Magnetic field tuned superconductor-to-insulator transition at the ${\mathrm{LaAlO}}_3$/${\mathrm{SrTiO}}_3$ interface

We present a study of the magnetic field tuned superconductor-to-insulator transition (SIT) in the electron gas that forms at the ${\mathrm{LaAlO}}_3$/${\mathrm{SrTiO}}_3$ interface. We find that the magnetic field induces a transition into a weakly insulating state, as is observed for the electrostatically tuned SIT at this interface. Finite size scaling of the magnetoresistance yields the critical exponent product $z\nu \simeq 7/3$, indicating that the transition is governed by quantum percolation effects. While such critical exponents have been reported previously for high resistance films, they have not been reported for a low resistance system like ours, with a maximum sheet resistance of $\approx 1.5 \mathrm{k}\Omega$, much less than the quantum of resistance $R_Q\equiv h/4e^2=6.45 \mathrm{k}\Omega$.

Figure 1

(a)–(c) are the MR at four different temperatures for the three different $V_g$'s, $V_g=60$, 40, and 20 V, respectively, in order of decreasing $T_C$'s. The insets show the zoomed-in region of the MR where the different isotherms cross each other.

Figure 2

The magnetic field induces a transition into a weakly insulating state as seen for $V_g=60$ V here. The transition happens close to $H_{\perp }=159$ mT. $T=50$ mK.

Figure 3

(a) $d^{3}V/d{I}^3$ vs $H_{\perp }$ for different $V_g$'s. The horizontal dashed line indicates the zero of $d^{3}V/d{I}^3$. When the third derivative crosses this line as a function of the field, the system passes into an insulating state. The inset shows the zoomed-in region of the zero crossings for the three $V_g$'s. The critical value of the field for $V_g=60$ V is indicated by the arrow, $H_C=159$ mT. $T=50$ mK. (b) Measured $H_C$ as a function of measured $T_C$'s for the different $V_g$'s.

Figure 4

$R_{\square }$ vs $|H-H_C|/T^{1/z\nu }$ for (a) $V_g=60$ V, (b) $V_g=40$ V, and (c) $V_g=20$ V. The critical exponent product $z\nu =7/3$ best fits the data, such that visually all the curves collapse onto each other.