Electrically controlled superconducting states at the heterointerface SrTiO$_3$/LaAlO$_3$

TL;DR

This study models the superconducting pairing symmetry at the SrTiO$_3$/LaAlO$_3$ heterointerface, showing it can be electrically tuned between different mixed states by adjusting the gate voltage.

Contribution

It introduces a minimal model incorporating Rashba spin-orbit interaction to explain how pairing symmetry at the heterointerface can be controlled electrically.

Findings

The gap function mixes spin-singlet and spin-triplet components.

The ratio of d-wave to p-wave components varies with carrier concentration.

Pairing symmetry can be tuned by gate voltage.

Abstract

We study the symmetry of Cooper pair in a two-dimensional Hubbard model with the Rashba-type spin-orbit interaction as a minimal model of electron gas generated at a heterointerface of SrTiO$_3$/LaAlO$_3$. Solving the Eliashberg equation based on the third-order perturbation theory, we find that the gap function consists of the mixing of the spin-singlet $d_{xy}$-wave component and the spin-triplet $(p_x\pm ip_y)$-wave one due to the broken inversion symmetry originating from the Rashba-type spin-orbit interaction. The ratio of the d-wave and the p-wave component continuously changes with the carrier concentration. We propose that the pairing symmetry is controlled by tuning the gate voltage.