Divergent bulk photovoltaic effect in Weyl semimetals

TL;DR

This paper reveals that Weyl semimetals exhibit divergent shift-current responses at low frequencies, with Type-II showing a unique divergence, highlighting novel nonlinear optical phenomena linked to their Berry curvature properties.

Contribution

It demonstrates the divergent behavior of the shift-current response in Type-II Weyl semimetals and compares it with Type-I, revealing new nonlinear optical effects due to Berry curvature singularities.

Findings

Type-II WSM show a diverging shift-current response as frequency approaches zero.

Both WSM types exhibit large peak responses at low doping levels.

The divergences are attributed to singular Berry connections and Pauli-blocking.

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 $\omega\rightarrow 0$ 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 $\sim |\mu|/\hbar$ 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.