Suppression of superconductivity across the Lifshitz transition in bulk SrTiO₃ and LaAlO₃/SrTiO₃ interfaces

The nature of the superconducting (SC) state of doped SrTiO₃ (STO) remains a subject of intense research. It is known experimentally that the SC transition temperature T_c displays a double-dome shape as function of the carrier density n. Quantum oscillations experiments reveal that multiple bands become occupied as the concentration n changes, i.e. STO is a multi-band superconductor. Surprisingly, around the critical concentration where the second band starts to be occupied, signaling a Lifshitz transition, a suppression of T_c is observed. The same phenomenon is also observed in LaAlO_3/SrTiO₃ interfaces. Here we show that such a suppression of T_c across a Lifshitz transition can be explained due to the combination of disorder and repulsive inter-band interactions, since in this case the pair-breaking caused by inter-band impurity scattering can overcome the increase of T_c favored by the enhancement of the density of states. We also show that this process is accompanied by a change of symmetry of the SC state from s^+- to s⁺⁺, indicating that STO is an unconventional multi-band superconductor.