Chiral anomaly and optical absorption in Weyl semimetals

Weyl semimetals are a three-dimensional topological phase of matter with isolated band touchings in the Brillouin zone. These points have an associated chirality, and many of the proposals to detect the Weyl semimetal state rely on the chiral anomaly. A consequence of the chiral anomaly is that under the application of an $\mathbf{E}·\mathbf{B}$ field, charge is transferred between points of opposite chirality. In this paper we propose an optical absorption experiment that provides evidence for the chiral anomaly. We use the Kubo formula, and find that an applied $\mathbf{E}·\mathbf{B}$ induces the formation of steplike features at finite frequency in the interband optical conductivity. We study the effect of scattering and finite temperatures on this feature and find that it should be observable at low temperatures in pure samples. Finally we discuss how the application of an $\mathbf{E}·\mathbf{B}$ field can be used to map out the frequency dependence of the scattering rate.

Figure 1

The finite frequency optical conductivity for a clean Weyl semimetal at $T=0$. In black we show the optical conductivity for a doped Weyl semimetal; we have used a small broadening, $\gamma =0.01$, to the Drude for graphing purposes. After the application of the applied $\mathbf{E}·\mathbf{B}$ field, charge is pumped from one Weyl point to the other, and steplike signatures appear in the interband portion of the optical conductivity. The missing interband spectral weight is transferred to the Drude peak. The measurement of these interband features is tied to the chiral anomaly and would be a direct signature of a Weyl semimetal.

Figure 2

Top: The finite frequency conductivity for several different values of the charge pumping. In this figure we show how disorder smears out the steplike features in the interband. The pictured curves are for a residual scattering rate of $\Gamma =0.1\mu$. The steplike features are most prominent when ${\mu }_p\approx \mu$ and are clearly visible as long as the scattering is not an appreciable fraction of $\mu$. Also notice the anomalous case, ${\mu }_p=\mu$, which contains a linear piece all the way to zero frequency. Bottom: The finite frequency conductivity for several different values of the charge pumping at finite temperature. Finite temperature shifts the chemical potential downward, as well as introducing thermal broadening. This figure has $T=0.1\mu$, the same energy as we used in the residual scatting figure. However, the effect of temperature is much more noticeable, and the steplike features have almost been completely washed out.

Figure 3

Here we show the effect of finite temperature on the shape of the Drude peak for two different types of scattering. Constant residual scattering is pictured on the left, and finite temperature simply causes the Drude peak to broaden. On the right we show the case of Born limit scattering. In this case the scattering rate is frequency dependent and the line shape depends on which energy is dominant. For $T<\left|\mu \right|$ the line shape has a Drude form, while for $T>\left|\mu \right|$ the line shape develops a sharp cusp.