Orbital magnetoelectric coupling in band insulators

Abstract

Magnetoelectric responses are a fundamental characteristic of materials that break time-reversal and inversion symmetries (notably multiferroics) and, remarkably, of "topological insulators" in which those symmetries are unbroken. Previous work has shown how to compute spin and lattice contributions to the magnetoelectric tensor. Here we solve the problem of orbital contributions by computing the frozen-lattice electronic polarization induced by a magnetic field. One part of this response (the "Chern-Simons term") can appear even in time-reversal-symmetric materials and has been previously shown to be quantized in topological insulators. In general materials there are additional orbital contributions to all parts of the magnetoelectric tensor; these vanish in topological insulators by symmetry and also vanish in several simplified models without time-reversal and inversion those magnetoelectric couplings were studied before. We give two derivations of the response formula, one based on a uniform magnetic field and one based on extrapolation of a long-wavelength magnetic field, and discuss some of the consequences of this formula.

13 pages

References in corpus (10)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Dynamical Axion Field in Topological Magnetic Insulators
• Orbital magnetization in periodic insulators
• Towards a microscopic theory of toroidal moments in bulk periodic crystals
• Three-dimensional Topological Insulators on the Pyrochlore Lattice
• Chiral Topological Insulators, Superconductors and other competing orders in three dimensions
• Magnetoelectric response of multiferroic BiFeO3 and related materials
• Relativistic analysis of magnetoelectric crystals: extracting a new 4-dimensional P odd and T odd pseudoscalar from Cr_2 O_3 data
• Ferrotoroidic Moment as a Quantum Geometric Phase

Cited by in corpus (130)

• Topological insulators and superconductors
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Maximally localized Wannier functions: Theory and applications
• Antiferromagnetic topological insulators
• Three-Dimensional Topological Insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
• Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems
• Surface quantized anomalous Hall current and magneto-electric effect in magnetically disordered topological insulators
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Twisted equivariant matter
• Axion Electrodynamics in Topological Materials
• Tunable Casimir repulsion with three dimensional topological insulators
• Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals
• Topological magneto-electric effects in thin films of topological insulators
• Theory of orbital magnetoelectric response
• Topological BF field theory description of topological insulators
• Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized θ-term
• Topological insulators and fractional quantum Hall effect on the ruby lattice
• Theory of Orbital Magnetization in Solids
• Sharp Raman Anomalies and Broken Adiabaticity at a Pressure Induced Transition from Band to Topological Insulator in Sb2Se3
• Chern-Simons orbital magnetoelectric coupling in generic insulators
• Role of Berry phase theory for describing orbital magnetism: From magnetic heterostructures to topological orbital ferromagnets
• Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule
• Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole
• Magneto-optical and Magneto-electric Effects of Topological Insulators in Quantizing Magnetic Fields
• Full magnetoelectric response of Cr2O3 from first principles
• Weyl semimetals with short-range interactions
• Phonon Magnetic Moment from Electronic Topological Magnetization
• Effect of finite temperature and uniaxial anisotropy on the Casimir effect with three-dimensional topological insulators
• The Magnetoelectric Effect in Transition Metal Oxides: Insights and the Rational Design of New Materials from First Principles
• Exactly soluble models for fractional topological insulators in 2 and 3 dimensions
• Theory of Orbital Magnetic Quadrupole Moment and Nonlinear Anomalous Thermoelectric Transport
• Microscopic Theory of Spin Toroidization in Periodic Crystals
• Photoinduced quantum spin and valley Hall effects and orbital magnetization in monolayer MoS2
• Noncommutative geometry for three-dimensional topological insulators
• Virtual Topological Insulators with Real Quantized Physics
• First-principles theory of spatial dispersion: Dynamical quadrupoles and flexoelectricity
• Current-density implementation for calculating flexoelectric coefficients
• Berry phase and Anomalous Hall Effect in a Three-orbital Tight-binding Hamiltonian
• Chiral Magnetic Effect and Anomalous Hall Effect in Antiferromagnetic Insulators with Spin-Orbit Coupling
• Band theory of spatial dispersion in magnetoelectrics
• Multiple magnetic topological phases in bulk van der Waals crystal MnSb4Te7
• Surface theorem for the Chern-Simons axion coupling
• Adiabatically Induced Orbital Magnetization
• Unified Formalism for calculating Polarization, Magnetization, and more in a Periodic Insulator
• Prototypical topological orbital ferromagnet $\gamma$-FeMn
• Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface
• Multicellularity of delicate topological insulators
• Thermoelectric Generation of Orbital Magnetization in Metals
• Theory of orbital magnetic quadrupole moment and magnetoelectric susceptibility
• Theory of optical axion electrodynamics and application to the Kerr effect in topological antiferromagnets
• The non-commutative n-th Chern number
• Magnetoelectric effect and orbital magnetization in skyrmion crystals: Detection and characterization of skyrmions
• Entanglement polarization for the topological quadrupole phase
• Dynamical piezoelectric and magnetopiezoelectric effects in polar metals from Berry phases and orbital moments
• Strain induced ${\mathbb{Z}}_2$ topological insulating state of $\beta$-As${}_2$Te${}_3$
• Teleportation of Berry curvature on the surface of a Hopf insulator
• Density-operator theory of orbital magnetic susceptibility in periodic insulators
• Unified role of Green's function poles and zeros in topological insulators
• Axion Insulator State in a Ferromagnet/Topological Insulator/Antiferromagnet Heterostructure
• Smooth gauge and Wannier functions for topological band structures in arbitrary dimensions
• Gate-tunable phonon magnetic moment in bilayer graphene
• Topological Insulators and Quantum Spin Liquids
• Geometric orbital magnetization in adiabatic processes
• Geometric and nongeometric contributions to the surface anomalous Hall conductivity
• $N$-band Hopf insulator
• Topological Insulator and the $\theta$-vacuum in a system without boundaries
• Abinit 2025: New Capabilities for the Predictive Modeling of Solids and Nanomaterials
• Fluctuation-induced magnetization dynamics and criticality at the interface of a topological insulator with a magnetically ordered layer
• Theory of inversion-${\mathbb{Z}}_4$ protected topological chiral hinge states and its applications to layered antiferromagnets
• Electrically Controlled Anomalous Hall Effect and Orbital Magnetization in Topological Magnet MnBi2Te4
• Theory of orbital magnetization in disordered systems
• Microscopic Theory of the Refractive Index
• Axionic Antiferromagnetic Insulator Phase in a Correlated and Spin-Orbit Coupled System
• Topological Invariants and Ground-State Wave Functions of Topological Insulators on a Torus
• Metric-wave approach to flexoelectricity within density-functional perturbation theory
• Vacuum anomalous Hall effect in gyrotropic cavity
• Quantum field theory of topological spin dynamics
• Gauge-discontinuity contributions to Chern-Simons orbital magnetoelectric coupling
• Functional Approach to Electrodynamics of Media
• Rotational $g$ factors and Lorentz forces of molecules and solids from density-functional perturbation theory
• A Non-Commutative Formula for the Isotropic Magneto-Electric Response
• Bosonic symmetry protected topological phases with reflection symmetry
• Quantized surface magnetism and higher-order topology: Application to the Hopf insulator
• The multi-state geometry of shift current and polarization
• Effective Quantum Theories for Transport in Inhomogeneous Systems with Non-trivial Band Structure
• Time-reversal-symmetric topological magnetoelectric effect in three-dimensional topological insulators
• Novel magneto-electric multiferroics from first-principles
• Magnetoelectric effect in topological insulator films beyond the linear response regime
• Cancellation of quantum anomalies and bosonization of three-dimensional time-reversal symmetric topological insulators
• From magnetoelectric response to optical activity
• Kinetic magnetoelectric effect in topological insulators
• A Comment On Berry Connections
• Kerr, Faraday, and Magnetoelectric Effects in MnBi${}_2$Te${}_4$ Thin Films
• Magnetoelectric polarizability: A microscopic perspective
• Dynamical correlation enhanced orbital magnetization in VI${}_3$
• Magnetoelectric polarizability and optical activity: spin and frequency dependence
• Collinear Orbital Antiferromagnetic Order and Magnetoelectricity in Quasi-2D Itinerant-Electron Paramagnets, Ferromagnets and Antiferromagnets
• Bulk photospin effect: Calculation of electric spin susceptibility to second order in an electric field
• Lyddane-Sachs-Teller relationship in linear magnetoelectrics
• When does Magnetization Depend on the Boundary?
• Magnetoelectric effect in bilayer graphene controlled by valley-isospin density
• Topological Magnetoelectric Effect: Nonlinear Time-Reversal-Symmetric Response, Witten Effect, and Half-Integer Quantum Hall Effect
• Dynamics of a Rydberg hydrogen atom near a topologically insulating surface
• Electric Polarization in Inhomogeneous Crystals
• Theory of Charge and Heat Polarizations with the Keldysh Formalism
• Polarization and orbital magnetization in Chern insulators: A microscopic perspective
• Electromagnetic coupling of spins and pseudospins in bilayer graphene
• In-plane magnetoelectric response in bilayer graphene
• Orbital magneto-optical response of periodic insulators from first principles
• Quantized electromagnetic response of three-dimensional chiral topological insulators
• Orbital magnetoelectric coupling at finite electric field
• Electric polarization and magnetization in metals
• Zone-Center Dynamical Matrix in Magnetoelectrics
• Capacitive scheme to detect the topological magnetoelectric effect
• Linear magnetoelectricity in the Zintl phase pnictides (Ba, Ca, Sr)${\mathrm{Mn}}_2{(\mathrm{P},\mathrm{As},\mathrm{Sb})}_2$ from first principles calculations
• Interaction Correction to the Magneto-Electric Polarizability of $Z_2$ Topological Insulators
• Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect
• Topological magnetoelectric pump in three dimensions
• Orbital Magnetization under an Electric Field and Orbital Magnetoelectric Polarizabilty for a Bilayer Chern System
• Bulk-Boundary Correspondence for Topological Insulators with Quantized Magneto-Electric Effect
• Anti-commutative dynamical magneto-electric response in certain solid state materials
• Correlation Effects in Orbital Magnetism
• Electric Field-Induced Skyrmion Crystals via Charged Monopoles in Insulating Helimagets
• Microscopic Theory of the Magnetic Susceptibility of Insulators
• Longitudinal magnetoconductivity and magnetodielectric effect in bilayer graphene
• Theta electromagnetism in quantum spin ice: Microscopic analysis of improper symmetries
• Synthetic magnetoelectric response of lattice bosonic insulators
• Exact expression for the Berry connection in the projection gauge