Superconducting quantum criticality in three-dimensional Luttinger semimetals

TL;DR

This paper investigates a quantum critical point in three-dimensional Luttinger semimetals, revealing novel scaling behaviors and emergent symmetries near the transition from a semimetal to an s-wave superconductor.

Contribution

It introduces a perturbatively accessible model of quantum criticality in 3D Luttinger fermions with new scaling properties and symmetry enhancements.

Findings

Identification of a quantum critical point between semimetal and superconductor

Emergent rotational and particle-hole symmetries at criticality

Oscillatory corrections to scaling observed near the critical point

Abstract

We study a simple model of three-dimensional fermions close to a quadratic band touching point, built from the celebrated Luttinger single-particle Hamiltonian and an attractive contact interaction between the particles. Such a system displays a novel quantum critical point between the semimetallic and an s-wave superconducting phase at which the low-energy "Luttinger fermions" are inextricably coupled to the order parameter fluctuations. The quantum critical point is perturbatively accessible near four spatial dimensions, where it features nontrivial scaling with dynamical exponent 1<z<2 and emergent rotational and particle-hole symmetries. Some features of the criticality, such as oscillatory corrections to scaling and its enhanced symmetry, are discussed.