New quantum transition in Weyl semimetals with correlated disorder

A Weyl semimetal denotes an electronic phase of solids in which two bands cross linearly. In this paper we study the effect of a spatially correlated disorder on such a phase. Using a renormalization-group analysis, we show that in three dimensions three scenarios are possible depending on the disorder correlations. A standard transition is recovered for short-range correlations. For disorder decaying slower than $1/r^2$, the Weyl semimetal is unstable to any weak disorder and no transition persists. In between, a new phase transition occurs. This transition still separates a disordered metal from a semimetal, but with a new critical behavior that we analyze to two-loop order.

Figure 1

Domains of existence of the transition as a function of $a$ and $d$: (i) in the left region there is no transition, the disorder is always relevant, and the disordered metal is the only phase. The typical RG flow computed at the point A $[a=3/2,d=3]$ is shown in Fig. 2; (ii) in the middle region there is a new transition from a semimetal phase to a metallic phase controlled by the LR FP. The typical RG flow computed at the point B $[a=5/2,d=3]$ is shown in Fig. 3; (iii) in the right region there is a transition from a semimetal phase to a metallic phase controlled by the SR FP. The typical RG flow computed at the point C $[a=3,d=3]$ is shown in Fig. 4.

Figure 2

Strongly disordered phase: runaway of the RG flow for $d=3$ ($\varepsilon =1$) and $a=3/2$ ($\delta =-1/2$) corresponding to the point A in Fig.  1. The red dot is the SR FP which is fully unstable. The blue dot is the Gaussian FP corresponding to the semimetal phase.

Figure 3

New LR transition: the RG flow for $d=3$ ($\varepsilon =1$) and $a=5/2$ ($\delta =1/2$) corresponding to the point B in Fig.  1. The right red dot is the SR FP which is fully unstable. The left red dot is the new LR FP which controls the transition between a semimetal and a disordered metal phase and which gives rise to a new universality class different from the SR case. The blue dot is the Gaussian FP corresponding to the semimetal phase.

Figure 4

SR transition: the RG flow for $d=3$ ($\varepsilon =1$) and $a=3$ ($\delta =1$) corresponding to the point C in Fig.  1. The red dot is the SR FP with a single unstable direction (relevant operator), describing the semimetal to disordered metal transition governed by the parameter ${\mathrm{\Delta }}_1$. The blue dot is the Gaussian FP corresponding to the semimetal phase.