Effects of time-periodic drive in the linear response for planar-Hall set-ups with Weyl and multi-Weyl semimetals

TL;DR

This work analyzes how a high-frequency time-periodic drive modulates the in-plane (planar) magnetoelectric and magnetothermal responses of Weyl and multi-Weyl semimetals using Floquet theory combined with van Vleck perturbation and a semiclassical Boltzmann framework. The authors derive explicit, $J$-dependent expressions for the longitudinal and planar Hall conductivities, as well as the corresponding thermoelectric and magnetothermal coefficients, revealing how the topological charge $J$ imprints signatures through Berry-curvature terms and how drive parameters $E_0$ and $\omega$ provide tunability. They show that, at zero temperature and to leading order in $B^2$, the drive-induced corrections scale as $E_0^4/\omega^6$ and decay with increasing frequency, while the static ($\omega\to\infty$) limits reproduce known results with characteristic $\mu$- and $J$-dependent scaling. The results offer experimentally accessible fingerprints of Berry curvature and topological charge in driven 3D semimetals and point to pump–probe setups as viable platforms to test Floquet-engineered transport in these systems.

Abstract

We investigate the influence of a time-periodic drive on three-dimensional Weyl and multi-Weyl semimetals in planar-Hall/planar-thermal-Hall set-ups. The drive is modelled here by circularly-polarized electromagnetic fields, whose effects are incorporated by a combination of the Floquet theorem and the van Vleck perturbation theory, applicable in the high-frequency limit. We evaluate the longitudinal and in-plane transverse components of the linear-response coefficients using the semiclassical Boltzmann formalism, thereby demonstrating the explicit analytical expressions of the conductivity for large frequencies. Our results corroborate the fact that the topological charges of the corresponding semimetals etch their trademark signatures in these transport properties, which can be detected in appropriate experiments.

Figures (3)

• Figure 1: (a) Dispersion characteristics of a single node in a Weyl, double-Weyl, and triple-Weyl semimetal, respectively,plotted against the $k_z k_x$-plane. The double(triple)-Weyl node shows an anisotropic hybrid dispersion with a quadratic(cubic)-in-momentum dependence along the $k_x$-direction. In order to pinpoint the direction-dependent features, the projections of the dispersion along the respective momentum axes are also shown. (b) Schematics showing the planar-Hall (or planar-thermal Hall) experimental configuration, where the sample is subjected to a uniform electric field $E\, {\boldsymbol{\hat{x}}}$ (and/or a temperature gradient $\partial_x T\, {\boldsymbol{\hat{x}}}$) along the $x$-axis. An external magnetic field $\boldsymbol B$ is applied as well, which makes an angle $\theta$ with the $x$-axis. The blue wave-packets represent a time-periodic drive implemented by shining circularly-polarized light.
• Figure 2: Left panel: Plots for $\tilde{\sigma}_{xx}$ (in the units of eV$^{-2}$) as a function of $\omega$, where $\tilde{\sigma}_{xx} =\left ( \sigma_{xx} -\sigma_{xx} \vert_{B=0} \right ) / (e^2 \,\tau \, v_z \,B^2)$, setting $\theta = \pi/6$. Right panel: Plots for $\tilde{\sigma}_{yx}$ (in the units of eV$^{-2}$) as a function of $\omega$, where $\tilde{\sigma}_{yx} = \sigma_{yx} / (e^2 \,\tau \, v_z \,B^2 \sin \theta \cos \theta)$. The values of $\mu$, $\alpha_J$'s, and $E_0$ are taken from Table \ref{['table_quantites']}.
• Figure 3: Plots for $\tilde{\sigma}_{xx}$ (in the units of eV$^{-2}$) as a function of $\theta$, where $\tilde{\sigma}_{xx} =\left ( \sigma_{xx} -\sigma_{xx} \vert_{B=0} \right ) / (e^2 \,\tau \, v_z \,B^2)$, setting $\omega = 0.75$ eV. The values of $\mu$, $\alpha_J$'s, and $E_0$ are taken from Table \ref{['table_quantites']}.