Quantum oscillations in an optically-illuminated two-dimensional electron system at the LaAlO$_3$/SrTiO$_3$ interface

We have investigated the illumination effect on the magnetotransport properties of a two-dimensional electron system at the LaAlO$_3$/SrTiO$_3$ 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 d$_{xz/yz}$ subbands of Ti:t$_{2g}$ orbital extending deep within the conducting sheet of SrTiO$_3$. 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 LaAlO 3 (LAO) and SrTiO 3 (STO) has opened a new research field of oxide electronics. 1 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, 2,3 superconductivity, 4-7 magnetism 8-10 or a combination of these, can be observed. These phenomena are interesting for fundamental research, as well as for novel oxide electronics applications. [11][12][13] One of the major challenges, however, is to predict the exact properties after a specific growth procedure, 8, 14 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. 4, 15,16 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 (µ). [17][18][19][20] Despite optically induced high-mobility carriers, quantum oscillations in the illuminated LAO/STO samples were not observed previously in magnetotransport experiments, 17 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 TiO 2 -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, 8 anisotropic magnetoresistance, 21 and multiband conduction 17,22,23 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 inter- face. More specifically, the high-mobility carriers exhibit a small density (∼ 2 × 10 12 cm −2 ) which is comparable to that estimated from the SdH oscillations' frequency. Furthermore, the cyclotron mass (∼ 1.7 m e ) estimated from the oscillations' amplitude suggests that the high-mobility electrons occupy heavy subbands d xz/yz of Ti:3d band existing away from the interface and extending deep within the conducting sheet.

A. Sample characterization
The epitaxial LAO film of 10 nm (26 u.c.) was grown on a TiO 2 -terminated STO substrate using pulsed laser deposition at temperature of 850 • C, oxygen pressure of 1.5 × 10 −2 mbar, and laser fluency of 1.3 J/cm 2 . 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.
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 chipcarrier 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 3 He 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 µA 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 = Rxx(+B)+Rxx(−B) 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 MΩ through a minimum around 15 K, after which it starts to increase logarithmically with decreasing T , reaching 2.7 kΩ around 0.35 K. This logarithmic behavior is typically assigned to Kondo scattering on the Ti 3+ ions 8,17,23 or magnetic moments from oxygen vacancies. 24 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 (∼ 0.10 K) 25 . However, no full superconducting phase transition is detected in the temperature range down to 0.15 K.

B. Illumination
The illumination was performed at T = 0.35 K in 3 He 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  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 kΩ, but in general the precise value depends on the cool-down history and the lightexposure 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 cooldowns, 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 · µ in the existing channels, or, alternatively, the creation of an additional channel with significantly higher n · µ. 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.

C. Magnetotransport
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 Ti 3+ ions. 8 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 ∼ 50 T (inset in Fig. 3(b)), which is typical behavior for a multi-channels system with channels of different carrier density 26 . 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.
(3) 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 postillumination to the Eq. (2) in such a way that the fitting parameters n 1,2 and µ 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 I. 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 × 10 13 cm −2 ) is almost three orders of magnitude larger than that of high-mobility ones (8.0 × 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 (µB ≥ 1), it is quite obvious that the high-mobility electrons are responsible for oscillations in R xx (B) above ∼ 5 T (Fig. 3b). In order to get further insight on high-mobility carriers, we investigate the quantum oscillations in the following section.

D. 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 ∼ 3 T. Fig. 3(a) shows the oscillating resistance (∆R xx ) after subtracting the polynomial background (second order polyomial fit in Fig. 2(b) 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, ∆R xx (B) in Fig. 3(a) and −d 2 R xx /dB 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).
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 2,30,31 , 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: 32 Most generally, ∆E is the energy between two extrema in the DOS (i.e. Landau level separation eB/m c with m c the cyclotron mass), τ the inelastic scattering time and n the 2D electron concentration. Using Eq. (4) we can extract the parameter α from our experimental data and relate it to ∆E. The fit to the temperature dependent oscillation's amplitude in Fig. 4(c) yields ∆E = 1.2 ± 0.2 meV. Relating this to a Landau level splitting we extract a cyclotron mass of 1.7 ± 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 ∆1/B = 0.04 T −1 , which corresponds to a frequency of 25 T, and carrier density of n SdH = 2ef /h ∼ 1.2 × 10 12 cm −2 . This value of the carrier density is comparable to that for highmobility 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 d xy , d xz , and d yz orbitals originated from the Ti:3d(t 2g ) orbital. While the d xy band is isotropic (m * x = m * y = 0.7m e ), both d xz and d yz bands are quite anisotropic in k x -k y space (for d xz , m * x = 0.7m e and m * y = 7-9 m e ; for d yz , m * x = 7-9 m e and m * y = 0.7m e ). 31,33,34 Considering the geometric mean, the average effective mass of electrons residing in the d xz/yz bands is estimated as ∼ 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 ∼ 1.7 m e with the ones calculated theoretically suggests that the high-mobility electrons occupy heavy d xz/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 31,34 . Just above the Lifshitz point where the d xz/yz subbands begin to populate, a majority of electrons located at the interface-adjacent STO layer occupy lower-lying d xy subbands and a minority of electrons populate the d xz/yz subbands extending farther from the interface 31,[34][35][36][37] . This remark may appear in disagreement with an ARPES study on a high-density sample (n tot = 6.5 × 10 13 cm −2 ) for which the Fermi sheet area of d xz/yz is comparable to that for d xy subbands. 38 However, the lower density (n tot = 4.9 ×10 13 cm −2 ) of our sample would lead to a reduction in the Fermi wave vector 37,38 , and subsequently, to the lower carrier density in the d xz/yz than the d xy subbands. In contrast to what would be expected from the comparison of effective masses, we find the mobility of the d xy electrons to be smaller than that of the d xz/yz electrons, in agreement with previous reports 30, 31,35,46 . 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 strain 39 , mixed Ti valence states 31,40 , or a relatively large concentration of oxygen vacancies 41,42 .
These strikingly observations strongly indicate that the illumination dopes a large amount of high-mobility electrons in the d xz/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 d xy subbands and are responsible for the magnetism at the LAO/STO interface, in support of the prior conclusion made through spectroscopic studies 43 . 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 ∼ 2.5 44 .

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