Non-linear transport in multifold semimetals

TL;DR

This paper derives the complete nonlinear DC transport response functions for multifold semimetals, revealing how their quantum geometry and band dispersion influence measurable responses, and enabling targeted nonlinear valley-tronics applications.

Contribution

It provides a comprehensive derivation of third-order DC transport responses in multifold semimetals, linking quantum geometry to nonlinear responses and proposing methods for selective excitation.

Findings

Derived third-order DC response functions within Boltzmann theory.

Identified symmetry conditions affecting nonlinear responses.

Demonstrated potential for nonlinear valley-tronics in specific space groups.

Abstract

Transport measurements are a powerful way to probe the electronic structure of quantum materials, but the information they contain is often convoluted. Yet, in particular for simple low-energy fermiologies, and by combining linear and non-linear responses, definite conclusion can be drawn -- such as, for instance, in the case of the circular photogalvanic effect in Weyl semimetals. Here, we derive the complete DC intrinsic transport response functions up to third order in the applied electric field within Boltzmann theory that hold combined information about quantum geometry and band dispersion. We discuss the responses for multifold fermions at high-symmetry momenta in time-reversal symmetric crystals as well as their reduction by symmetry constraints. We exemplify in detail the cases of space group 213 and space group 199, which realize different multifold fermions, and show under which conditions these low-energy excitations can be differentially addressed through their bulk nonlinear responses, enabling nonlinear valley-tronics.