Non-adiabatic corrections to chiral charge pumping in topological nodal semimetals

TL;DR

This paper investigates non-adiabatic effects on chiral charge pumping in topological semimetals, revealing how topological invariants influence conductivity and magnetoresistance, especially in non-symmorphic systems.

Contribution

It systematically includes non-adiabatic corrections in $k \, \cdot \, p$ models of Weyl and Dirac semimetals, linking topological invariants to observable transport phenomena.

Findings

Non-adiabatic corrections depend on topological invariants.

Chiral anomaly effects are sensitive to magnetic field direction.

Anisotropic magnetoresistance arises in non-symmorphic systems.

Abstract

Studying many-body versions of Landau-Zener-like problems of non-interacting electrons in the Slater formalism for several $k \cdot p$ models representing Weyl and Dirac semimetals, we systematically include non-adiabatic corrections to a quantum limit of chiral charge pumping in these models. In this paper, we show that relative homotopy invariant [Sun et al., Phys. Rev. Lett. 121, 106402 (2018)] and Euler class invariant [Bouhon et al., Nat. Phys. 16, 1137 (2020)] non-trivially manifest in the non-adiabatic corrections to the quantum limit of chiral charge pumping. These corrections could affect conductivity channels connected with the presence of chiral anomaly. Moreover, we show that, for non-symmorphic systems, this contribution is sensitive to the direction of the applied magnetic field (in respect to the so-called non-symmorphic nodal loop), suggesting that the conjectured direction-selective chiral anomaly in non-symmorphic systems [Bzdu\v{s}ek et al., Nature (London) 538, 75 (2016)] could lead to a strongly anisotropic longitudinal magnetoresistance. The presented approach can be easily applied to other $k \cdot p$ or tight-binding models.