Electric Polarization in Inhomogeneous Crystals
arXiv:2009.09306 · doi:10.1103/PhysRevB.104.144203
Abstract
We derive the charge density up to second order in spatial gradient in inhomogeneous crystals using the semiclassical coarse graining procedure based on the wave packet method. It can be recast as divergence of polarization, whose first-order contribution consists of three parts, a perturbative correction to the original Berry connection expression, a topological part that can be written as an integral of the Chern-Simons 3-form, and a previously-unknown, quadrupole-like contribution. The topological part can be related to the quantized fractional charge carried by a vortex in two dimensional systems. We then generalize our results to the multi-band case and show that the quadrupole-like contribution plays an important role, as it makes the total polarization gauge-independent. Finally, we verify our theory in several model systems.
arXiv comment15 pages, 3 figures
References in corpus (45)
- Berry Phase Effects on Electronic Properties
- Spontaneous polarization and piezoelectric constants of III-V nitrides
- Spin current and magneto-electric effect in non-collinear magnets
- Quantized Electric Multipole Insulators
- First-principles study of spontaneous polarization in multiferroic BiFeO
- Ferroelectricity in spiral magnets
- Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
- Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
- Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
- The virtual crystal approximation revisited: Application to dielectric and piezoelectric properties of perovskites
- Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3
- Topological Defects and Gapless Modes in Insulators and Superconductors
- Magnetically driven ferroelectric order in NiVO
- Berry phase effect in anomalous thermoelectric transport
- Berry phase correction to electron density of states in solids
- Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
- Spin-polarization coupling in multiferroic transition-metal oxides
- First-principles theory and calculation of flexoelectricity
- Semiclassical theory of spin transport in spin-orbit coupled systems
- Direct transition from a disordered to a multiferroic phase on a triangular lattice
- Bond electronic polarization induced by spin
- Orbital magnetoelectric coupling in band insulators
- First-principles study of improper ferroelectricity in TbMnO3
- Towards a bulk theory of flexoelectricity
- Theory of orbital magnetoelectric response
- First-principles theory of frozen-ion flexoelectricity
- General Theory for the Ferroelectric Polarization Induced by Spin-Spiral Order
- Erratum: Landau Analysis of the Symmetry of the Magnetic Structure and Magnetoelectric Interaction in Multiferroics [Phys. Rev. B 76, 05447 (2007)]
- Flexoelectricity from density-functional perturbation theory
- Topological Invariants of Metals and Related Physical Effects
- Chern-Simons orbital magnetoelectric coupling in generic insulators
- Origin of Negative Longitudinal Piezoelectric Effect
- Microscopic theory of temperature-dependent magnetoelectric effect in Cr2O3
- Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole
- Full magnetoelectric response of Cr2O3 from first principles
- Semi-classical wave packet dynamics in non-uniform electric fields
- The importance of the electronic contribution to linear magnetoelectricity
- Theory of Orbital Magnetic Quadrupole Moment and Nonlinear Anomalous Thermoelectric Transport
- Irrational vs. rational charge and statistics in two-dimensional quantum systems
- Fractionalization in a square-lattice model with time-reversal symmetry
- Intrinsic Magnetoconductivity of Non-magnetic Metals
- Unified Model of Ferroelectricity Induced by Spin Order
- Fractional charge bound to a vortex in two dimensional topological crystalline insulators
- Dependence of electronic polarization on octahedral rotations in TbMnO3 from first principles
- Metric-wave approach to flexoelectricity within density-functional perturbation theory