# Nonlinear Hall effect in topological Dirac semimetals in parallel magnetic field

## TL;DR

This paper theoretically investigates the nonlinear Hall effect in 2D topological Dirac semimetals under in-plane magnetic fields, deriving quantum kinetic equations and proposing experimental tests in various materials.

## Contribution

The authors develop a quantum kinetic framework to analyze second-harmonic responses and nonlinear Hall effects in topological Dirac semimetals with in-plane magnetic fields.

## Key findings

- Derived the quantum kinetic equation for the Wigner distribution function.
- Analyzed Berry curvature dipole and field-induced current contributions.
- Proposed experimental measurements of Hall resistivity dependence on magnetic field.

## Abstract

We compute the second-harmonic response of two-dimensional topological Dirac semimetals subjected to an external in-plane magnetic field. The quantum kinetic equation for the Wigner distribution function is derived and then solved to evaluate the second-order electric-field contributions to the current density. Both the Berry curvature dipole and the field-induced terms in the current are analyzed across a broad range of model parameters. We propose that our theory can be tested experimentally by measuring the dependence of the anomalous Hall resistivity on the in-plane magnetic field in the surface states of the topological insulator SnTe, in WTe$_2$ and WSe$_2$ monolayers, as well as in the Kondo lattice material Ce$_3$Bi$_4$Pd$_3$ at very low temperatures.