Fate of superconductivity in three-dimensional disordered Luttinger semimetals

TL;DR

This paper investigates how short-range correlated disorder affects the superconducting quantum critical point in three-dimensional quadratic band crossing semimetals, finding that disorder destroys the criticality and leads to strong disorder regimes.

Contribution

It provides a controlled RG analysis showing that disorder destroys superconducting quantum critical points in 3D Luttinger semimetals.

Findings

Disorder causes a runaway flow to strong disorder.

Superconducting criticality is suppressed by disorder.

The study uses dimensional regularization and loop-expansion techniques.

Abstract

Superconducting instability can occur in three-dimensional quadratic band crossing semimetals only at a finite coupling strength, due to the vanishing of density of states at the quadratic band touching point. Since realistic materials are always disordered to some extent, we study the effect of short-ranged correlated disorder on this superconducting quantum critical point, using a controlled loop-expansion applying dimensional regularization. The renormalization group (RG) scheme allows us to determine the RG flows of the various interaction strengths, and shows that disorder destroys the superconducting quantum critical point. In fact, the system exhibits a runaway flow to strong disorder.