Effect of electrostatic confinement on the dome-shaped superconducting phase diagram at the LaAlO3/SrTiO3 interface

Abstract

The two-dimensional electron gas (2DEG) at the LaAlO[Formula: see text]/SrTiO[Formula: see text] (LAO/STO) interface exhibits gate-tunable superconductivity with a dome-like shape of critical temperature as a function of electron concentration. This behavior has not been unambiguously explained yet. Here, we develop a microscopic model based on the Schrödinger-Poisson approach to determine the electronic structure of the LAO/STO 2DEG, which we then apply to study the principal characteristics of the superconducting phase within the real-space pairing mean-field approach. For the electron concentrations reported in the experiment, we successfully reproduce the dome-like shape of the superconducting gap. According to our analysis such behavior results from the interplay between the Fermi surface topology and the gap symmetry, with the dominant extended s-wave contribution. Similarly as in the experimental report, we observe a bifurcation effect in the superconducting gap dependence on the electron density when the 2DEG is electrostatically doped either with the top gate or the bottom gate. Our findings explains the dome-shaped phase diagram of the considered heterostucture with good agreement with the experimental data which, in turn, strongly suggest the appearance of the extended s-wave symmetry of the gap in 2DEG at the LAO/STO interface.

Keywords: LAO/STO interface; Oxide interfaces; Unconventional superconductivity.

Fig. 1

Results of the Schrödinger–Poisson calculations for and . (a) 2D electron density vs. back-gate voltage extracted from the experimental data (Fig. 3 in Ref.). Experimental points are marked by dots and the line represents the interpolation. The data are extrapolated by  V relative to the voltage range of  V reported in the experiment - marked by dashed lines. (b) Self-consistent potential V(z) (black line) and relative permittivity (red line) profiles in the close vicinity of the LAO/STO interface. In the inset, the potential profile V(z) is plotted over the entire simulated range with  nm. (c) Electron density distribution near the LAO/STO interface, divided into and bands. (d) Dependence of the electronic structure on the electron mass . (e) Dispersion relation E(k) together with the density of states DOS (f). Results in panels (b, c, e, f) evaluated for .

Fig. 2

Results of the Schrödinger–Poisson calculations under the back-gating. (a, d) Electronic structure vs. back-gate voltage, . (b, e) Electron density profiles near the LAO/STO interface divided into and orbitals, calculated for  V and 20 V. In the inset of panel (b), the potential profile V(z) is plotted for  V. (c, f) The electron density for the and orbitals on the back gate voltage . Results for (a–c) and (d–f).

Fig. 3

(a, b) Superconducting energy gap as a function of back-gate voltage, . The upper x axis displays the corresponding 2D electron density extracted from the experimental data (cf. Fig. 3 in Ref.). Panels (c, d) present the dominant extended s-wave component of superconducting gap in the bands for different strength of electronic band anisotropy determined by . Results for (a, c) and (b, d) .

Fig. 4

Fermi surfaces of the (red) (blue) bands plotted on the map of isolines determined for the extended s-wave symmetry factor corresponding to (gray lines). Results are shown for (a)  V, where the superconducting phase is not observed, (b)  V, just above the superconductivity onset, (c)  V, at the maximum and above the maximum, for (d)  V in the regime of decreasing .

Fig. 5

Superconducting energy gap as a function of back-gate voltage and temperature T. The evaluated critical temperature at the maximum is 450 mK. Results for .

Fig. 6

(a) Electronic structure as a function of doping with the top gate voltage. Panels (b, c) present the dominant extended s-wave component of superconducting gap for the bands calculated for the bottom (black) and top (red) gating, assuming in the latter case  V (b) and  V (c).