Triangle anomaly in Weyl semimetals

Weyl semimetals possess massless chiral quasiparticles, and they are thus affected by the triangle anomalies. We discuss the features of the chiral magnetic and chiral vortical effects specific to Weyl semimetals, and then propose three phenomena caused by the triangle anomalies in this material: (i) anomaly cooling; (ii) charge transport by soliton waves as described by Burgers' equation, and (iii) the shift of the Berezinskii-Kosterlitz-Thouless phase transition of superfluid vortices coupled to Weyl fermions. In addition, we establish the conditions under which the chiral magnetic current exists in real materials.

Figure 1

A schematic illustration of the energy dispersion relation of a Weyl semimetal considered in Ref. [17]. The existence of the chiral magnetic current depends on how the levels are filled as denoted by the shaded regions. Part (a) corresponds to the absence of the chiral chemical potential, and thus the absence of the chiral magnetic current. In contrast, (b) describes the situation with a nonzero chiral chemical potential, in which the chiral magnetic current exists.

Figure 2

Anomaly cooling of Weyl semimetal by rotation and electric field. The semimetal could be either cooled or heated depending on the relative orientation of electric field and the angular momentum.

Figure 3

Anomaly-induced solitary wave of charge governed by Burgers' equation.