Emergence of superconductivity in a doped single-valley quadratic band crossing system of spin-1/2 fermions

TL;DR

This paper demonstrates that in a doped single-valley quadratic band crossing system, superconductivity emerges as the dominant phase due to electron interactions, with the type of pairing depending on lattice symmetry and interaction range.

Contribution

It reveals how crystal symmetry and electron interactions in single-valley quadratic band systems lead to specific superconducting phases, extending understanding beyond two-valley systems like bilayer graphene.

Findings

Superconductivity becomes dominant upon doping and chemical potential introduction.

Different lattice symmetries favor different superconducting pairing symmetries.

The type of superconductivity depends on interaction range and symmetry, with s-wave and d-wave observed.

Abstract

For two-dimensional single-valley quadratic band crossing systems with weak repulsive electron-electron interactions, we show that upon introducing a chemical potential, particle-hole order is suppressed and superconductivity becomes the leading instability. In contrast to the two-valley case realized in bilayer graphene, the single-valley quadratic band touching is protected by crystal symmetries, and the different symmetries and number of fermion flavors can lead to distinct phase instabilities. Our results are obtained using a weak-coupling Wilsonian renormalization group procedure on a low-energy effective Hamiltonian relevant for describing electrons on checkerboard or kagom\'e lattices. In 4-fold symmetric systems we find that $d$-wave and $s$-wave superconductivity are realized for short-ranged (Hubbard) and longer-ranged (forward scattering), respectively. In the 6-fold symmetric case, we find either $s$-wave superconductivity or no superconducting instability.