelengths, as the speckle halo and low-order errors are less
pronounced. Figure 10 (b) shows the radial profile of each band (solid lines),
compared to an ideal profile (dotted lines). The impact of the residual
speckle halo is noticeable especially in J and H-band, after 0.2 arcsec
separations.

---
Figure 11: (a) Strehl measurements between 1.1 and 2.4 ¯m using CHARIS, on
several targets with various magnitudes. (b) The same measurements displayed
as Strehl versus H-band magnitude (corrected for extinction due to clouds).
The performance starts to decrease after magnitudes 9-10 in this case.

We observed a wide variety of star magnitudes, between 0 and 12th magnitudes
in H-band. The Strehl measurements for each star are presented in Fig. 11 (a).
Figure 11 (b) presents the same results, but as Strehl versus mH-band
magnitude (taking into account the extinction from high-altitude clouds we had
during some of the measurements). Similarly to what we saw in Fig. 1 (b), the
Strehl ratio is high up to magnitude 9, then starts to go down as we get less
photons in the NIR WFS. But even close to the magnitude limit of 12, the loop
was still providing some decent correction.

These first results show that, with the NIR WFS, AO3k provides very stable
high-quality PSFs already, thanks to the high number of actuators and the high
loop speed. We should expect similar results with the nlCWFS in the near
future, which will then complete phase Ib of the upgrade of AO188 into AO3k.

Since the DM upgrade was successful, the science programs already expected to
use the NIR WFS will see a significant improvement in the data quality going
forward. Most notably, we looked at the galactic center with IRCS and produced
the highest quality data ever recorded at Subaru.

##  5 CONCLUSION AND PERSPECTIVE

With this work, we demonstrated that the well deserved upgrades of AO188 into
AO3k were successful. Despite plenty of delays, we managed to replace the DM
with ALPAO’s DM3k in time for our scheduled on-sky demonstrations, without
compromising on the capabilities of the facility AO, and without impacting the
scheduled Open-Use observations.

Combined with the NIR WFS installed during Phase Ia of the scheduled upgrades,
the new DM3k provided the most stable PSFs for a facility adaptive optics on
an 8-m class telescope. In addition, we corrected the atmospheric turbulence
with two XAO systems simultaneously, AO3k and SCExAO, producing very stable
high-contrast images with tip/tilt residuals down to a few milliarcseconds
level. This will open new capabilities, with for example on-sky dark digging,
or in combination with innovative astrophotonics technologies. Even more
classical all-purpose instruments like IRCS will benefit from AO3k, with
better and deeper image quality, or higher spectroscopic resolutions. Phase Ib
will be fully complete this year with the addition of the nlCWFS, which should
provide similar correction than the NIR WFS, without having to share the NIR
science photons. With the addition of the NBS early next year, we will have
the most complete and versatile AO platform of any telescope.

The next few years are truly going to be exciting for high-contrast imaging at
the Subaru Telescope, as we will be able to reach deeper and more stable
contrasts, around much redder targets. The technologies tested now will also
be essential for the next generation of telescopes like TMT.

###### Acknowledgements.

Based on data collected at Subaru Telescope, which is operated by the National
Astronomical Observatory of Japan. The development of AO3k is supported by the
Japan Society for the Promotion of Science (Grant-in-Aid for Research
#21H04998, #19H00695 and #17H06129), the Subaru Telescope, the National
Astronomical Observatory of Japan, the Astrobiology Center of the National
Institutes of Natural Sciences, Japan, and the Heising-Simons Foundation. The
development of SCExAO is supported by the Japan Society for the Promotion of
Science (Grant-in-Aid for Research #23340051, #26220704, #23103002, #19H00703,
#19H00695 and #21H04998), the Subaru Telescope, the National Astronomical
Observatory of Japan, the Astrobiology Center of the National Institutes of
Natural Sciences, Japan, the Mt Cuba Foundation and the Heising-Simons
Foundation. Maunakea is a mountain that connects Kanaka Maoli (Native
Hawaiians) to their ancestral and universal origins. We, as scientists and
educators, acknowledge this interconnectedness between Kanaka and their ‘Āina
(land). We recognize that we have a kuleana (responsibility) that comes with
the opportunity to pursue astronomical research on Maunakea. It is our kuleana
to build and strengthen healthy relationships with the land and the people of
this place based on mutuality and trust. J.L. would like to thank Leinani and
Makali‘i for allowing him to write this proceeding between feedings, burping
and diaper changes.

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