Hall conductivity as topological invariant in phase space
arXiv:1910.04730 · doi:10.1088/1402-4896/ab7ce4
Abstract
It is well known that the quantum Hall conductivity in the presence of constant magnetic field is expressed through the topological TKNN invariant. The same invariant is responsible for the intrinsic anomalous quantum Hall effect (AQHE), which, in addition, may be represented as one in momentum space composed of the two point Green's functions. We propose the generalization of this expression to the QHE in the presence of non-uniform magnetic field. The proposed expression is the topological invariant in phase space composed of the Weyl symbols of the two-point Green's function. It is applicable to a wide range of non-uniform tight-binding models, including the interacting ones.
arXiv commentLatex, 11 pages, proceedings of ICNFP2019, misprints corrected. arXiv admin note: text overlap with arXiv:1905.11097
References in corpus (30)
- Topological Insulators
- Topological insulators and superconductors
- Topological Field Theory of Time-Reversal Invariant Insulators
- Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
- A Method for Simulating Chiral Fermions on the Lattice
- The Chiral Magnetic Effect and Anomaly-Induced Transport
- Anomalous Axion Interactions and Topological Currents in Dense Matter
- Single particle Green's functions and interacting topological insulators
- Stability of Fermi Surfaces and K-Theory
- Bulk-boundary correspondence of topological insulators from their Green's functions
- Quantization Methods: A Guide for Physicists and Analysts
- Quantum phase transitions from topology in momentum space
- Quark Wigner Distributions and Orbital Angular Momentum
- Schwinger pair production in space- and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory
- Quantum Mechanics in Phase Space
- Chern-Simons Currents and Chiral Fermions on the Lattice
- Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
- Four-dimensional graphene and chiral fermions
- Absence of equilibrium chiral magnetic effect
- HBT Correlators -- Current Formalism vs. Wigner Function Formulation
- Spacetime as a topological insulator: Mechanism for the origin of the fermion generations
- Topological invariants for Standard Model: from semi-metal to topological insulator
- Wigner Functions for the Landau Problem in Noncommutative Spaces
- Anomalous Transport Due to the Conformal Anomaly
- Wigner transformation, momentum space topology, and anomalous transport
- Chiral Separation Effect in lattice regularization
- Notes on topological insulators
- Hall conductivity as the topological invariant in phase space in the presence of interactions and non-uniform magnetic field
- Scale Magnetic Effect in Quantum Electrodynamics and the Wigner-Weyl Formalism
- A Note on Bloch theorem