Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances

2005/06/01 by Takahiro Fukui, Yasuhiro Hatsugai, Hiroshi Suzuki · 46 citations
Physics and Astronomy · Materials Science · #Topological Materials and Phenomena #Quantum and electron transport phenomena #Chemical and Physical Properties of Materials

paper · doi:10.1143/jpsj.74.1674

Abstract

We present a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone. It provides an efficient method of computing (spin) Hall conductances without specifying gauge-fixing conditions. We demonstrate that it correctly reproduces quantized Hall conductances even on a coarsely discretized Brillouin zone. A gauge-dependent integer-valued field, which plays a key role in the formulation, is evaluated in several gauges. An extension to the non-Abelian Berry connection is also given.

Cited by

• Intrinsic Nonlinear Hall Effect and Gate-Switchable Berry Curvature Sliding in Twisted Bilayer Graphene
• Adiabatic Error Cancellation in Berry Phase Estimation
• Relaxation toward an Ideal Chern Band through Coupling to a Markovian Bath
• Relation between winding numbers and energy dispersions
• Multiple topological phases of magnons induced by Dzyaloshinskii-Moriya and pseudodipolar anisotropic exchange interactions in Kagome ferromagnets
• Weyl Magnons in the Non-Coplanar Antiferromagnet MnTe₂
• Chiral topological superconductivity in twisted bilayer and double bilayer graphene
• Emergent topological properties in spatially modulated sub-wavelength barrier lattices
• Spin-fluctuation-mediated chiral d+id'-wave superconductivity in the α-T₃ lattice with an incipient flat band
• Chiral topological superconductivity in hole-doped Sn/Si(111)
• Topological spin-up triplet excitonic condensation in two-dimensional electron-hole systems
• Floquet Chern Insulators and Radiation-Induced Zero Resistance in Irradiated Graphene
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
• Generation of Ultrahigh Anomalous Hall Conductivities via Optimally Prepared Topological Floquet States
• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory
• Adiabatic charge transport through non-Bloch bands
• Floquet Engineering Magnetism and Superconductivity in the Square-Lattice Hubbard Model
• Gradient flow and Bogomolny bounds for quantum metric actions
• Quantum Entanglement as a Cohomological Obstruction
• Proximity-induced superconductivity and emerging topological phases in altermagnet-based heterostructures
• Topological Charges of Periodically Kicked Molecules
• Topological Vibration Analysis of Elastic Lattices via Bloch Sphere Mapping
• Topological Magnon-Plasmon Hybrids
• Semiconductor Meta-Graphene and Valleytronics
• Continuum theory for topological phase transitions in exciton systems
• Angular momentum of vortex-core Majorana zero modes
• A basis-free, octonionic criterion for Weyl points in solids
• Relaxation and Its Effects on Electronic Structure in Twisted Systems: An Analytical Perspective
• Topological energy pumping in a quasi-periodically driven four-level system
• Tunable multi-magnon Floquet topological edge states
• Emergent topology of flat bands in a twisted bilayer α-T₃ lattice
• When Does a Single Repulsive Dirac Cone Superconduct?
• Quantized nonlinear kink movement through topological boundary state instabilities
• Light induced transitions of valley Chern numbers and flat bands in a non-twisted moire graphene-hexagonal boron nitride superlattice
• Berry Curvature of Low-Energy Excitons in Rhombohedral Graphene
• Counting topological interface modes using simplicial characteristic classes
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Spin-Type Photonic Topological Insulators on a Rhombic Lattice
• Equivariant Parameter Families of Spin Chains: A Discrete MPS Formulation
• Topological Majorana flat bands in the Kitaev model on a Bishamon-kikko lattice
• Majorana edge reconstruction and the ν=5/2 non-Abelian thermal Hall puzzle
• Topological phase diagram of twisted bilayer graphene as a function of the twist angle
• Triplet nodal lines and Chern bands in XCuCl₃ (X= K, Tl)
• Topological two-body interaction obstructing trivial ground states: an indicator of fractional Chern insulators
• Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• Quantized and nonquantized Hall response in topological Hatsugai-Kohmoto systems

Related

• Non-Abelian Stokes theorem and quantized Berry flux
• Topological Current in Fractional Chern Insulators
• Engineering high Chern number insulators
• Chern numbers in two-dimensional systems with spiral boundary conditions
• Nonequilibrium superfield and lattice Weyl transform transport approach to quantum Hall effect