Interplay of Coulomb interactions and disorder in three dimensional quadratic band crossings without time-reversal symmetry and with unequal masses for conduction and valence bands

TL;DR

This paper investigates how Coulomb interactions, disorder, and mass asymmetry influence the stability of non-Fermi liquid phases in three-dimensional quadratic band crossing semimetals, revealing a tendency towards strong disorder and mass divergence.

Contribution

It extends previous work by analyzing the effects of time-reversal symmetry breaking disorder and unequal band masses on the non-Fermi liquid phase, showing relevance of mass asymmetry and dominance of certain disorder types.

Findings

Disorder causes runaway flow to strong disorder in the system.

Time-reversal-symmetry-breaking disorder grows more slowly than preserving disorder.

Unequal electron and hole masses become sharply distinct at low energies due to disorder.

Abstract

Coulomb interactions famously drive three dimensional quadratic band crossing semimetals into a non-Fermi liquid phase of matter. In a previous work, Phys. Rev. B 95, 205106 (2017), the effect of disorder on this non-Fermi liquid phase was investigated, assuming that the bandstructure was isotropic, assuming that the conduction and valence bands had the same band mass, and assuming that the disorder preserved exact time-reversal symmetry and statistical isotropy. It was shown that the non-Fermi liquid fixed point is unstable to disorder, and that a runaway flow to strong disorder occurs. In this work, we extend that analysis by relaxing the assumption of time-reversal symmetry and allowing the electron and hole masses to differ (but continuing to assume isotropy of the low energy bandstructure). We first incorporate time-reversal symmetry breaking disorder, and demonstrate that there do not appear any new fixed points. Moreover, while the system continues to flow to strong disorder, time-reversal-symmetry-breaking disorder grows asymptotically more slowly than time-reversal-symmetry-preserving disorder, which we therefore expect should dominate the strong-coupling phase. We then allow for unequal electron and hole masses. We show that whereas asymmetry in the two masses is irrelevant in the clean system, it is relevant in the presence of disorder, such that the 'effective masses' of the conduction and valence bands should become sharply distinct in the low-energy limit. We calculate the RG flow equations for the disordered interacting system with unequal band masses, and demonstrate that the problem exhibits a runaway flow to strong disorder. Along the runaway flow, time-reversal-symmetry-preserving disorder grows asymptotically more rapidly than both time-reversal-symmetry-breaking disorder and the Coulomb interaction.