# Unconventional multi-band superconductivity in bulk SrTiO$_{3}$ and LaAlO$_{3}$/SrTiO$_{3}$ interfaces

## TL;DR

This paper investigates the unconventional multi-band superconductivity in doped SrTiO$_{3}$ and LaAlO$_{3}$/SrTiO$_{3}$ interfaces, revealing how disorder-induced pair-breaking explains the suppression of $T_c$ across Lifshitz transitions.

## Contribution

It introduces a disorder-based explanation for the suppression of superconducting transition temperature in multi-band systems with subleading, repulsive inter-band interactions.

## Key findings

- Disorder causes pair-breaking that suppresses $T_c$ across Lifshitz transitions.
- The two-band gap sign changes from opposite to same sign away from the Lifshitz point.
- The behavior aligns with experimental observations in SrTiO$_{3}$ and LaAlO$_{3}$/SrTiO$_{3}$.

## Abstract

Although discovered many decades ago, superconductivity in doped SrTiO$_{3}$ remains a topic of intense research. Recent experiments revealed that, upon increasing the carrier concentration, multiple bands cross the Fermi level, signaling the onset of Lifshitz transitions. Interestingly, $T_{c}$ was observed to be suppressed across the Lifshitz transition of oxygen-deficient SrTiO$_{3}$; a similar behavior was also observed in gated LaAlO$_{3}$/SrTiO$_{3}$ interfaces. Such a behavior is difficult to explain in the clean theory of two-band superconductivity, as the additional electronic states provided by the second band should enhance $T_{c}$. Here, we show that this unexpected behavior can be explained by the strong pair-breaking effect promoted by disorder, which takes place if the inter-band pairing interaction is subleading and repulsive. A consequence of this scenario is that, upon moving away from the Lifshitz transition, the two-band superconducting state changes from opposite-sign gaps to same-sign gaps.