SciPost Physics Core

SciPost Phys. Core 5, 014 (2022) · published 16 March 2022

• doi: 10.21468/SciPostPhysCore.5.1.014
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

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

• Zhang et al., Two types of three-dimensional quantum Hall effects in multilayer WTe2
  Phys. Rev. B 107, 245410 (2023) [Crossref]
• Li et al., Planar Hall effect in topological Weyl and nodal-line semimetals
  Phys. Rev. B 108, 085120 (2023) [Crossref]
• Marques et al., Kaleidoscopes of Hofstadter butterflies and Aharonov-Bohm caging from 2n -root topology in decorated square lattices
  Phys. Rev. Research 5, 023110 (2023) [Crossref]
• Abdulla, Pairwise annihilation of Weyl nodes induced by magnetic fields in the Hofstadter regime
  Phys. Rev. B 109, 155142 (2024) [Crossref]
• Xiong et al., Understanding the three-dimensional quantum Hall effect in generic multi-Weyl semimetals
  Phys. Rev. B 106, 045424 (2022) [Crossref]
• Herzog-Arbeitman et al., Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
  Phys. Rev. Lett. 130, 236601 (2023) [Crossref]