Time-reversal-broken Weyl semimetal in the Hofstadter regime

Abstract

We study the phase diagram for a lattice model of a time-reversal-broken three-dimensional Weyl semimetal (WSM) in an orbital magnetic field $B$ with a flux of $p/q$ per unit cell ($0\le p\le q-1$), with minimal crystalline symmetry. We find several interesting phases: (i) WSM phases with $2q$, $4q$, $6q$, and $8q$ Weyl nodes and corresponding surface Fermi arcs, (ii) a layered Chern insulating (LCI) phase, gapped in the bulk, but with gapless surface states, (iii) a phase in which some bulk bands are gapless with Weyl nodes, coexisting with others that are gapped but topologically nontrivial, adiabatically connected to an LCI phase, (iv) a new gapped trivially insulating phase (I${}^{\prime }$) with (non-topological) counter-propagating surface states, which could be gapped out in the absence of crystal symmetries. Importantly, we are able to obtain the phase boundaries analytically for all $p,q$. Analyzing the gaps for $p=1$ and very large $q$ enables us to smoothly take the zero-field limit, even though the phase diagrams look ostensibly very different for $q=1,B=0$, and $q\to \infty ,B\to 0$.

arXiv comment31 pages, 13 figures

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• Two Types of 3D Quantum Hall Effects in Multilayer WTe${}_2$
• Pairwise annihilation of Weyl nodes induced by magnetic fields in the Hofstadter regime
• Quantum description of Fermi arcs in Weyl semimetals in a magnetic field
• Magneto tunnel conductance across twisted Weyl semimetal junctions
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