Exotic Superconductivity with Enhanced Energy Scales in Three Band Crossing Materials

TL;DR

This paper explores how three band crossings in quantum materials can host exotic superconductivity with significantly enhanced critical temperatures, especially in spin singlet and quintet channels, due to unique band structures.

Contribution

It introduces a minimal BCS framework for three band crossing materials, revealing enhanced superconductivity in specific pairing channels and proposing these materials as platforms for high-energy-scale superconducting states.

Findings

Superconductivity is greatly enhanced in spin singlet and quintet channels.

Critical temperature can be linear in interaction strength in these channels.

Conventional BCS behavior persists in the spin triplet channel.

Abstract

Three band crossings can arise in three dimensional quantum materials with certain space group symmetries. The low energy Hamiltonian supports spin $\textit{one}$ fermions and a flat band. We study the pairing problem in this setting. We write down a minimal BCS Hamiltonian and decompose it into spin-orbit coupled irreducible pairing channels. We then solve the resulting gap equations in channels with zero total angular momentum. We find that in the spin singlet channel (and also in an unusual `spin quintet' channel), superconductivity is enormously enhanced, with a possibility for the critical temperature to be $\textit{linear}$ in interaction strength. Meanwhile, in the spin triplet channel, the superconductivity exhibits features of conventional BCS theory due to the absence of flat band pairing. Three band crossings thus represent an exciting new platform for realizing exotic superconducting states with enhanced energy scales. We also discuss the effects of doping, nonzero temperature, and of retaining additional terms in the $\mathbf{k} \cdot \mathbf{p}$ expansion of the Hamiltonian.