Multi-band theory of superconductivity at the LaAlO$_3$/SrTiO$_3$ interface

TL;DR

This paper develops a multi-band model for superconductivity at the LaAlO$_3$/SrTiO$_3$ interface, revealing how spin-orbit interactions and external fields influence pairing mechanisms and transition temperatures, aligning well with experimental observations.

Contribution

It introduces a realistic multi-band Bogoliubov-de Gennes model incorporating spin-orbit effects and disorder, providing new insights into pairing channels and superconducting behavior at oxide interfaces.

Findings

Rashba and atomic spin-orbit interactions induce inter-band singlet and intra/inter-band triplet pairing.

Gate voltage variations match experimental superconductivity trends.

External in-plane magnetic field can enhance the superconducting transition temperature.

Abstract

We present a multi-band model for superconductivity at the metallic interface between insulating oxides LaAlO$_3$ and SrTiO$_3$ (001). Using a self-consistent Bogoliubov-de Gennes theory, formulated with the realistic bands at the interface, we investigate the spin-singlet and spin-triplet pairings in intra-band and inter-band channels. We find that the Rashba and atomic spin-orbit interactions at the interface induce singlet pairing in the inter-band channel and triplet pairing in both the intra-band and inter-band channels when the pairing amplitude in the singlet intra-band channel is finite. The gate-voltage variation of superconductivity is resolved in different pairing channels, compared with experimental results and found to match quite well. Interestingly, an enhancement of the superconducting transition temperature by external in-plane magnetic field is found revealing the existence of a hidden superconducting state above the observed one. As the interface is known to possess high level of inhomogeneity, we explore the role of non-magnetic disorder incorporating thermal phase fluctuations by using a Monte-Carlo method. We show that even after the transition to the non-superconducting phase, driven by temperature or magnetic field, the interface possesses localized Cooper pairs whose signature was observed in previous experiments.