Theory of the fractional quantum Hall effect in Weyl semimetals

Abstract

We develop a hydrodynamic field theory of the three-dimensional fractional quantum Hall effect, which was recently proposed to exist in magnetic Weyl semimetals, when the Weyl nodes are gapped by strong repulsive interactions. This theory takes the form of a BF theory, which contains both one-form and two-form gauge fields, coupling to quasiparticle and loop excitations correspondingly. It may be regarded as a generalization of the Chern-Simons theory of two-dimensional fractional quantum Hall liquids to three dimensions.

8 pages, 3 figures, published version

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• The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios
• Unquantized anomalies in topological semimetals
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• Topological polarization, dual invariants, and surface flat band in crystalline insulators
• Dimensionless physics
• Non-Hermitian higher-Order Weyl semimetal with surface diabolic points
• Time-reversal-broken Weyl semimetal in the Hofstadter regime
• Floquet Exceptional Topological Insulator
• Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime
• Translation symmetry-enriched toric code insulator
• Topological order in interacting semimetals
• Fermionic dualities with axial gauge fields
• Flat Bands in Three-dimensional Lattice Models with Non-trivial Hopf Index
• Dynamical Effects from Anomaly: Modified Electrodynamics in Weyl Semimetal
• Hydrodynamic description of Weyl fermions in condensed state of matter
• Optical Response from Charge-Density Waves in Weyl Semimetals