Dirty Weyl semimetals: Stability, phase transition, and quantum criticality

Abstract

We study the stability of three-dimensional incompressible Weyl semimetals in the presence of random quenched charge impurities. Combining numerical analysis and scaling theory we show that in the presence of sufficiently weak randomness (i) Weyl semimetal remains stable, while (ii) double-Weyl semimetal gives rise to compressible diffusive metal where the mean density of states at zero energy is finite. At stronger disorder, Weyl semimetal undergoes a quantum phase transition and enter into a metallic phase. Mean density of states at zero energy serves as the order parameter and displays single-parameter scaling across such disorder driven quantum phase transition. We numerically determine various exponents at the critical point, which appear to be insensitive to the number of Weyl pairs. We also extract the extent of the quantum critical regime in disordered Weyl semimetal and the phase diagram of dirty double Weyl semimetal at finite energies.

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

“…Previous numerical studies of the SM-DM transition [24,28,[33][34][35][36] used periodic boundary conditions and even L, which produces a very strong finite-size effect on the zero-energy DOS in the semimetal. In the current model with Dirac points occurring at momenta commensurate with the lattice, even L and periodic boundary conditions place the lowest-energy eigenstates into the Dirac-peak centered around E ¼ 0.…”

“…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 disordered type-II Weyl semimetals

“…However, comparing to WSM1 (without the tilt term) whose global phase diagram have been thoroughly investigated [22][23][24][25] , disorder-induced phase transitions for tilted WSM, especially WSM2, have not been paid much attention yet. The diffusive phase has been reported in the presence of disorder for single tilted type-I Weyl cone 26 .…”