Two-Dimensional Quantum Oscillations of the Conductance at ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ Interfaces

We report on a study of magnetotransport in ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interfaces characterized by mobilities of the order of several thousands ${\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$. We observe Shubnikov–de Haas oscillations whose period depends only on the perpendicular component of the magnetic field. This observation directly indicates the formation of a two-dimensional electron gas originating from quantum confinement at the interface. From the temperature dependence of the oscillation amplitude we extract an effective carrier mass $m^{*}\simeq 1.45m_e$. An electric field applied in the back-gate geometry increases the mobility, the carrier density, and the oscillation frequency.

Figure 1

Shubnikov–de Haas oscillations of the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface. (a) Variation of resistance $\Delta R=R(B)-R(0)$ in response to the application of a magnetic field $B$ oriented perpendicular to the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface, recorded at different temperatures $T$. (b) Numerical derivative $dR/dB$ as a function of the inverse of the magnetic field.

Figure 2

Angular dependence of the quantum oscillations. (a) Sheet resistance $R$ as a function of magnetic field $B$ recorded at different orientations (measured by the angle $\theta$) with respect to the direction normal to the substrate. (b) Numerical derivative $dR/dB$ as a function of the inverse of the magnetic field recorded at different orientations. (c) Numerical derivative $dR/dB$ as a function of the inverse of the component of the magnetic field perpendicular to the plane of the interface. An offset has been introduced in each curve for clarity. The lines are a guide to the eye.

Figure 3

Temperature dependence of the Shubnikov–de Haas oscillations. (a) Oscillatory component of the sheet resistance $\Delta R$ as a function of the inverse of the magnetic field oriented perpendicular to the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface, recorded at different temperatures $T$. (b) Fourier spectrum of the resistance oscillation measured at 250 mK. (c) Blue dots: temperature dependence of the amplitude of the oscillation at 13.5 T. Solid line: best fit to Eq. (3) of the experimental data.

Figure 4

Field effect modulation of the Shubnikov–de Haas oscillations. (a) Sheet resistance $R$ as a function of magnetic field $B$ recorded at different gate voltages $V$ at $T=250\mathrm{mK}$. (b) Numerical derivative $dR/dB$ as a function of the inverse of the magnetic field showing the effect of the gate voltage on the resistance oscillations. (c) Main frequency of the oscillation $\omega$ as a function of carrier density $n_{2\mathrm{D}}$.