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 interband 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.
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