Present address: ]Applied physics, TNW, Fontys University of Applied Sciences,
Eindhoven, The Netherlands

Present address: ]Wuhan National Magnetic Field Center, Huazhong University of
Science and Technology, Wuhan 430074, P. R. China

Present address: ]School of Engineering and Technology, BML Munjal University
(Hero Group), Gurgaon, India – 122413

Present address: ]Max Planck Institute for Solid State Research,
Heisenbergstraße 1, 70569 Stuttgart, Germany

# Quantum oscillations in an optically-illuminated two-dimensional electron
system at the LaAlO3/SrTiO3 interface

I. Leermakers  [  High Field Magnet Laboratory (HFML-EMFL) and Institute for
Molecules and Materials, Radboud University, Nijmegen, The Netherlands  K.
Rubi<EMAIL_ADDRESS>High Field Magnet Laboratory (HFML-EMFL) and Institute for
Molecules and Materials, Radboud University, Nijmegen, The Netherlands  M.
Yang  [  Laboratoire National des Champs Magnétiques Intenses (LNCMI-EMFL),
CNRS, Univ. Grenoble Alpes, INSA-T, UPS, Toulouse, France  B. Kerdi
Laboratoire National des Champs Magnétiques Intenses (LNCMI-EMFL), CNRS, Univ.
Grenoble Alpes, INSA-T, UPS, Toulouse, France  M. Goiran  Laboratoire National
des Champs Magnétiques Intenses (LNCMI-EMFL), CNRS, Univ. Grenoble Alpes,
INSA-T, UPS, Toulouse, France  W. Escoffier  Laboratoire National des Champs
Magnétiques Intenses (LNCMI-EMFL), CNRS, Univ. Grenoble Alpes, INSA-T, UPS,
Toulouse, France  A. S. Rana  [  MESA+ Institute for Nanotechnology,
University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands  A. E.
M. Smink  [  MESA+ Institute for Nanotechnology, University of Twente, P.O.
Box 217, 7500 AE Enschede, The Netherlands  A. Brinkman  H. Hilgenkamp  MESA+
Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE
Enschede, The Netherlands  J. C. Maan  High Field Magnet Laboratory (HFML-
EMFL) and Institute for Molecules and Materials, Radboud University, Nijmegen,
The Netherlands  U. Zeitler<EMAIL_ADDRESS>High Field Magnet Laboratory
(HFML-EMFL) and Institute for Molecules and Materials, Radboud University,
Nijmegen, The Netherlands

###### Abstract

We have investigated the illumination effect on the magnetotransport
properties of a two-dimensional electron system at the LaAlO3/SrTiO3
interface. The illumination significantly reduces the zero-field sheet
resistance, eliminates the Kondo effect at low-temperature, and switches the
negative magnetoresistance into the positive one. A large increase in the
density of high-mobility carriers after illumination leads to quantum
oscillations in the magnetoresistance originating from the Landau
quantization. The carrier density ($\sim 2\times 10^{12}$ cm-2) and effective
mass ($\sim 1.7~{}m_{e}$) estimated from the oscillations suggest that the
high-mobility electrons occupy the dxz/yz subbands of Ti:t2g orbital extending
deep within the conducting sheet of SrTiO3. Our results demonstrate that the
illumination which induces additional carriers at the interface can pave the
way to control the Kondo-like scattering and study the quantum transport in
the complex oxide heterostructures.

##  I Introduction

The discovery of a conducting interface between the two band insulators LaAlO3
(LAO) and SrTiO3 (STO) has opened a new research field of oxide
electronics.Ohtomo2004  Considerable efforts have been made to understand the
mechanisms for the formation of this two-dimensional electron system (2DES)
and to gain control over its electronic properties. Specifically, depending on
the growth parameters, properties such as high mobility, McCollam2014 ;
Xie2014  superconductivity,Caviglia2008 ; Gariglio2009 ; Richter2013 ;
Prawiroatmodjo2016  magnetism Brinkman2007 ; Bert2011 ; Gorkov2015  or a
combination of these, can be observed. These phenomena are interesting for
fundamental research, as well as for novel oxide electronics
applications.Bal2015 ; Goswami2016 ; Liang2013

One of the major challenges, however, is to predict the exact properties after
a specific growth procedure,Brinkman2007 ; Xu2016  and to manipulate them. The
most common tool in the latter category is back- or top-gating experiments.
The gating affects the Fermi energy and the confinement potential, thereby
changing the electron concentration, shifting the critical temperature of the
superconductivity and/or changing the magnetic properties in
LAO/STO.Caviglia2008 ; Caviglia2010 ; Fete2012  Another way to manipulate the
electronic state of the material is by illumination. It has been shown that
UV-light influences the 2DES significantly, for example, it can lower the
resistivity by orders of magnitude due to the large enhancement in carrier
density ($n$) and mobility ($\mu$).Guduru2013 ; DiGennaro2013 ; Lu2014 ;
Liu2016b  Despite optically induced high-mobility carriers, quantum
oscillations in the illuminated LAO/STO samples were not observed previously
in magnetotransport experiments,Guduru2013  most likely because of
insufficient magnetic field and temperature required for Landau quantization.

In this paper, we have studied the magnetotransport properties of the
illuminated LAO/STO heterostructure, with 26 unit cells of LAO grown on a
TiO2-terminated STO (100) substrate, in high magnetic fields and low
temperatures. This particular heterostructure grown with slightly different
growth parameters has been systematically investigated and primary features
such as Kondo effect,Brinkman2007  anisotropic magnetoresistance, wang2011
and multiband conduction Guduru2013b ; Guduru2013 ; Jost2015  have been
reported. Here, we observed that the illumination completely eradicates the
Kondo-like features at low temperatures ($<15$ K) and switches the
magnetoresistance from negative ($-20\%$) to positive ($+60\%$).
Interestingly, very small amplitude Shubnikov-de Haas (SdH) oscillations,
barely visible in the raw data, superimpose the positive magnetoresistance.
Executing two-band Drude model analysis to the non-linear Hall resistance, we
reveal the coexistence of low- and high-mobility electron channels at the
interface. More specifically, the high-mobility carriers exhibit a small
density ($\sim 2~{}\times~{}10^{12}$ cm-2) which is comparable to that
estimated from the SdH oscillations’ frequency. Furthermore, the cyclotron
mass ($\sim 1.7~{}m_{e}$) estimated from the oscillations’ amplitude suggests
that the high-mobility electrons occupy heavy subbands dxz/yz of Ti:3d band
existing away from the interface and extending deep within the conducting
sheet.

##  II Experimental methods and results

###  II.1 Sample characterization

The epitaxial LAO film of 10 nm (26 u.c.) was grown on a TiO2-terminated STO
substrate using pulsed laser deposition at temperature of $850$ ∘C, oxygen
pressure of $1.5\times 10^{-2}$ mbar, and laser fluency of $1.3$ J/cm2. The
growth of LAO was monitored by means of _in-situ_ reflective high-energy
electron diffraction (RHEED). As shown in Fig.1, the observed RHEED
oscillations specified a layer-by-layer growth of 26 u.c. of LAO on the STO
substrate.

Figure 1: RHEED oscillations for the LAO layers grown on a STO substarte. The
inset shows the RHEED pattern after growth of 26 u.c. LAO layers. The maxima
in the RHEED intensity clearly show the controlled layer-by-layer growth with
the number of layers indicated on top of them.

For magnetotransport measurements, we use both dc-field (up to $30$ T) at the
High Field Magnet Laboratory in Nijmegen and pulsed-field (up to $55$ T) at
the Laboratoire National des Champs Magnétiques Intenses in Toulouse. The
sample was mounted on a ceramic chip-carrier and electrically contacted in van
der Pauw geometry with aluminum wires using an ultrasonic wire-bonder. We used
a custom-designed probe suitable for illumination at low temperatures. While
the illumination and magnetotransport measurements were performed at $T$ =
0.35 K in a 3He system, the temperature dependence of zero-field resistance of
the pristine sample was also measured in a dilution fridge down to 0.15 K. The
_in-situ_ illumination in the dilution fridge was not possible in the setup
used because of no optical access. The excitation current of $1$ $\mu$A was
passed through two contacts on the middle of the sample (see Fig. 2d) and
voltages were measured on both sides parallel to the current path for the
longitudinal resistance $R_{xx}$, and perpendicular to the current path for
the Hall resistance $R_{yx}$. Due to some inhomogeneity, there were slight
differences between the $R_{xx}$ signal, measured on the different sides of
the sample. In order to avoid geometric admixtures, we measured $R_{xx}$ and
$R_{yx}$ for both positive and negative magnetic field directions and
calculated the symmetrised $R_{xx}$ and antisymmetrised $R_{yx}$ using the
formula $R_{xx}=\frac{R_{xx}(+B)+R_{xx}(-B)}{2}$ and
$R_{yx}=\frac{R_{yx}(+B)-R_{yx}(-B)}{2}$, respectively.

Mounting the sample on our measurement setup requires it to be in the open air
and light for several minutes. This means that the sample gets enough UV-light
at room temperature to possibly be in an excited state before the experiment
starts. To minimise this effect, after mounting, the sample was kept in the
dark at room temperature for several hours, allowing the system to recover to
its ground state before start cooling. Fig. 2(a) shows the temperature
dependence of $R_{xx}$ before and after illuminating the sample. Before
illumination, $R_{xx}$ (black curve) was measured while cooling the sample
from room temperature to $0.35$ K. From the black curve, $R_{xx}$ decreases
from a several M$\Omega$ through a minimum around $15$ K, after which it
starts to increase logarithmically with decreasing $T$, reaching 2.7 k$\Omega$
around $0.35$ K. This logarithmic behavior is typically assigned to Kondo
scattering on the Ti3+ ions Brinkman2007 ; Guduru2013 ; Jost2015  or magnetic
moments from oxygen vacancies.Li2015c  Measuring the same sample at lower
temperatures (< $0.35$ K) in the dilution fridge, we noticed an additional
rapid drop in $R_{xx}$, most likely related to the onset of a superconducting
phase at low $T$ ($\sim$ 0.10 K) Reyren2007a . However, no full
superconducting phase transition is detected in the temperature range down to
0.15 K.

Figure 2: (a) Resistance $R_{xx}$ versus temperature $T$ on a log-log scale.
The high resistance cool-down curve is represented by a black line. At the
orange star, the sample is illuminated, visible in the time dependent
measurement in (b). The post-illumination low-resistance warm-up curve is
shown in red. At three temperatures ($3$, $8$, $30$ K) the warm-up (red) is
interrupted by a partial cool-down (black). (b) $R$ as a function of time $t$
while illuminating with an intensity of few $\mu$W (blue area). (c) A sketch
of the band bending at the LAO/STO interface. Arrows indicate excited
electrons. (d) A schematic diagram of the illumination setup (not to scale)
with the contacts used for resistance measurements.

###  II.2 Illumination

The illumination was performed at $T$ = 0.35 K in 3He system with a $3.3$ eV
($373$ nm) laser, which is slightly higher than the bandgap energy of STO (3.2
eV). The sketch in Fig. 2(d) shows how the light is brought to the sample by a
multimode optical fiber. This fiber terminates $2$ cm above the sample which
is far enough away for the light to diverge and illuminate the entire surface
of the sample homogeneously. When the light reaches the sample, it is first
transmitted through the LAO, which has a bandgap energy of $5.4$ eV; and then
reaches the STO where it excites electrons. Our understanding is that the
electrons are transported to, and trapped at the interface due to the
confinement potential. The electrons follow the arrows drawn in the band-
bending sketch of Fig. 2(c) (not to scale), while the simultaneously created
holes move in the opposite direction.

In Fig. 2(b), the effect of the illumination on the sample resistance $R_{xx}$
is shown as a function of time. The start temperature and time of the
illumination are indicated with a star in Fig. 2(a) and (b), respectively.
After a stable value prior to the illumination (here $2.7$ k$\Omega$, but in
general the precise value depends on the cool-down history and the light-
exposure history of the sample), the resistance drops within $200$ seconds by
nearly one order of magnitude, depending on the incident power (blue shaded
area). Once the illumination is stopped, the resistance remains stable for
several hours as long as the sample is kept at low temperature. If the
illumination power is increased, the resistance reaches a slightly lower
value, however, as soon as the light is turned off, the resistance increases
and stabilizes to a persistent value that is only weakly dependent on the
incident illumination power. For instance, in Fig. 2(b), we observe a 1%
increase of resistance after the light is turned off which is barely visible
on the scale of the figure. The remaining conductivity is then persistent for
more than several hours. The effects of subsequent heating on the resistance
is shown in Fig. 2(a) (red curve), which is of different character to that
obtained pre-illumination (black curve). The post-illumination sample shows
metallic behavior with a monotonically rising $R_{xx}(T)$ wihtout any Kondo-
like features. At three temperatures, $3$ K, $8$ K and $30$ K, the warm-up was
intentionally interrupted by a partial cool-down (black lines) to verify
stability. As seen in the figure, the resistance already recovers partially at
each of the partial cool-downs, and substantially at $30$ K. The fact that the
system recovers to its original state when warming above $50$ K for a
substantial time period (many hours), suggests that the persistent
conductivity is related to the 2DES observed at low temperature.

The decrease of resistivity during illumination suggests that the subsequent
persistent conductivity is due to either an increase of $n\cdot\mu$ in the
existing channels, or, alternatively, the creation of an additional channel
with significantly higher $n\cdot\mu$. While the first scenario can be
exemplified by analyzing magnetotransport data in terms of a two-channel Drude
model, the second scenario requires a dedicated theoretical calculation which
is beyond the scope of this work. In next section, we discuss the magnetic
field dependence of $R_{xx}$ and $R_{yx}$ for pre- and post-illumination and
analyze the data through Drude model for two parallel channels.

###  II.3 Magnetotransport

Figure 3: Magnetic field dependence of $R_{xx}$ from (a) pre-illumination and
(b) post-illumination measurements at $T=0.35$ K and upto $B$ = 30 T. (c) Hall
resistances $R_{yx}(B)$ from pre-illumination (black circle) and post-
illumination (blue triangle). While the solid line (red color) in (b) is a
second order polynomial fit, the lines in (c) are two-band Drude model fits.
Insets show the magnetoresistance MR $=\frac{R(B)-R(0)}{R(0)}$ and the Hall
resistance $R_{yx}$ measured pre- and post-illumination in pulsed magnetic
fields up to $55$ T and at $T$ = 0.50 K.

The pre-illumination value of $R_{xx}$ measured while sweeping the dc-field
from 0 to 30 T at $T=0.35$ K is shown in the main panel of Fig. 3(a). A rapid
increase in low fields, below $1~{}T$, is most probably due to low-resistance
phase (onset of superconducting phase) which is destroyed by a small magnetic
field. For $B>1$ T, a pronounced negative magnetoresistance is observed, which
can be attributed to a reduction of spin scattering on magnetically oriented
Ti3+ ions.Brinkman2007  From post-illumination (Fig. 3(b)), $R_{xx}$ drops by
almost an order of magnitude and the negative MR is no longer observable,
instead, a positive MR now dominates. Interestingly, we also observed very
small amplitude oscillations superimposed on the positive MR for post-
illumination, which will be discussed in detail later. The insets in Fig. 3
show data measured in pulsed magnetic field up to 55 T at $T$ = 0.5 K. The
data obtained in pulsed-field are in line with those measured in dc-field,
thereby evidencing the reproducibility of the main sample’s charateristics.
From the inset of Fig. 3(b), the positive MR starts to saturate at high fields
$\sim 50$ T (inset in Fig. 3(b)), which is typical behavior for a multi-
channels system with channels of different carrier density
sondheimer1947theory . To extract the charge carrier’s properties from the
Hall-effect and the quantum oscillations, we focus on the dc-field data, which
has a higher signal-to-noise ratio.

We compare the Hall resistance $R_{yx}$ from pre- and post-illumination
measurements in Fig. 3(c). Unlike to the previously reported linear
$R_{yx}(B)$ before illumination,Guduru2013 ; Guduru2013b  we observed a
nonlinear $R_{yx}(B)$ in low-field regime (0-15 T) and a linear $R_{yx}(B)$ in
high-field regime ($B~{}>$ 15 T). The distinct $R_{yx}(B)$ behavior for the
same heterostructure, 26 uc-LAO/STO, could be because of slightly different
growth parameters, particularly, the oxygen pressure and the growth
temperature which significantly affect the carrier density and mobility in the
2DES wang2011 ; Hernandez2012 ; han2016 . Interestingly, the illumination does
merely affect the Hall resistance at low magnetic fields which only starts to
deviate from its pre-illumination behavior in fields above $\sim 20$ T. This
simple observation underlines the importance of high magnetic fields for a
proper two conduction-channel analysis of the Hall resistance of this sample.
Keeping in mind that the Drude-model may not give full and reliable
qualitative information of multichannels, we can still use it to quantify the
properties of two channels of different carrier densities, $n_{1,2}$ and
mobilities $\mu_{1,2}$. According to two-band Drude model, the zero-field
sheet resistance $R_{s}(0)$ and the magnetic field dependence of $R_{yx}$ and
$R_{xx}$ are defined as

$R_{s}(0)=\frac{1}{e}\left(\frac{1}{n_{1}\mu_{1}+n_{2}\mu_{2}}\right),$ (1)

$R_{yx}(B)=-\frac{B}{e}\frac{(n_{1}\mu_{1}^{2}+n_{2}\mu_{2}^{2})+(\mu_{1}\mu_{2}B)^{2}(n_{1}+n_{2})}{(n_{1}\mu_{1}+n_{2}\mu_{2})^{2}+(\mu_{1}\mu_{2}B)^{2}(n_{1}+n_{2})^{2}},~{}~{}~{}~{}\rm{and}~{}~{}~{}~{}$
(2)

$R_{xx}(B)=R_{s}(0)\left[1+\frac{(n_{1}\mu_{1}n_{2}\mu_{2}(\mu_{1}-\mu_{2})^{2}B^{2}}{(n_{1}\mu_{1}+n_{2}\mu_{2})^{2}+((n_{1}+n_{2})\mu_{1}\mu_{2}B)^{2})}\right].$
(3)

| $n_{1}$ | $\mu_{1}$ | $n_{2}$ | $\mu_{2}$ |  $R_{s}$ (fit) |  $R_{s}$ (exp.)
---|---|---|---|---|---|---
| (cm-2) | (cm2V-1s-1) | (cm-2) | (cm2V-1s-1) | ($\Omega/\square$) | ($\Omega/\square$)
Pre-illumination | 4.4 $\times 10^{13}$ | 34 | 8.0 $\times 10^{10}$ | 845 | 3997 | 4000
Post-illumination | 4.7 $\times 10^{13}$ | 135 | 2.4 $\times 10^{12}$ | 1000 | 714 | 708
Table 1: Values of the carrier density $n_{1,2}$, mobility $\mu_{1,2}$, and
the zero-field sheet resistance $R_{s}$ (fit) estimated from the two-channel
Drude model fit to the Hall resistance data for pre- and post-illumination.
The experimental value of $R_{s}$ is calulated using the relation
$R_{s}=\alpha R_{xx}$, where $\alpha(\sim 1.5)$ is a numerical ratio between
$R_{s}$ and $R_{xx}$ determined by van der pauw measurements on different
contact configurations.Guduru2013b ; guduru2014

Since the negative magnetoresistance can not be described using the simple
Drude model, we discarded the $R_{xx}(B)$ from this analysis. We fit the Hall
resistance data for pre- and post-illumination to the Eq. (2) in such a way
that the fitting parameters $n_{1,2}$ and $\mu_{1,2}$ could satisfy Eq. (1)
where $R_{s}(0)$ is experimental value of the sheet-resistance at zero-field.
The best-fit to the experimental data are shown as solid red-colour lines in
the Fig.3(c), and the yield values of carrier densities and mobilities are
listed in Table 1. As one can see, the fittings are quite fair, and justify
the simultaneous existence of low-mobility and high-mobility subbands. For
pre-illumination, the density of low-mobility carriers
($4.4~{}\times~{}10^{13}$ cm-2) is almost three orders of magnitude larger
than that of high-mobility ones ($8.0~{}\times~{}10^{10}$ cm-2).
Interestingly, a large increament in the density of high-mobility carriers is
observed post illumination. Following the requirements for observing quantum
oscillations ($\mu B\geq 1$), it is quite obvious that the high-mobility
electrons are responsible for oscillations in $R_{xx}(B)$ above $\sim 5$ T
(Fig. 3b). In order to get further insight on high-mobility carriers, we
investigate the quantum oscillations in the following section.

###  II.4 Quantum oscillations

Despite comparable mobility of carriers for pre- and post-illumination, we
perceived SdH oscillations only for post-illumination. We understood that the
absence of oscillations for pre-illumination is because of small density of
high-mobility carriers, which indicates a region of extreme quantum limit
above $\sim$ 3 T. Fig. 3(a) shows the oscillating resistance ($\Delta R_{xx}$)
after subtracting the polynomial background (second order polyomial fit in
Fig. 2(b)) from the $R_{xx}(B)$ for post-illumination. The oscillations of
amplitude $\sim 0.2-0.3~{}\%$ of $R_{xx}$ start developing at $\sim 5$ T field
and vanish at $\sim$ 25 T. For cyclotron mass analysis, the post-illumination
$R_{xx}(B)$ is measured at a few different temperatures and the second
derivative of $R_{xx}(B)$, $-$d${}^{2}R_{xx}$/d$B^{2}$ is displayed in Fig.
4(b). To analyze the oscillations clearly, we have smoothed the $R_{xx}(B)$
data before taking the second derivative. We point out that the oscillations’
frequency is similar in both cases, $\Delta R_{xx}(B)$ in Fig. 3(a) and
$-$d${}^{2}R_{xx}$/d$B^{2}$ in Fig. 3(b). The $R_{xx}(B)$ and $R_{yx}(B)$ are
of the same order of magnitude, which means the matrix inversion relates a
maximum in the resistance oscillations to a maximum of the conductivity, which
is then proportional to the density of states (DOS).

Figure 4: (a) Magnetic field dependence of oscillating resistance ($\Delta
R_{xx}$) after subtracting polynomial background from $R_{xx}(B)$ for pre- and
post-illumination. (b) The second order derivative of the sheet resistance
$R_{xx}$ (post-illumination) versus magnetic field for five different
temperatures. (c) A normalized plot of the oscillation’s amplitude (maximum-
to-minimum difference for a oscillation’s period in the field range of 13-25
T) with temperature. The fit is of the temperature dependent part of the
Lifshitz-Kosevich formula and results in $\Delta E=1.2\pm 0.2$ meV.

A straightforward interpretation of an oscillating DOS in a magnetic field is
Landau quantization leading to quantum oscillations, such as SdH oscillations
in the magnetoresistance. As high-mobility LAO/STO samples have been reported
to show quantum oscillations McCollam2014 ; Fete2014a ; rubi2020 , we have
attempted to apply standard SdH oscillation analysis to our data. The
temperature dependence of the oscillations’ amplitude in Fig. 4(b) shows a
decrease with increasing temperature following the expected Lifshitz-Kosevich
behavior:Lifshitz1956

$\begin{split}\frac{\rho_{xx}}{\rho_{0}}(B,T)&=1-2e^{-\beta}\frac{\alpha
T}{\sinh\alpha T}\cos\Big{(}2\pi\frac{hn}{2eB}+\phi\Big{)}\\\ \text{with
}\alpha&=\frac{2\pi^{2}k_{B}}{\Delta E},\beta=\frac{\hbar\pi}{\Delta
E\tau}\end{split}$ (4)

Most generally, $\Delta E$ is the energy between two extrema in the DOS (i.e.
Landau level separation $\hbar eB/m_{c}$ with $m_{c}$ the cyclotron mass),
$\tau$ the inelastic scattering time and $n$ the 2D electron concentration.
Using Eq. (4) we can extract the parameter $\alpha$ from our experimental data
and relate it to $\Delta E$. The fit to the temperature dependent
oscillation’s amplitude in Fig. 4(c) yields $\Delta E=1.2\pm 0.2$ meV.
Relating this to a Landau level splitting we extract a cyclotron mass of
$1.7\pm 0.3~{}m_{e}$. Because there is only one complete oscillation visible
in our data, the period is difficult to evaluate. However, a rough estimate
yields $\Delta 1/B=0.04$ T-1, which corresponds to a frequency of $25$ T, and
carrier density of $n_{SdH}=2ef/h\sim 1.2\times 10^{12}$ cm-2. This value of
the carrier density is comparable to that for high-mobility electrons
estimated from the two-channel model fitting.

##  III Discussion

In order to get an insight on the origin of low- and high-mobility carriers in
the illuminated LAO/STO system, we compare experimental results with
electronic subband properties predicted theoretically. From the density
functional theory (DFT) calculations, the conduction band of the 2DES at the
LAO/STO interface is dominated by dxy, dxz, and dyz orbitals originated from
the Ti:3d($t_{2g}$) orbital. While the dxy band is isotropic
($m^{*}_{x}=m^{*}_{y}=0.7m_{e}$), both dxz and dyz bands are quite anisotropic
in $k_{x}$-$k_{y}$ space (for dxz, $m^{*}_{x}=0.7m_{e}$ and $m^{*}_{y}$ = 7-9
$m_{e}$; for dyz, $m^{*}_{x}$ = 7-9 $m_{e}$ and
$m^{*}_{y}=0.7m_{e}$).popovic2008 ; delugas2011 ; rubi2020  Considering the
geometric mean, the average effective mass of electrons residing in the dxz/yz
bands is estimated as $\sim$ 1.3-1.8 $m_{e}$. Since the SdH oscillations probe
the $k$-averaged cyclotron mass, a direct comparison of the experimentally
estimated cyclotron mass $\sim$ 1.7 $m_{e}$ with the ones calculated
theoretically suggests that the high-mobility electrons occupy heavy dxz/yz
subbands. Interestingly, the smaller density of the high-mobility electrons,
as listed in Table 1, also agrees well with the layer-resolved density of
states predicted by DFT calculations delugas2011 ; rubi2020 . Just above the
Lifshitz point where the dxz/yz subbands begin to populate, a majority of
electrons located at the interface-adjacent STO layer occupy lower-lying dxy
subbands and a minority of electrons populate the dxz/yz subbands extending
farther from the interface Joshua2012 ; Ruhman2014 ; delugas2011 ; rubi2020 ;
smink2017 . This remark may appear in disagreement with an ARPES study on a
high-density sample ($n_{tot}$ = 6.5 $\times$ $10^{13}$ cm-2) for which the
Fermi sheet area of dxz/yz is comparable to that for dxy subbands.
cancellieri2014  However, the lower density ($n_{tot}$ = 4.9 $\times 10^{13}$
cm-2) of our sample would lead to a reduction in the Fermi wave vector
cancellieri2014 ; smink2017 , and subsequently, to the lower carrier density
in the dxz/yz than the dxy subbands. In contrast to what would be expected
from the comparison of effective masses, we find the mobility of the dxy
electrons to be smaller than that of the dxz/yz electrons, in agreement with
previous reports Joshua2012 ; Fete2014a ; Yang2016 ; rubi2020 . The low-
mobility of the $d_{xy}$ electrons is most likely due to increased scattering
in the interface-adjacent STO layers, mediated by, e.g., a large
straincantoni2012 , mixed Ti valence stateslee2016 ; rubi2020 , or a
relatively large concentration of oxygen vacanciesschutz2017 ; chikina2021 .

These strikingly observations strongly indicate that the illumination dopes a
large amount of high-mobility electrons in the dxz/yz subbands, which leads to
the elimination of the Kondo-like features and negative magnetoresistance.
However, the low-mobility electrons having large carrier density in the
studied sample belong to the dxy subbands and are responsible for the
magnetism at the LAO/STO interface, in support of the prior conclusion made
through spectroscopic studies lee2013 . It is worth mentioning here that the
experimentally observed cyclotron mass could also be explained by electron-
phonon renormalization for light subband using a mass enhancement factor of
$\sim$ 2.5 cancellieri2016 .

##  IV Conclusion

To conclude, we have shown that an as-grown magnetic LAO/STO sample can
exhibit higher mobility electrons by illuminating with a laser of higher
energy than the bandgap of STO. The high-mobility electrons ensue the quantum
oscillations in high magnetic fields and at low temperatures. The carrier
density and effective mass of the high-mobility electrons estimated from
quantum oscillations evidenced that these electrons occupy heavy dxz/yz
subbands. These findings are in line with the quantum transport studies in the
high mobility LAO/STO samples acheived by optimising growth conditions
BenShalom2010 ; Caviglia2010 ; Yang2016 ; rubi2020 . Furthermore, this work
establishes an important bridge between the high-field magnetotransport
studies on the low-mobility magnetic LAO/STO samples Guduru2013 ; Guduru2013b
and the high-mobility capped SrCuO2/LAO/STO samples McCollam2014 .

##  V acknowledgments

We thank A. McCollam for discussions and a careful reading of the manuscript.
We acknowledge the support of HFML-RU/FOM and LNCMI-CNRS, members of the
European Magnetic Field Laboratory (EMFL). This work is part of the DESCO
research program of the Netherlands Organization for Scientific Research
(NWO).

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