Current-induced second harmonic generation in inversion-symmetric Dirac and Weyl semimetals

Abstract

Second harmonic generation (SHG) is a fundamental nonlinear optical phenomenon widely used both for experimental probes of materials and for application to optical devices. Even-order nonlinear optical responses including SHG generally require breaking of inversion symmetry, and thus have been utilized to study noncentrosymmetric materials. Here, we study theoretically the SHG in inversion-symmetric Dirac and Weyl semimetals under a DC current which breaks the inversion symmetry by creating a nonequilibrium steady state. Based on analytic and numerical calculations, we find that Dirac and Weyl semimetals exhibit strong SHG upon application of finite current. Our experimental estimation for a Dirac semimetal Cd${}_3$As${}_2$ and a magnetic Weyl semimetal Co${}_3$Sn${}_2$S${}_2$ suggests that the induced susceptibility ${\chi }^{(2)}$ for practical applied current densities can reach $10^5\mathrm{pm}\cdot {\mathrm{V}}^{-1}$ with mid-IR or far-IR light. This value is 10${}^2$-10${}^4$ times larger than those of typical nonlinear optical materials. We also discuss experimental approaches to observe the current-induced SHG and comment on current-induced SHG in other topological semimetals in connection with recent experiments.

7+6 pages, 4+2 figures

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