Impact of crystal symmetries and Weyl nodes on high-harmonic generation in Weyl semimetal TaAs

TL;DR

This paper develops a theoretical framework linking crystal symmetries to high-harmonic generation (HHG) in Weyl semimetals, revealing that HHG signals are governed by lattice symmetries rather than Weyl node topology.

Contribution

The authors introduce a universal Jones matrix formalism to relate pulse-crystal symmetries with HHG selection rules, applied specifically to TaAs.

Findings

HHG in TaAs is governed by lattice symmetries, not Weyl nodes.

Common HHG observables do not reveal Weyl cone signatures.

The formalism can be used to probe crystal symmetry and control harmonic polarization.

Abstract

High-harmonic generation (HHG) offers an all-optical approach to discern structural symmetries through its selection rules and probe topological phases with its spectral signatures. Here we develop a universal theoretical framework -- the Jones matrix formalism -- establishing the fundamental relationship between pulse-crystal shared symmetries and HHG selection rules. Applying this to the Weyl semimetal (WSM) material TaAs, shows that the anomalous harmonics excited by linearly and circularly polarized pulses are governed respectively by the shared twofold and fourfold rotational symmetries of laser pulses and lattice, rather than the topology of Weyl nodes. The common observables of HHG, including intensity, circular dichroism, ellipticity dependence, and carrier-envelope phase dependence, are not found to carry a signature of the Weyl cones. This insight into TaAs can be extended to other WSMs, indicating that HHG is not a particularly effective tool for investigating the topological features of WSMs. However, the Jones matrix formalism lays the groundwork for both HHG probing crystal symmetry and controlling harmonic polarization states.