Tunable circular dichroism due to the chiral anomaly in Weyl semimetals

Weyl semimetals are a three-dimensional gapless topological phase in which bands intersect at arbitrary points—the Weyl nodes—in the Brillouin zone. These points carry a topological quantum number known as the chirality and always appear in pairs of opposite chiralities. The notion of chirality leads to anomalous nonconservation of chiral charge, known as the chiral anomaly, according to which charge can be pumped between Weyl nodes of opposite chiralities by an electromagnetic field with nonzero $\mathit{E}·\mathit{B}$. Here, we propose probing the chiral anomaly by measuring the optical activity of Weyl semimetals via circular dichroism. In particular, we observe that applying such an electromagnetic field on this state gives it a nonzero gyrotropic coefficient or a Hall-like conductivity, which may be detectable by routine circular dichroism experiments. This method also serves as a diagnostic tool to discriminate between Weyl and Dirac semimetals; the latter will give a null result. More generally, any experiment that probes a bulk correlation function that has the same symmetries as the gyrotropic coefficient can detect the chiral anomaly as well as differentiate between Dirac and Weyl semimetals.

Figure 1

Illustration of gyrotropy induced by an $\mathit{E}·\mathit{B}$ field in WSMs. Colored (white) regions denote filled (empty) states and the two colors indicate Weyl nodes of opposite chiralities, which are located at different points in momentum space. In the absence of $\mathit{E}·\mathit{B}$, the Fermi levels at the two nodes are equal. An $\mathit{E}·\mathit{B}$ field pumps charge across the nodes, shown by the curved red arrow, resulting in a charge imbalance between the nodes and a consequent net anomalous contribution to $\gamma$. Since WSMs break $\mathcal{I}$ or $\mathcal{T}$, they are in general optically active in the absence of external fields as well. The anomalous contribution, proportional to $\mathit{E}·\mathit{B}$, can be isolated by applying electromagnetic fields at distinct finite frequencies.