Josephson-like dynamics of the superconducting ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface

In this article, we show that the two-dimensional electron gas formed at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface behaves as a Josephson junction array. In particular, it exhibits a stochastic switching of the superconducting critical current, which qualitatively follows the dynamics of the resistively and capacitively shunted Josephson junction model. The switching current distribution (SCD) has been measured as a function of temperature and back-gate voltage. At low temperatures a clear saturation of the standard deviation of the SCD is observed, possibly indicating the presence of a macroscopic quantum tunneling regime with phase diffusion. Through the gate voltage we modify the damping of the array and compare it to artificial arrays of junctions.

Figure 1

Sheet resistance as a function of temperature for different values of the gate voltage. (Inset) Superconducting transition $T_{\mathrm{c}}$, defined as a $50\%$ drop in sheet resistance, as a function of $V_{\mathrm{G}}$.

Figure 2

(a) Example of a current-voltage characteristic at $V_{\mathrm{G}}=-5\mathrm{V}$ and $T=20\mathrm{mK}$, showing the switching ($I_{\mathrm{sw}}$) and return currents ($I_{\mathrm{R}}$). Arrows indicate the direction of the current sweep. The dashed line is a RCSJ numerical simulation with $Q=2.7$ [28]. (Inset) Scheme of the tilted washboard potential. (b) SCD (bars) for 10 000 switching events measured at $V_{\mathrm{G}}=-5\mathrm{V}$ and $T=20\mathrm{mK}$ (see Supplemental Material for the measurement procedure [28]). The full line corresponds to a smoothed distribution. (c) Sketch of the array of superconducting islands coupled by Josephson effect through a metallic 2-DEG.

Figure 3

(a) Switching current distribution at $V_{\mathrm{G}}=-5\mathrm{V}$ for different temperatures. Distance between two ticks corresponds to 2 nA. (b) Evolution of $\overline{I_{\mathrm{sw}}},I_{\mathrm{R}}$, and ${\sigma }_{\mathrm{sw}}$ as a function of temperature at $V_{\mathrm{G}}=-5\mathrm{V}$. Solid lines are guides to the eyes.

Figure 4

(a) Current-voltage characteristics measured at $T$ = 20 mK for different values of $V_{\mathrm{G}}$. (b) Evolution of $\overline{I_{\mathrm{sw}}},I_{\mathrm{R}},{\sigma }_{\mathrm{sw}}$ as a function of $V_{\mathrm{G}}$ (left axis) taken from the SCD reported in the Supplemental Material. Evolution of the experimental ($Q_{\exp }$) and calculated ($Q_{\mathrm{e}}$) quality factors as a function of $V_{\mathrm{G}}$. (c) Ratio $R_{\mathrm{e}}/R_{\mathrm{n}}$ as a function of $Q_{\mathrm{J}}^2$ on a log-log scale, where $Q_{\mathrm{J}}$ is the quality factor of an individual junction (see Supplemental Material). Blue squares: ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interfaces. Red circles: data taken from Ref. [41] for a regular array made of aluminum junctions. Straight lines have a slope of $-0.35$.