Divergent bulk photovoltaic effect in Weyl semimetals

Abstract

Weyl semimetals (WSM) have been discovered in time-reversal symmetric materials, featuring monopoles of Berry's curvature in momentum space. WSM have been distinguished between Type-I and II where the velocity tilting of the cone in the later ensures a finite area Fermi surface. To date it has not been clear whether the two types results in any qualitatively new phenomena. Here we focus on the shift-current response (${\sigma }_{shift}(\omega )$), a second order optical effect generating photocurrents. Surprisingly we find that up to an order unity constant, ${\sigma }_{shift}(\omega )\sim \frac{e^3}{h^2}\frac{1}{\omega }$ in Type-II WSM, diverging in the low frequency $\omega \to 0$ limit. This is in stark contrast to the vanishing behavior (${\sigma }_{shift}(\omega )\propto \omega$) in Type-I WSM. In addition, in both Type-I and Type-II WSM, a nonzero chemical potential $\mu$ relative to nodes leads to a large peak of shift-current response with a width $\sim |\mu |/\hslash$ and a height $\sim \frac{e^3}{h}\frac{1}{|\mu |}$, the latter diverging in the low doping limit. We show that the origin of these divergences is the singular Berry's connections and the Pauli-blocking mechanism. Similar results hold for the real part of the second harmonic generation, a closely related nonlinear optical response.

10 pages, 4 figures, a new appendix is added, which expands the discussion of second-harmonic generation

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