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.

arXiv commentUpdated version after correcting typos

References in corpus (44)

• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Weyl Semimetal in a Topological Insulator Multilayer
• Experimental discovery of Weyl semimetal TaAs
• Topological nodal semimetals
• Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
• Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals
• Kwant: a software package for quantum transport
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Experimental observation of Weyl points
• Observation of Weyl nodes in TaAs
• Discovery of a Weyl Fermion semimetal state in NbAs
• Topological response in Weyl semimetals and the chiral anomaly
• Quantum Hall effects in a Weyl Semi-Metal: possible application in pyrochlore Iridates
• Dirac Semimetals in Two Dimensions
• Quantum Oscillations from Surface Fermi-Arcs in Weyl and Dirac Semi-Metals
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Transport evidence for Fermi-arc mediated chirality transfer in the Dirac semimetal Cd${}_3$As${}_2$
• Chiral anomaly as origin of planar Hall effect in Weyl semimetals
• Adler-Bell-Jackiw anomaly in Weyl semi-metals: Application to Pyrochlore Iridates
• Negative longitudinal magnetoresistance in Dirac and Weyl metals
• 3D quantum Hall effect of Fermi arcs in topological semimetals
• Magnetic-field-induced relativistic properties in type-I and type-II Weyl semimetals
• Two-dimensional Weyl Half Semimetal and Tunable Quantum Anomalous Hall Effect in Monolayer PtCl${}_3$
• Chiral anomaly, dimensional reduction, and magnetoresistivity of Weyl and Dirac semimetals
• Quantum Transport in Topological Semimetals under Magnetic Fields
• Giant anisotropic magnetoresistance and planar Hall effect in the Dirac semimetal Cd3As2
• Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus
• Linear magneto-chiral transport in tilted type-I and type-II Weyl Semimetals
• Magnetic tunneling induced Weyl node annihilation in TaP
• Ferromagnetic hybrid nodal loop and switchable type-I and type-II Weyl fermions in two-dimension
• Quantum oscillations from generic surface Fermi arcs and bulk chiral modes in Weyl semimetals
• Quantum limit transport and destruction of the Weyl nodes in TaAs
• 3D Quantum Hall Effect Manipulated by Chiral Landau Levels in Weyl Semimetals
• 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
• Two-dimensional Dirac Semimetals without Inversion Symmetry
• 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
• Three-dimensional quantum Hall effect and magnetothermoelectric properties in Weyl semimetals
• Chiral anomalies induced transport in Weyl semimetals in quantizing magnetic field
• 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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