Band Interplay and Finite-Bandwidth Effects on the Superconducting Critical Temperature of Heavily Disordered Interfaces Hosting Multi-band Superconductivity

LaAlO₃/SrTiO₃ interfaces are a nice example of a two-dimensional electron gas, whose carrier density can be varied by top- and back-gating techniques. The interplay of two-dimensionality, multi-band character and disorder affects the superconducting critical temperature T_c of these heavily disordered multi-band superconductors. In this framework, finite-bandwidth effects are called for a better understanding, as well as the attractive or repulsive nature of the bands involved.

A single band toy model is the starting point to highlight finite bandwidth effects. We then extend the study to a two-band disordered model [1]. In both cases, we find a suppression of T_c due to disorder.

In the one-band model, this might shed light on some experimentally relevant features of the band structure such as bandwidth and band edge positions.

Moreover, while confirming that a repulsive inter-band coupling favors the T_c suppression, we show that disorder alone can mix the two bands, generating a more pronounced suppression of the critical temperature in the vicinity of the Lifshitz transition.

[1] T. V. Trevisan, M. Schütt, R. M. Fernandes, Phys. Rev. Lett. 121, 127002 (2018)