Electric polarization in correlated insulators

Abstract

We derive a formula for the electric polarization of interacting insulators, expressed in terms of the full Green's and vertex functions. We exemplify this method in the half-filled ionic Hubbard model treated within dynamical mean field theory (DMFT). The electric polarization of a correlated band insulator is determined by the interplay of ionicity and covalency, and both quantities are renormalized by the electron-electron interactions. We introduce quasiparticle approximation to the exact equation for the polarization, and compare the results of this approximation with those of the exact DMFT formulation and of static mean field theories such as the LDA+ U. The latter overestimates the electronic contribution to the electric polarization when the quasiparticle weight of the active bands is very small.

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• End states in a 1-D topological Kondo insulator
• Bulk angular momentum and Hall viscosity in chiral superconductors
• Many-Body Invariants for Chern and Chiral Hinge Insulators
• Correlation-driven electronic multiferroicity in (TMTTF)${}_2$-$X$ organic crystals
• Microscopic polarization and magnetization fields in extended systems
• Orbital magnetization of correlated electrons with arbitrary band topology
• Hall and Faraday effects in interacting multi-band systems with arbitrary band topology and spin-orbit coupling
• Electric polarization of Sr${}_{0.5}$Ba${}_{0.5}$MnO${}_3$: a multiferroic Mott insulator
• Orbital magnetization and anomalous Hall effect in interacting Weyl semimetals
• Cavity-induced charge transfer in periodic systems: length-gauge formalism
• Statistical mechanics approach to the electric polarization and dielectric constant of band insulators
• Theory of Charge and Heat Polarizations with the Keldysh Formalism
• Effects of correlations on honeycomb lattice in ionic-Hubbard Model
• Non-linear response in extended systems: a real-time approach