Landau levels with magnetic tunnelling in Weyl semimetal and magnetoconductance of ballistic $p$-$n$ junction

TL;DR

This paper investigates how magnetic tunneling affects Landau levels and magnetoconductance in Weyl semimetals with two Weyl nodes, revealing non-monotonic conductance behavior influenced by magnetic field orientation and tunneling effects.

Contribution

It introduces a detailed analysis of Landau levels with magnetic tunneling in Weyl semimetals with two nodes, highlighting the impact on magnetoconductance and spectrum rearrangement based on magnetic field orientation.

Findings

Magnetic tunneling induces a gap in the zeroth Landau level.

The magnetoconductance $G(B)$ exhibits non-monotonic behavior with a maximum at a critical magnetic field.

The spectrum and conductance depend on the angle between magnetic field and Weyl node separation vector.

Abstract

We study Landau levels (LLs) of Weyl semimetal (WSM) with two adjacent Weyl nodes. We consider different orientations $\eta=\angle(\mathbf{B},\mathbf{k}_0)$ of magnetic field $\mathbf{B}$ with respect to $\mathbf{k}_0$, the vector of Weyl nodes splitting. Magnetic field facilitates the tunneling between the nodes giving rise to a gap in the transverse energy of the zeroth LL. We show how the spectrum is rearranged at different $\eta$ and how this manifests itself in the change of behavior of differential magnetoconductance $dG(B)/dB$ of a ballistic $p$-$n$ junction. Unlike the single-cone model where Klein tunneling reveals itself in positive $dG(B)/dB$, in the two-cone case $G(B)$ is non-monotonic with maximum at $B_c \propto \Phi_0k_0^2/\ln(k_0l_E)$ for large $k_0l_E$, where $l_E=\sqrt{\hbar v/|e|E}$ with $E$ for built in electric field and $\Phi_0$ for magnetic flux quantum.