Pairwise annihilation of Weyl nodes induced by magnetic fields in the Hofstadter regime

Abstract

Weyl semimetal, which does not require any symmetry except translation for protection, is a robust gapless state of quantum matters in three dimensions. When translation symmetry is preserved, the only way to destroy a Weyl semimetal state is to bring two Weyl nodes of opposite chirality close to each other to annihilate pairwise. An external magnetic field can destroy a pair of Weyl nodes (which are separated by a momentum space distance $2k_0$) of opposite chirality, when the magnetic length $l_B$ becomes close to or smaller than the inverse separation $1/2k_0$. In this work, we investigate pairwise annihilation of Weyl nodes induced by external magnetic field which ranges all the way from small to a very large value in the Hofstadter regime $l_B\sim a$. We show that this pairwise annihilation in a WSM featuring two Weyl nodes leads to the emergence of either a normal insulator or a layered Chern insulator. In the case of a Weyl semimetal with multiple Weyl nodes, the potential for generating a variety of states through external magnetic fields emerges. Our study introduces a straightforward and intuitive representation of the pairwise annihilation process induced by magnetic fields, enabling accurate predictions of the phases that may appear after pairwise annihilation of Weyl nodes.

Updated version after correcting typos

References in corpus (14)

• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological response in Weyl semimetals and the chiral anomaly
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Negative longitudinal magnetoresistance in Dirac and Weyl metals
• Quantum Transport in Topological Semimetals under Magnetic Fields
• Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus
• Ferromagnetic hybrid nodal loop and switchable type-I and type-II Weyl fermions in two-dimension
• Weyl fermions with arbitrary monopole in magnetic fields: Landau levels, longitudinal magnetotransport, and density-wave ordering
• Breakdown of the Chiral Anomaly in Weyl Semimetals in a Strong Magnetic Field
• Planar Hall effect in topological Weyl and nodal line semimetals
• Emergence of Gapped Bulk and Metallic Side Walls in the Zeroth Landau level in Dirac and Weyl semimetals
• Anisotropic three-dimensional quantum Hall effect and magnetotransport in mesoscopic Weyl semimetals
• Time-reversal-broken Weyl semimetal in the Hofstadter regime
• Topological van Hove singularities at phase transitions in Weyl metals

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• Breakdown of chiral anomaly and emergent phases in Weyl semimetals under orbital magnetic fields