Enhanced Kohn-Luttinger topological superconductivity in bands with nontrivial geometry

TL;DR

This paper demonstrates how the geometry and topology of electronic bands influence Kohn-Luttinger superconductivity, showing that optimal band structures can exponentially enhance the transition temperature and robustness of topological superconductors.

Contribution

It introduces a complex form factor to encode band geometry effects on superconductivity and applies this to models including rhombohedral graphene multilayers.

Findings

Exponential enhancement of Tc with certain band geometries

Optimal band topology for maximizing superconducting transition temperature

Band geometry critically affects the robustness of topological superconductivity

Abstract

We study the effect of the electron wavefunction on Kohn-Luttinger superconductivity. The role of the wavefunction is encoded in a complex form factor describing the topology and geometry of the bands. We show that the electron wavefunction significantly impacts the superconducting transition temperature and superconducting order parameter. We illustrate this using the lowest Landau level form factor and find exponential enhancement of Tc for the resulting topological superconductor. We find that the ideal band geometry, which favors a fractional Chern insulator in the flat band limit, has an optimal Tc. Finally, we apply this understanding to a model relevant to rhombohedral graphene multilayers and unravel the importance of the band geometry for achieving robust superconductivity.