Time-reversal-broken Weyl semimetal in the Hofstadter regime

TL;DR

This paper explores the complex phase diagram of a time-reversal-broken Weyl semimetal in a magnetic field, revealing multiple Weyl phases, topological insulators, and trivial insulators, with analytical phase boundary calculations.

Contribution

It provides a comprehensive analytical study of phase boundaries in a Weyl semimetal under magnetic flux, including novel phases and the zero-field limit analysis.

Findings

Identification of multiple Weyl node phases with different node counts.

Discovery of layered Chern insulator and trivial insulating phases.

Analytical determination of phase boundaries for all flux ratios.

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$'$) 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 $q\to\infty, B\to 0$.