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 ($σ_{shift}(ω)$), a second order optical effect generating photocurrents. Surprisingly we find that up to an order unity constant, $σ_{shift}(ω)\sim \frac{e^3}{h^2}\frac{1}ω$ in Type-II WSM, diverging in the low frequency $ω\rightarrow 0$ limit. This is in stark contrast to the vanishing behavior ($σ_{shift}(ω)\propto ω$) in Type-I WSM. In addition, in both Type-I and Type-II WSM, a nonzero chemical potential $μ$ relative to nodes leads to a large peak of shift-current response with a width $\sim |μ|/\hbar$ and a height $\sim \frac{e^3}{h}\frac{1}{|μ|}$, 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.