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

2005/03/31 by Takahiro Fukui, Yasuhiro Hatsugai, Hiroshi Suzuki · 1,372 citations
Materials Science · Physics and Astronomy · #Brillouin zone #Chemical and Physical Properties of Materials #Connection (principal bundle) #Discretization #Extension (predicate logic) #Key (lock) #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall #hep-lat

paper · pdf · doi:10.1143/jpsj.74.1674

published in Journal of the Physical Society of Japan 74(6), 1674-1677 (Physical Society of Japan) · 4 pages, 3 figures, to appear in JPSJ

arxiv created 2005/04/06 · openalex publication_date 2005/06/01 · arxiv updated 2014/11/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

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
• Experimental evidence of the topological obstruction in twisted bilayer graphene
• 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
• Two dimensional sub-wavelength topological dark state lattices
• From Fractionalization to Chiral Topological Superconductivity in a Flat Chern Band
• Intra-unit-cell singlet pairing mediated by altermagnetic fluctuations
• Impact of the honeycomb spin-lattice on topological magnons and edge states in ferromagnetic 2D skyrmion crystals
• Direct determination of layer anomalous Hall conductivity using uniaxial Wannier functions
• Spin-dependent transport through edge states in 2D semi-Dirac materials with Rashba spin-orbit coupling and band inversion
• Quantum anomalous Hall effects and emergent \rmSU(2) Hall ferromagnets at fractional filling of helical trilayer graphene
• Time reversal symmetry broken quantum spin hall effect in pseudospin-1 Dirac-Rashba system
• Symmetry-broken magneto-toroidal artificial spin ices: magnetization states and dynamics
• Numerical Block Diagonalization and Linked-Cluster Expansion for Deriving Effective Hamiltonians: Applications to Spin Excitations
• High Chern Number Quantum Anomalous Hall States in Haldane-Graphene Multilayers
• Spin Nernst and thermal Hall effects of topological triplons in quantum dimer magnets on the maple-leaf and star lattices
• Quantum Hall Effect without Chern Bands
• Higher-order Topological Parity Anomaly and Half-integer Hall Effect in High-dimensional Synthetic Lattices
• Coulomb Interaction-Stabilized Isolated Narrow Bands with Chern Numbers C > 1 in Twisted Rhombohedral Trilayer-Bilayer Graphene
• General First-Principles Approach to Crystals in Finite Magnetic Fields
• Exotic topological point and line nodes in the plaquette excitations of a frustrated Heisenberg antiferromagnet on the honeycomb lattice
• Non-Hermitian Haldane-Hubbard model: Effective description of an open system with balanced gain and loss
• Degeneracy and consistency condition for Berry phases: Gap closing under a local gauge twist
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Non-Hermitian band topology in twisted bilayer graphene aligned with hexagonal boron nitride
• Topological classification of gapped spin chains: Quantized Berry phase as a local order parameter
• Creating anomalous Floquet Chern insulators with magnetic quantum walks
• Berry's Phase in the Multimode Peierls States
• Wilson polygons and the topology of zero-dimensional systems
• Linearly Polarized Light-Induced Anomalous Hall Effect and Topological Phase Transitions in an Altermagnetic Topological Insulator
• Dirac-Weyl fermions with arbitrary spin in two-dimensional optical superlattices
• Photonic band structure of two-dimensional atomic lattices
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• Many-Body Chern Numbers of ν = 1/3 and 1/2 States on Various Lattices
• Quantum Spin Hall Effect in Three Dimensional Materials: Lattice Computation of Z2 Topological Invariants and Its Application to Bi and Sb
• Band Structure and topology of a periodically deformed Kitaev honeycomb model
• Paired Parton Trial States for the Superfluid-Fractional Chern Insulator Transition
• A Universal Spin-Orbit-Coupled Hamiltonian Model for Accelerated Quantum Material Discovery
• Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model
• Identifying Topological Invariants of Non-Hermitian Systems via Domain-Adaptive Multimodal Model for Mathematics
• Electronic structure of spontaneously strained graphene on hexagonal boron nitride
• Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations
• Entangling Topological Invariants
• Strain-induced topological phase transition in phosphorene and in phosphorene nanoribbons
• Quantum Hall Effect of Massless Dirac Fermions and Free Fermions in Hofstadter’s Butterfly
• Correlation effects in pyrochlore iridate thin films grown along the [111] direction
• Chiral degeneracies and Fermi-surface Chern numbers in bcc Fe
• Topological identification of a spin-12two-leg ladder with four-spin ring exchange
• Exotic magnetic orderings in the kagome Kondo-lattice model
• Chiral two-dimensional electron gas in a periodic magnetic field: Persistent current and quantized anomalous Hall effect
• Topologically nontrivial Andreev bound states
• Quantum Monte Carlo simulation of topological phase transitions
• Topological quantum pump in serpentine-shaped semiconducting narrow channels
• Topological magnons in ferromagnetic Kitaev-Heisenberg model on CaVO lattice
• A new non-Abelian topological superfluid of cold Fermi gases in anisotropic and spin-dependent optical lattices
• Phase diagram and orbital Chern insulator in twisted double bilayer graphene
• Infrared Topological Plasmons in Graphene
• Moiré flat Chern bands and correlated quantum anomalous Hall states generated by spin-orbit couplings in twisted homobilayer MoS₂
• First-principles study of electric-field-induced topological phase transition in one-bilayer Bi(111)
• Quasicrystalline Analogue of the Haldane Model
• Interplay of local order and topology in the extended Haldane-Hubbard model
• Entanglement modes and topological phase transitions in superconductors
• Synthetic gauge field and pseudospin–orbit interaction in a stacked two-dimensional ring-network lattice
• Photonic realization of a transition to a strongly driven Floquet topological phase
• Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
• Floquet Hofstadter butterfly on the kagome and triangular lattices
• Section Chern number for a three-dimensional photonic crystal and the bulk-edge correspondence
• Measuring Chern numbers in Hofstadter strips
• Topological phase transitions in finite-size periodically driven translationally invariant systems
• Dynamical Topological Transitions in the Massive Schwinger Model with a θ Term
• Berry flux diagonalization: Application to electric polarization
• Deep learning topological invariants of band insulators
• Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop
• Quantized Berry Phases as a Local Order Parameter of a Quantum Liquid
• Flat topological bands and eigenstate criticality in a quasiperiodic insulator
• Multipolar edge states in the anisotropic kagome antiferromagnet
• Topological Meaning of Z2 Numbers in Time Reversal Invariant Systems
• Predicted photoinduced topological phases in organic salt α−(BEDT-TTF)2I3
• Topological phases of lattice bosons with a dynamical gauge field
• Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride
• Effective Theory of Floquet Topological Transitions
• Dynamical competition between quantum Hall and quantum spin Hall effects
• Various topological Mott insulators and topological bulk charge pumping in strongly-interacting boson system in one-dimensional superlattice
• Pressure-Tunable Generalized Wigner Crystal and Fractional Chern Insulator in twisted MoTe₂
• Tri-component-pairing chiral superconductivity on the honeycomb lattice with mixed s- and d-wave symmetries
• Symmetry-protected spinful magnetic Weyl nodal loops and multi-Weyl nodes in 5dn cubic double perovskites (n=1,2)
• Designing Topological High-Order Van Hove Singularities: Twisted Bilayer Kagomé
• How quantum fluctuations freeze a classical liquid and then melt it into a topological one
• Exciton fractional Chern insulators in moiré heterostructures
• Breakdown of Bulk-Radiation Correspondence in Radiative Photonic Lattices
• New scheme for braiding Majorana fermions. [europepmc]
• Direct observation of valley-polarized topological edge states in designer surface plasmon crystals. [europepmc]
• Measurement of the Berry curvature of solids using high-harmonic spectroscopy. [europepmc]
• A silicon-on-insulator slab for topological valley transport. [europepmc]
• Magnonic Floquet Quantum Spin Hall Insulator in Bilayer Collinear Antiferromagnets. [europepmc]
• Topological magnon amplification. [europepmc]
• Non-Hermitian fractional quantum Hall states. [europepmc]
• Realization of Lieb lattice in covalent-organic frameworks with tunable topology and magnetism. [europepmc]
• Valley-polarized domain wall magnons in 2D ferromagnetic bilayers. [europepmc]
• Studying local Berry curvature in 2H-WSe 2 by circular dichroism photoemission utilizing crystal mirror plane. [europepmc]
• Topological features without a lattice in Rashba spin-orbit coupled atoms. [europepmc]
• Anisotropic scaling for 3D topological models. [europepmc]
• Three-dimensional photonic topological insulator without spin-orbit coupling. [europepmc]
• Experimental demonstration of adversarial examples in learning topological phases. [europepmc]
• Universal numerical calculation method for the Berry curvature and Chern numbers of typical topological photonic crystals. [europepmc]
• General framework for E(3)-equivariant neural network representation of density functional theory Hamiltonian. [europepmc]
• Phase of Topological Lattice with Leaky Guided Mode Resonance. [europepmc]
• Second order topology in a band engineered Chern insulator. [europepmc]
• Emergent topological quantum orbits in the charge density wave phase of kagome metal CsV 3 Sb 5 . [europepmc]
• Topological flat bands in a family of multilayer graphene moiré lattices. [europepmc]
• Robust non-Abelian even-denominator fractional Chern insulator in twisted bilayer MoTe 2 . [europepmc]
• Gapped nodal planes and large topological Nernst effect in the chiral lattice antiferromagnet CoNb 3 S 6 . [europepmc]
• Probing the Kitaev honeycomb model on a neutral-atom quantum computer. [europepmc]
• Unconventional superconductivity in the presence of long-range interactions in transition metal dichalcogenide moiré heterobilayers. [europepmc]
• Magnetism and hidden quantum geometry in charge neutral twisted trilayer graphene. [europepmc]

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