Shape resonance at a Lifshitz transition for high temperature superconductivity in multiband superconductors

TL;DR

This paper explores how tuning the chemical potential near a Lifshitz transition in multiband superconductors can induce a shape resonance that enhances high-temperature superconductivity through complex interband interactions.

Contribution

It introduces a novel mechanism involving shape resonance at a Lifshitz transition, combining BCS and boson-like condensates to explain high-temperature superconductivity in multiband materials.

Findings

Shape resonance enhances superconducting gaps near Lifshitz transition.

Interband coupling controls the resonance and superconducting properties.

The phase exhibits a topological superconductivity with multiple condensates.

Abstract

We discuss the shape resonance in the superconducting gaps of a two band superconductor by tuning the chemical potential at a Lifshitz transition for Femi surface neck collapsing and for spot appearing. The high temperature superconducting scenario for complex matter shows the coexistence of a first BCS condensate made of Cooper pairs in the first band and a second boson-like condensate made of bosons like bipolarons, in the second band where the chemical potential is tuned near a Lifshitz transition. The interband coupling controls the shape resonance in the pair exchange between the two condensates. We discuss the particular BCS-Bose crossover that occurs at the shape resonance tuning the Lifshitz parameter (the energy difference between the chemical potential and the Lifshitz topological transition) like tuning the external magnetic field for the Feshbach resonances in ultracold gases. This superconducting phase provides a particular case of topological superconductivity with multiple condensates of different winding numbers