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

Abstract

We study Landau levels (LLs) of Weyl semimetal (WSM) with two adjacent Weyl nodes. We consider different orientations $η=\angle(\mathbf{B},\mathbf{k}_0)$ 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 $η$ 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 $B_c \propto Φ_0k_0^2/\ln(k_0l_E)$ for large $k_0l_E$, where $l_E=\sqrt{\hbar v/|e|E}$ with $E$ for built in electric field and $Φ_0$ for magnetic flux quantum.