Shape resonance for the anisotropic superconducting gaps near a Lifshitz transition: the effect of electron hopping between layers

TL;DR

This paper presents a theoretical study of multigap superconductivity in quantum well superlattices, focusing on shape resonances near Lifshitz transitions and the effects of electron hopping between layers, revealing complex physics and deviations from standard BCS behavior.

Contribution

It introduces a BCS-based model capturing shape resonances and matrix element effects in multigap superconductors near Lifshitz transitions, highlighting the role of electron hopping between layers.

Findings

Deviations of 2Δ/Tc ratio from BCS value near Lifshitz points.

Complex physics due to matrix element effects at quantum critical points.

Comparison of condensate response with ultracold gases in BCS-BEC crossover.

Abstract

The multigap superconductivity modulated by quantum confinement effects in a superlattice of quantum wells is presented. Our theoretical BCS approach captures the low-energy physics of a shape resonance in the superconducting gaps when the chemical potential is tuned near a Lifshitz transition. We focus on the case of weak Cooper-pairing coupling channels and strong pair exchange interaction driven by repulsive Coulomb interaction that allows to use the BCS theory in the weak-coupling regime neglecting retardation effects like in quantum condensates of ultracold gases. The calculated matrix element effects in the pairing interaction are shown to yield a complex physics near the particular quantum critical points due to Lifshitz transitions in multigap superconductivity. Strong deviations of the ratio $2\Delta/T_c$ from the standard BCS value as a function of the position of the chemical potential relative to the Lifshitz transition point measured by the Lifshitz parameter are found. The response of the condensate phase to the tuning of the Lifshitz parameter is compared with the response of ultracold gases in the BCS-BEC crossover tuned by an external magnetic field. The results provide the description of the condensates in this regime where matrix element effects play a key role.