Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs

TL;DR

This paper reports a resonance-enhanced second harmonic generation in the Weyl semimetal TaAs, revealing a giant nonlinear optical response linked to fundamental polarization distribution properties, with implications for understanding and maximizing nonlinear effects.

Contribution

It introduces a new theorem connecting frequency-integrated nonlinear response to polarization skewness, explaining the potential for unbounded second-order nonlinearities in materials.

Findings

SHG response at 1.5 eV is from a resonance at 0.7 eV with 200x larger response than GaAs.

Theoretical insight shows spectral weight can be unbounded with next-neighbor hopping.

Ground state polarization skewness relates to maximum nonlinear response.

Abstract

While all media can exhibit first-order conductivity describing current linearly proportional to electric field, $E$, the second-order conductivity, $\sigma^{(2)}$ , relating current to $E^2$, is nonzero only when inversion symmetry is broken. Second order nonlinear optical responses are powerful tools in basic research, as probes of symmetry breaking, and in optical technology as the basis for generating currents from far-infrared to X-ray wavelengths. The recent surge of interest in Weyl semimetals with acentric crystal structures has led to the discovery of a host of $\sigma^{(2)}$ -related phenomena in this class of materials, such as polarization-selective conversion of light to dc current (photogalvanic effects) and the observation of giant second-harmonic generation (SHG) efficiency in TaAs at photon energy 1.5 eV. Here, we present measurements of the SHG spectrum of TaAs revealing that the response at 1.5 eV corresponds to the high-energy tail of a resonance at 0.7 eV, at which point the second harmonic conductivity is approximately 200 times larger than seen in the standard candle nonlinear crystal, GaAs. This remarkably large SHG response provokes the question of ultimate limits on $\sigma^{(2)}$ , which we address by a new theorem relating frequency-integrated nonlinear response functions to the third cumulant (or "skewness") of the polarization distribution function in the ground state. This theorem provides considerable insight into the factors that lead to the largest possible second-order nonlinear response, specifically showing that the spectral weight is unbounded and potentially divergent when the possibility of next-neighbor hopping is included.