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Coulomb interactions famously drive three dimensional quadratic band crossingsemimetals 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 phasewas investigated, assuming that the bandstructure was isotropic, assuming thatthe conduction and valence bands had the same band mass, and assuming that thedisorder preserved exact time-reversal symmetry and statistical isotropy. Itwas shown that the non-Fermi liquid fixed point is unstable to disorder, andthat a runaway flow to strong disorder occurs. In this work, we extend thatanalysis by relaxing the assumption of time-reversal symmetry and allowing theelectron and hole masses to differ (but continuing to assume isotropy of thelow energy bandstructure). We first incorporate time-reversal symmetry breakingdisorder, 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 thantime-reversal-symmetry-preserving disorder, which we therefore expect shoulddominate the strong-coupling phase. We then allow for unequal electron and holemasses. We show that whereas asymmetry in the two masses is irrelevant in theclean system, it is relevant in the presence of disorder, such that the'effective masses' of the conduction and valence bands should become sharplydistinct in the low-energy limit. We calculate the RG flow equations for thedisordered interacting system with unequal band masses, and demonstrate thatthe problem exhibits a runaway flow to strong disorder. Along the runaway flow,time-reversal-symmetry-preserving disorder grows asymptotically more rapidlythan both time-reversal-symmetry-breaking disorder and the Coulomb interaction.

physical review. b./physical review. b

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