Quantum Transport of Disordered Weyl Semimetals at the Nodal Point

Abstract

Weyl semimetals are paradigmatic topological gapless phases in three dimensions. We here address the effect of disorder on charge transport in Weyl semimetals. For a single Weyl node with energy at the degeneracy point and without interactions, theory predicts the existence of a critical disorder strength beyond which the density of states takes on a nonzero value. Predictions for the conductivity are divergent, however. In this work, we present a numerical study of transport properties for a disordered Weyl cone at zero energy. For weak disorder, our results are consistent with a renormalization group flow towards an attractive pseudoballistic fixed point with zero conductivity and a scale-independent conductance; for stronger disorder, diffusive behavior is reached. We identify the Fano factor as a signature that discriminates between these two regimes.

Density of states and magnetotransport in Weyl semimetals with long-range disorder

“…[20][21][22][23][24][25] The prevailing point of view is that a weak disorder has negligible effect on the density of states, which vanishes quadraticaly with the energy counted from the nodal point. This behavior persists up to a certain critical disorder strength beyond which the density of states acquires a finite value at zero energy.…”

Rare-Region-Induced Avoided Quantum Criticality in Disordered Three-Dimensional Dirac and Weyl Semimetals

“…Interestingly, the one-loop perturbative renormalization group (RG) calculations of the critical exponents for the proposed SM to DM QCP are consistent with the CCFS inequality (since ν ¼ 1, Refs. [22,23]) as, in fact, are the two-loop RG calculations [26,39] and all numerical estimates in the literature [24,25,32,33,35,36]; therefore, it is not a priori obvious that rare region effects should change the universality of this transition. Given the field theoretic RG analyses and the large body of direct numerical studies of the disorder-driven SM-DM QCP, finding the various critical exponents and identifying the critical coupling, as well as the apparent consistency between the theoretical (and numerical) correlation exponent with the CCFS inequality, it seems reasonable to assume that the rare regions arising out of nonperturbative disorder effects do not change the nature of the QCP in any substantial manner.…”

“…The goal of the current work is to settle this question definitively. Although the disordered Dirac-Weyl systems have been theoretically studied very extensively in the literature [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], essentially all of this work, except for a very recent one (Ref. [27]), study the properties of the disorder-driven SM-DM quantum phase transition, taking it for granted that such a disorder-induced QCP indeed exists in three dimensions following the predictions of the perturbative field theory.…”

“…Because of the invariable presence of disorder in all solid-state materials, there has been a substantial amount of theoretical activity studying the effect of disorder on noninteracting Dirac and Weyl fermions [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Focusing on the undoped (i.e., Fermi energy at E ¼ 0) Dirac point (i.e., the band touching point), the quadratically vanishing density of states at zero energy [ρðEÞ ∼ E 2 ] associated with the linear three-dimensional energy band dispersion places these problems in a different class than that of a conventional metal with a parabolic energy dispersion and a nonzero Fermi energy.…”

Global Phase Diagram of a Three-Dimensional Dirty Topological Superconductor

“…The metallic phase, where disorder is a relevant perturbation, is topologically trivial. Recently, there has been a surge of analytical [34][35][36][37][38][39][40][41][42] and numerical [43][44][45][46][47][48][49][50][51][52] works, exploring the effects of disorder in regular Dirac and Weyl semimetals.…”