Electrostatic gate-controlled quantum interference in a high-mobility two-dimensional electron gas at the (La$_{0.3}$Sr$_{0.7}$)(Al$_{0.65}$Ta$_{0.35}$)O$_3$/SrTiO$_3$ interface

Abstract

We report quantum oscillations in magnetoresistance that are periodic in magnetic field ($B$), observed at the interface between (La$_{0.3}$Sr$_{0.7}$)(Al$_{0.65}$Ta$_{0.35}$)O$_3$ and SrTiO$_3$. Unlike Shubnikov-de Haas oscillations, which appear at magnetic fields $ > 7$ T and diminish quickly as the temperature rises, these $B$-periodic oscillations emerge at low fields and persist up to 10 K. Their amplitude decays exponentially with both temperature and field, specifying dephasing of quantum interference. Increasing the carrier density through electrostatic gating results in a systematic reduction in both the amplitude and frequency of the oscillations, with complete suppression beyond a certain gate voltage. We attribute these oscillations to the Altshuler-Aronov-Spivak effect, likely arising from naturally formed closed-loop paths due to the interconnected quasi-one-dimensional conduction channels along SrTiO$_3$ domain walls. The relatively long phase coherence length ($\sim$ 1.8 $μ$m at 0.1 K), estimated from the oscillation amplitude, highlights the potential of complex oxide interfaces as a promising platform for exploring quantum interference effects and advancing device concepts in quantum technologies, such as mesoscopic interferometers and quantum sensors.

Figures (9)

• Figure 1: $B$-periodic oscillations in magnetoresistance suggesting quantum interference. (a) Magnetic field dependence of longitudinal resistance $R_{xx}(B)$ at a few selected temperatures and at a back-gate voltage $V_g$ = 3 V. The curves are shifted vertically with spacing of 0.1 k$\Omega$ for better visuality of oscillations. The $B$-periodic oscillations in $R_{xx}(B)$ in low fields (0 - 7 T), depicted by vertical dashed lines, survive above 1 K. Inset is a optical microscope image of the Hall-bar device with schematic of transport measurements scheme. (b) A second order derivative of $R_{xx}(B)$ (blue solid line and left y axis) reveals $B$-periodic oscillation along with higher harmonics. $R_{xx}(B)$ is displayed with red solid line and on right y axis. (c) Conductance (Inverse of $R_{xx}(B)$) in the unit of conductance quantum $e^2/h$ (right y axis) and the oscillating conductance after subtracting the background of $1/R_{xx}$ (left y axis). The black solid lines are the $2^{nd}$ order polynomial fit to the $1/R_{xx}$ data to subtract the monotonic background.
• Figure 2: Gating effect on electrical properties and quantum oscillations. (a) $R_{xx}(B)$ and (b) $R_{yx}(B)$ at different values of $V_g$. Dashed line in (b) is the linear fit to $R_{yx}(B)$ at $V_g$ = 3.8 V. (c) Zero-field offset of $R_{yx}$ as a function $R_{xx}$. Non-linear dependence of $R_{yx}$ on $R_{xx}$ in zero field indicates the existence of charge inhomogeneity at the interface. (d) Carrier density, $n$ (left y axis), and mobility, $\mu$ (right y axis) as a function of $V_g$. (e) An evolution of oscillations with varying $V_g$. $B$-periodic oscillations completely suppress for $V_g >$ 20 V. (f) FFT of $B$-periodic oscillations reveals two peaks, the main peak at 0.58 T$^{-1}$ and the harmonic peak at 1.16 T$^{-1}$. (g) Variation in the oscillations frequency with $V_g$. For the best estimation of frequency, we assign the minima to integer and linear fit the plot of minima positions vs their number.
• Figure 3: Impact of $B$ orientation on quantum oscillations (a) $R_{xx}$ and (b) $-$d$^2R_{xx}$/d$B^2$ at different tilt angles measured at 0.1 K. The inset of (a) is a schematic of the magnetic field orientation, where $\theta$ = 0$^\circ$ and 90$^\circ$ are the angles when the field is perpendicular and parallel to the (001) plane, respectively. (c) Inverse field dependence of quantum oscillations measured at $\theta$ = 90$^\circ$. (d) FFT spectra of oscillations at different temperatures. (e) Thermal damping of oscillations amplitude fitted with Lifshitz-Kosevich formula for cyclotron mass estimation.
• Figure 4: Phase coherence length $L_\phi$ estimation from the temperature dependence of $B$-periodic oscillations. (a) Oscillating component of resistance at different temperatures. (b) Main panel: FFT of $B$-periodic oscillations producing 3 additional harmonic peaks. Inset: Temperature dependence of FFT amplitude with linear fit. (c) Temperature and (d) gate dependence of estimated $L_\phi$.
• Figure 5: (a) Damping of $B$-periodic oscillations with magnetic field and temperature. No oscillations are observed above 9 K (b) Oscillations follow exponential decay with magnetic fields.