# Second Dome of Superconductivity in YBa2Cu3O7 at High Pressure

Johannes Nokelainen<EMAIL_ADDRESS>Department of Physics,
Northeastern University, Boston, Massachusetts 02115, USA  Department of
Physics and Astrophysics, Howard University, Washington, D.C 20059, USA
Department of Physics, School of Engineering Science, LUT University, FI-53850
Lappeenranta, Finland  Matthew E. Matzelle  Department of Physics,
Northeastern University, Boston, Massachusetts 02115, USA  Christopher Lane
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico
87545, USA  Nabil Atlam  Department of Physics, Northeastern University,
Boston, Massachusetts 02115, USA  Ruiqi Zhang  Department of Physics and
Engineering Physics, Tulane University, Louisiana 70118 New Orleans, USA
Robert S. Markiewicz  Department of Physics, Northeastern University, Boston,
Massachusetts 02115, USA  Bernardo Barbiellini  Department of Physics, School
of Engineering Science, LUT University, FI-53850 Lappeenranta, Finland
Department of Physics, Northeastern University, Boston, Massachusetts 02115,
USA  Jianwei Sun  Department of Physics and Engineering Physics, Tulane
University, Louisiana 70118 New Orleans, USA  Arun Bansil
<EMAIL_ADDRESS>Department of Physics, Northeastern University,
Boston, Massachusetts 02115, USA

###### Abstract

Evidence is growing that a second dome of high-$T_{\mathrm{c}}$
superconductivity can be accessed in the cuprates by increasing the doping
beyond the first dome. Here we use _ab initio_ methods without invoking any
free parameters, such as the Hubbard $U$, to reveal that pressure could turn
YBa2Cu3O7 into an ideal candidate for second-dome-superconductivity,
displaying the predicted signature of strongly hybridized $d_{x^{2}-y^{2}}$
and $d_{z^{2}}$ orbitals. Notably, pressure is found to induce a phase
transition replacing the antiferromagnetic phases with an orbitally-degenerate
$d$–$d$ phase. Our study suggests that the origin of the second dome is
correlated with the oxygen-hole fraction in the CuO2 planes and the collapse
of the pseudogap phase.

In the search for superconductivity (SC) at higher temperatures, one of the
more intriguing possibilities is that the high-$T_{\mathrm{c}}$ cuprate
superconductors also feature another superconducting dome in the extremely
overdoped metallic and non-magnetic (NM) regime [1; 2; 3; 4; 5; 6; 7; 8; 9;
10; 11; 12; 13; 14]. This is in stark contrast to the long-studied ‘first
dome’ that can be characterized as a lightly doped Mott insulator with a
partially occupied Cu $d_{x^{2}-y^{2}}$ band and short-range antiferromagnetic
(AFM) order [15]. Evidence for the existence of such a ‘second dome’ has been
building in recent years, as SC has been observed even when the doping levels
have been driven far beyond the first dome via high-pressure oxygenation (HPO)
synthesis [13]. Findings of $T_{\mathrm{c}}=95$ K in Sr2CuO4-y [1] and
$T_{\mathrm{c}}=70$ K in Ba2CuO4-y [7] have heightened interest since these
$T_{\mathrm{c}}$s are clearly higher than $T_{\mathrm{c}}\sim 44$ K of their
isostructural counterpart La2CuO4+δ. Also, a variety of other types of
unconventional superconductors have been shown to feature two or more SC domes
with distinct characteristics [16; 17; 18; 19; 20; 21].

To explain the second dome, Maier _et al._ have constructed a model where the
valency is increased by introducing holes on the Cu $d_{z^{2}}$ orbitals,
resulting in a new peak in the pairing function [8; 9]. Similar models [5; 14]
have been invoked to explain the presence of a second dome in a single CuO2
plane grown on top of Bi2Sr2Can-1CunO2n+4+δ (BSCCO), $n=2$ [4]. However, this
system is not practical for transport measurements, while for the HPO-cuprates
the polycrystalline samples contain many SC phases with a multiplicity of
oxygen vacancy orderings and it is unclear which of the phases are the best
superconductors [11].

Besides chemical doping, pressure ($P$) is also known to increase doping
levels [22] and enhance $T_{c}$ in a number of cuprates [23]. Pressure has
also been observed to trigger a second, anomalous, rise of $T_{\mathrm{c}}$ in
BSCCO, $n=1,2,3$; when the pressure is applied to optimally doped samples,
$T_{\mathrm{c}}$ first decreases but then increases into a second dome [3;
10]. However, the notoriously complicated multi-phase structure of BSCCO
involving supermodulation and complex oxygen ordering [24; 25; 26] makes it
difficult to characterize the underlying physics and the second dome has not
been observed in other recent studies [27; 28].

Here, we present an ab initio study of pressure-induced doping of the
prototypical cuprate superconductor YBa2Cu3O7 (YBCO7) and discuss its high-
pressure states from the viewpoint of the second dome physics. YBCO7 offers
the advantages that it is in the overdoped regime yet stoichiometric, as
illustrated in Fig. 1 (a). Thus, pressure can more easily drive the material
to the extremely overdoped regime in which the structure remains single-phase,
reducing the challenges associated with complex distributions and pressure
effects of dopant atoms. Our first-principles computations employ the
strongly-constrained-and-appropriately-normed (SCAN) density-functional [29;
30; 31; 32], which has been shown to provide a good parameter-free first-
principles description of electronic correlation and Cu–O charge transfer
physics [33; 34; 35; 36; 37; 38; 39; 40; 41]. Various magnetic orders are
considered under hydrostatic pressure, which we increase adiabatically from
zero up to 170 GPa. The Supplemental Material (SM) [42] contains the details
of our computations. Our analysis shows that pressure induces three key
effects in YBCO7 that facilitate the transition to the second dome:

Figure 1: (a): Atomic structure of YBCO7. Cu${}_{\text{pl}}$ atoms reside in
pyramidal cages formed by the O${}_{\text{pl}}$ and O${}_{\text{ap}}$ atoms.
The CuO2 planes are separated by a Y buffer layer. Sandwiched between the BaO
layers are the CuO chains, which contain the oxygen dopants. Note that YBCO7
is the fully doped compound of the YBCO6+δ family with complete CuO chains,
while YBCO6 is the undoped system in which all the O${}_{\text{ch}}$ sites are
vacant. The chains are arranged along the $b$-axis, which is 1.2 % longer than
the $a$-axis ($a_{0}=3.83\,$Å). (b): Definitions of the $d_{\text{pl}}$ and
$d_{\text{ap}}$ Cu–O distances and $\Delta z_{\text{pl}}$. (c): Schematics of
the G-AFM and C-AFM magnetic configurations. (d): In % units, $P$-evolution of
relative elongation of the Cu–O pyramids
$(d_{\text{ap}}-d_{\text{pl}})/d_{\text{pl}}$, relative orthorhombicity of the
unit cell $(b-a)/a$, dimpling ratio $\Delta z_{\text{pl}}/d_{\text{pl}}$
(separately for the $a$\- and $b$-directions) and lattice parameter
modifications $\Delta a=(a-a_{0})/a$ and $\Delta c=(c-c_{0})/c$.

_(1): Change in the pyramidal Cu–O environment_. Figure 1 (d) presents the
pressure-evolution of several structural parameters. There are no substantial
structural differences between the NM state and the G-AFM and C-AFM orders,
see Fig. 1 (c) for definitions. The lattice constants are in excellent
agreement with Ref. [43] (within 0.4 % at $P=0$ and 0.7 % at $P\approx 12.7$
GPa). However, we did not observe the structural instabilities found in Ref.
[44], see SM Sec. S6 [42] for details. As is typical of layered materials such
as the cuprates, the $c$-axis shrinks more rapidly than the $a$ and $b$-axes
(e.g. at 140 GPa $c$ has decreased by about 20 % while $a$ and $b$ have
decreased by about 10 %). Concurrently, there is a decrease in the elongation
of the pyramidal Cu–O cages, which is intimately connected to the relative
energies of the Cu-$d_{x^{2}-y^{2}}$ and $d_{z^{2}}$ orbitals. Interestingly,
enhanced elongation is known to be favorable for the first dome of SC [45]
while the opposite seems to be the case in Ba2CuO4-y [7]. YBCO7 has a
relatively large elongation of about 18 % but it is quickly reduced under
pressure and at 170 GPa it is only about 5 %. Notably, the strong dimpling
[Fig. 1 (b)] of $14.2\,\%$ is reduced under pressure until it reverses sign at
80 GPa such that the Cu${}_{\text{pl}}$ atoms bulge out from the pyramids
towards the Y layer. At $170\,$GPa the dimpling is $-8.4\,\%$ ($-6.3\,\%$) in
the $a$ ($b$)-direction. Also the slight non-orthorhombicity $(b>a)$ of 2 % is
removed under pressure and weakly reversed above 120 GPa.

_(2): Pressure-induced doping_. Figure 2 (a) presents the hole contents ($x$)
based on the Bader charge analysis [46; 47]. The zero-pressure doping on the
CuO2 planes is
$x([\text{CuO${}_{2}$}]_{\text{pl}})=x(\text{Cu}_{\text{pl}})+2x(\text{O}_{\text{pl}})=0.11$
holes 111The value $x([\text{CuO${}_{2}$}]_{\text{pl}})=0.11$ holes is smaller
than the value 0.18 holes found in the literature for YBCO7 [79]; this
difference is discussed in the SM Sec. S3.1 [42]. and the CuO chains assume a
negative doping of $x([\text{CuO}]_{\text{ch}})=-0.57$ holes, with weak
magnetic configuration dependence. This reflects charge transfer from the CuO2
planes to the CuO chains as YBCO6 is doped to YBCO7. Significant doping
($0.11$ holes) is found also on the O${}_{\text{ap}}$ sites. Under pressure,
the CuO2 plane is doped further up to $0.28$ holes at 170 GPa, an increase of
$0.17$ holes over the zero-pressure value. The sources of this doping are the
Ba and Y ions, which capture electrons at an almost linear rate until about 60
GPa, after which this electron capture rate slows down, especially for Ba.
This could simply be the result of the large ionic radii of Y and Ba. When the
lattice contracts under pressure, $e$–$e$ repulsion would tend to force the
electrons to migrate from the tightly packed CuO2 planes to the buffer layers
with smaller electron density. Interestingly, the $P$-induced doping has been
previously attributed only to the CuO chains, either due to an increased
charge transfer between the chains and the CuO2 planes or to the reordering of
the O${}_{\text{ch}}$ vacancies [49; 50; 51; 52]. However, we find that the
chains also become doped with $0.09$ holes over the pressure range considered.

Figure 2: (a): Hole contents for various ions and groups obtained as Bader
charge differences between YBCO7 and the undoped base compound YBCO6, see SM
Sec. S3 [42] for details. (b): _Left axis:_ Pressure-evolution of the
Cu${}_{\text{pl}}$ magnetic moments. _Right axis:_ Magnetic enthalpy $\Delta
H=H_{\text{AFM}}-H_{\text{NM}}$.

The distribution of the doping within the CuO2 planes deserves special
attention. Below $P\approx 40\,$GPa, $x(\text{Cu}_{\text{pl}})$ grows rapidly
while $x(\text{O}_{\text{pl}})$ stagnates, i.e., the additional doping ends up
on the Cu ions. But this trend starts to change at higher pressures. Beyond 80
GPa the situation is reversed; $x(\text{Cu}_{\text{pl}})$ even starts to
decrease while $x(\text{O}_{\text{pl}})$ grows steadily. We will return to
discuss the implications of this behavior below.

_(3): Stabilization of the NM state_. Figure 2 (b) presents the
Cu${}_{\text{pl}}$ magnetic moments ($M$) and enthalpies relative to the NM
phase ($\Delta H$) for the studied magnetic phases. At zero pressure the G-AFM
and C-AFM states and a $3\times 2$ bond-centered stripe (B-stripe) phase 222
This stripe phase was the most stable $2\times 3$ or $3\times 2$ stripe phase
in our pressure tests, see SM Sec. S4 [42] for details. Larger stripe phases
could be energetically more favorable at zero pressure [36] but considering
them was not feasible due to computational reasons.  are below the NM state by
57 meV, 54 meV and 50 meV, respectively, which is consistent with the
multiplicity of near degenerate magnetic phases found in Ref. [36]. A direct
effect of the pressure-induced doping is the suppression of the magnetic
moments. $M_{\text{G-AFM}}$ and $M_{\text{stripe}}$ start to decrease as soon
as pressure is applied, but $M_{\text{C-AFM}}$ is robust up to 30 GPa before
it starts to decrease. The pressure also decreases the stability of the
magnetic phases, but the competition between them persists. The C-AFM state
becomes the new ground state over the G-AFM state at 27.5 GPa. The G-AFM state
further rises above the NM phase at 75.7 GPa and transitions to the C-AFM
state at pressures beyond 86.3 GPa. The B-stripe also goes through a phase
transition into a site-centered stripe phase (S-stripe) around 60 GPa (where
it shows mixed characteristics) and rises above the NM phase at 88.5 GPa.
Finally, the C-AFM state becomes metastable at 96.3 GPa so that the NM state
is the ground state at high pressures. In this NM region, we were able to
preserve the C-AFM phase up to the highest studied pressure of 170 GPa and
S-stripe up to 115 GPa by increasing pressure adiabatically 333At these
pressures these states become fragile and can be preserved only with the most
accurate technical settings, see SM Sec.S1.4 [42] for details.. Notably, the
C-AFM state remains robust about $1.5\,$meV above the NM state while the
magnetic moments weaken. At 170 GPa,
$M_{\text{C-AFM}}=0.13\,\mu_{\mathrm{B}}$, but we expect the C-AFM phase to
finally vanish at still higher pressures. The relative stability of the C-AFM
configuration could be due to its ferromagnetic interlayer coupling [Fig. 1
(c)], which allows covalent bonding between the magnetic Cu orbitals when the
pressure moves the CuO2 planes closer to each other.

Figure 3: Orbital-decomposed YBCO7 electronic structures and Fermi surfaces
(spectral functions at the Fermi energy) at $k_{z}=0$ for Cu${}_{\text{pl}}$
$d_{x^{2}-y^{2}}$, Cu${}_{\text{pl}}$ $d_{z^{2}}$ and Cu${}_{\text{ch}}$
$d_{z^{2}}$ for (a) $P=0$ G-AFM phase ($M=0.462\,\mu_{\mathrm{B}}$), (b) $100$
GPa C-AFM phase ($M=0.326\,\mu_{\mathrm{B}}$) and (c) $100$ GPa NM phase. In
the AFM cases the Cu${}_{\text{pl}}$ PDOS has been plotted only for ions with
positive $M$ and the energy bands and spectral functions have been unfolded
into the primitive NM cell. The three highest bands of our four-band TB model
are plotted for the $100$ GPa NM case.

_Electronic structure under pressure._ Figure 3 (a) shows the YBCO7 electronic
structure at ambient pressure for the G-AFM state, which is typical of the
cuprates—dominated by planar Cu $d_{x^{2}-y^{2}}$. Also chain Cu $d_{z^{2}}$
bands are present, but they only have negligible hybridization with the
Cu${}_{\text{pl}}$ $d_{x^{2}-y^{2}}$ bands. The bilayer splitting leads to two
distinct $d_{x^{2}-y^{2}}$ Fermi surface rings that partly disappear due to
unfolding into the primitive NM unit cell [55; 56]. The $d_{z^{2}}$ states
display Hund’s coupling with the $d_{x^{2}-y^{2}}$ bands [33], as seen from
the spin polarization in the partial density of states (PDOS), and have a
slight Fermi level contribution through hybridization with the
$d_{x^{2}-y^{2}}$ and chain bands.

At 100 GPa, the $d_{z^{2}}$ band rises to the Fermi level for both the
metastable C-AFM state [Fig 3 (b)] and the NM ground state [Fig. 3 (c)]. This
increases the Cu${}_{\text{pl}}$ $d_{z^{2}}$ hole content at 100 GPa despite
of decrease in the total Cu${}_{\text{pl}}$ hole content, see SM Sec. S3.3
[42] for details. The 100 GPa C-AFM state has little hybridization between the
two $d$ orbitals but significant $d_{x^{2}-y^{2}}$–chain hybridization. The
$d_{z^{2}}$ bands are pinned to the Fermi level, possibly because they are
pushed upwards by Hund’s coupling but acquire holes at a slow rate. This flat
band dominates the states at the Fermi energy ($k_{z}=0$), but due to slight
three-dimensionality of the $d_{z^{2}}$ bands this is less prominent for
$k_{z}\neq 0$, see SM Sec. S2.3 [42] for details. Once the magnetization is
suppressed, in the NM phase, $d_{z^{2}}$ and $d_{x^{2}-y^{2}}$ hybridize
strongly around the $X$ point (where the AFM bands overlap) and the
$d_{x^{2}-y^{2}}$–chain hybridization is absent, contrary to the C-AFM case.
The NM phase spectral function at Fermi energy has mainly $d_{x^{2}-y^{2}}$
and chain contributions and the $d_{z^{2}}$ flat band is only weakly visible
around $M$.

To explore the second dome physics under pressure, we have adopted a minimal
NM tight binding (TB) model that accounts for bilayer splitting and
$d_{x^{2}-y^{2}}$—$d_{z^{2}}$ hybridization [57]. The model is overlaid in
frame (c) of Fig. 3 for $P=100$ GPa and plotted for $P=0$ in the SM Fig. S10
[42]. The model is based on using symmetric and anti-symmetric intra-orbital
combinations, so that the Hamiltonian becomes block-diagonal. The strong
bilayer splitting between the $d_{z^{2}}$ orbitals shifts the anti-symmetric
$d_{z^{2}}$ band to much lower energies. This separation keeps the anti-
symmetric $d_{z^{2}}$ and $d_{x^{2}-y^{2}}$ bands from hybridizing. However,
the symmetric bands remain close in energy, leading to the strong
hybridization near the $X$-point. Our symmetric bands are strikingly similar
to Maier  _et al._ ’s model at $x=0.85$ [8], which is within their second
dome. The two TB models can be directly mapped onto each other with the
exception of a few next-nearest neighbor terms, see SM Sec. S7 [42]. Based on
this intimate connection, NM YBCO7 at 100 GPa sits within the underdoped side
of the second dome predicted by Ref. [8].

Figure 4: _Left axis:_ Experimental $P$-dependence of $T_{\mathrm{c}}$ in
selected samples; Y1: YBCO6.98 [58]. Y2: YBCO6+δ with $\delta$ estimated to be
between 0.85 and 1.00 [59]. B1: Slightly overdoped $n=2$ BSCCO [10]. B2 and
B3: Optimally doped $n=2$ [3] and $n=3$ [28] BSCCO. _Right axis:_ The
fractional planar O hole content obtained from the Bader analysis as
$\tilde{x}^{\text{O}}_{\text{pl}}=2x(\text{O}_{\text{pl}})/x([$CuO${}_{2}]_{\text{pl}})$.

_Importance of O ${}_{\text{pl}}$ hole content:_ The long-sought explanation
for the pairing mechanism in the first dome might have recently been verified
to be superexchange [60], as proposed just a few months after the discovery of
high-$T_{\mathrm{c}}$s [61]. There is a correlation between the maximal
$T_{\mathrm{c}}$ and the planar O hole content [62], which can be understood
within the superexchange model [63]. In this spirit, we plot in Fig. 4 the
fraction of the YBCO7 oxygen holes within the CuO2 planes
($\tilde{x}^{\text{O}}_{\text{pl}}$), as well as the available experimental
$T_{\mathrm{c}}$ data, which we supplement with BSCCO data that extends to
higher pressures. Below 20 GPa, the pressure-induced doping leads to the
suppression of $T_{\mathrm{c}}$ in YBCO (Y1 and Y2) and $n=2$ BSCCO samples
(B1 and B2), which is consistent with these samples either being close to
optimal doping or sitting on the overdoped side of the first SC dome. Pressure
also causes $\tilde{x}^{\text{O}}_{\text{pl}}$ to decrease, which is
consistent both with the superexchange model and Ref. [63], in that it shows a
correlation between $T_{\mathrm{c}}$ and $\tilde{x}^{\text{O}}_{\text{pl}}$
for the first dome. However, recent YBCO6.9 low-pressure Cu–O charge transfer
results [64] based on nuclear magnetic resonance measurements [65] are
somewhat different from our results, see SM Sec. S3.2 [42] for a discussion of
this point.

Based on our TB analysis, we expect YBCO7 to enter the second dome regime
around $100$ GPa. Even though experimental $T_{\mathrm{c}}$ data for YBCO7 is
limited, the B1 and B3 BSCCO datasets display a pressure-induced revival in SC
above $\sim 30$ GPa. Also, $\tilde{x}^{\text{O}}_{\text{pl}}$ begins to
increase with pressure, with striking similarity to the B1 dataset. At 100
GPa, the $\tilde{x}^{\text{O}}_{\text{pl}}$ reaches the $P=0$ AFM values,
raising the possibility of a correlation between
$\tilde{x}^{\text{O}}_{\text{pl}}$ and $T_{\mathrm{c}}$ in the second dome. If
so, how does this affect the pairing mechanism? Here there are many more
possibilities than in the case of the first dome since both Cu
$d_{x^{2}-y^{2}}$ and $d_{z^{2}}$ are involved. Notably, Ref. [8] finds two
pairing channels: $d$-wave and $s^{\pm}$-wave, with both channels dominated by
spin fluctuations of the $d_{z^{2}}$ electrons. Scenarios for multi-orbital
pairing have been discussed in Ref. [6]. In the orbital fluctuation
model—another early proposal for explaining high $T_{\mathrm{c}}$—pairing
between oxygen holes is mediated by the $d$-orbitals [66; 67; 68], potentially
explaining the importance of $\tilde{x}^{\text{O}}_{\text{pl}}$ and the oxygen
holes for the second dome. Alternatively, the pressure-induced enhancement in
$\tilde{x}^{\text{O}}_{\text{pl}}$ and intraplanar covalency could revive the
superexchange mechanism for the second dome [63] or the $d_{z^{2}}$ flat band
could induce pairing-effective $s^{\pm}$ spin fluctuations [12], as discussed
in the SM Sec. S5.2 [42]. Finally, we note that the near degeneracy of the NM
state with the metastable high-pressure C-AFM state could lead to enhanced
pairing fluctuations.

_Relationship with pseudogap collapse:_ Cuprates are characterized by a
mysterious pseudogap phase that involves intertwined orders [69; 70; 71; 72;
73]. The abundance of near-degenerate stripe phases found in ambient-pressure
YBCO7 have been proposed to be a signature of the pseudogap phase [36]. Our
results show that the multiplicity of these phases persists to high pressures,
where these phases rise about $1.5\,$meV above the NM state (which is 54 meV
above the ground state without pressure), indicating termination of the
pseudogap phase. This is reminiscent of La2CuO4, where the NM phase is 150 meV
above the ground state at zero doping [33] while the magnetic phases have been
pushed up to 60 meV above the NM phase at 30% doping [74]. We also observe a
Van Hove singularity crossing the Fermi level near 126 GPa, another signature
of pseudogap collapse [75]. Note that the pseudogap collapse with pressure
appears to be at a higher doping than that found in Ca-substituted YBCO [76],
which may be due to pressure pushing the $d_{z^{2}}$ band above the Fermi
level while preserving the $d_{x^{2}-y^{2}}$ band occupation, see SM Sec. S5.1
[42] for discussion.

Using the prototypical stoichiometric cuprate superconductor YBCO7, our study
explores in-depth evolution of the electronic structure on a first principles
basis when this cuprate is doped continuously via pressure to a higher Cu
valency configuration with active $d_{z^{2}}$ orbitals. Under high pressure
(100 GPa), YBCO7 is shown to become compatible with the second-dome SC model
proposed in Ref. [8]; the pressure could presumably be lowered below 100 GPa
via chemical doping to allow access to the second dome under experimentally
more accessible pressures. Our analysis show that pressure leads to
significant intraplanar Cu–O hole transfer and indicates that the planar
oxygen-hole content correlates with $T_{\mathrm{c}}$ for the second dome, as
is the case for the first dome. All studied magnetic phases are found to
become unstable around the pressure range of the proposed second dome in
YBCO7, which is a signature of pseudogap collapse, hinting at a new connection
between the second dome and the pseudogap phase.

###### Acknowledgements.

We thank Yubo Zhang for his contribution in the early phase of the work and
Sugata Chowdhury for useful discussions. J. N. thanks Osk. Huttunen foundation
and INERCOM platform for financial support. The work at Northeastern
University was supported by the U.S. Department of Energy (DOE), Office of
Science, Basic Energy Sciences Grant No. DE-SC0022216 and benefited from
Northeastern University’s Advanced Scientific Computation Center and the
Discovery Cluster and the National Energy Research Scientific Computing Center
through U.S. DOE Grant No. DE-AC02-05CH11231. The work at Los Alamos National
Laboratory was carried out under the auspices of the U.S. DOE National Nuclear
Security Administration under Contract No. 89233218CNA000001. It was supported
by the LANL LDRD Program, the Quantum Science Center, a U.S. DOE Office of
Science National Quantum Information Science Research Center, and in part by
the Center for Integrated Nanotechnologies, a U.S. DOE BES user facility, in
partnership with the LANL Institutional Computing Program for computational
resources. Additional computations were performed at the National Energy
Research Scientific Computing Center (NERSC), a U.S. DOE Office of Science
User Facility located at Lawrence Berkeley National Laboratory, operated under
Contract No. DE-AC02-05CH11231 using NERSC award ERCAP0020494. The work at
Tulane University was supported by the U.S. Office of Naval Research Grant No.
N00014-22-1-2673. B. B. acknowledges support from the COST Action CA16218.

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