Nonlinear magnetotransport in a two-dimensional system with merging Dirac points

TL;DR

This paper analyzes the nonlinear magnetotransport properties of a two-dimensional semi-Dirac system with merging Dirac points, revealing how band geometry and Fermi energy influence conductivities and current orientations under magnetic fields.

Contribution

It provides exact analytical expressions for nonlinear conductivities and explores their dependence on Fermi energy, gap parameter, and magnetic field, highlighting novel current behaviors in semi-Dirac systems.

Findings

Nonlinear conductivities depend on Fermi energy and gap parameter.

Fermi surface topology change causes kink in conductivities.

NL dc current orientation varies with Fermi energy and light polarization.

Abstract

We study the linear, second-order nonlinear (NL) current and voltage responses of a two-dimensional gapped semi-Dirac system with merging Dirac nodes along the $x$ direction under the influence of a weak magnetic field ($B$), using the semiclassical Boltzmann formalism. We investigate the effect of band geometric quantities like Berry curvature and orbital magnetic moment in the responses up to linear order in $B$. We derive exact analytical expressions of the linear magnetoconductivities, second-harmonic NL anomalous Hall (NAH), and anomalous velocity and Lorentz force induced (NAL) conductivities, unveiling their dependence on Fermi energy and a gap parameter $\delta_0$. For $\delta_0 > 0$, the Fermi surface topology changes at a particular Fermi energy, which is reflected in the nature of conductivities through a kink. The ratio of NAL and NAH conductivities is found to be independent of $\delta_0$ and inversely related to Fermi energy. The NL dc current exhibits distinct orientations depending on the Fermi energy, magnetic field, polarization of the electromagnetic wave. In the presence of magnetic field, the NL dc current vector can be rotated through large angles on variation of Fermi energy. For high Fermi energies, the NL dc current is directed nearly along the $y$-axis for $x$-polarized and low-frequency circularly polarized light, whereas it aligns close to $x$-axis for high-frequency circularly polarized light. These orientations of the NL dc current are predominantly governed by the mirror symmetry of the system along the $x$ direction. Additionally, we also study the NL voltage responses of the system by applying current along the $x$ and $y$ directions. The system exhibits asymmetry in the $B$-dependencies of the NL resistivities, which may serve as an experimentally relevant signature for band geometric quantities and merging Dirac nodes in such systems.