2003/09/30 by Ivo Souza, Jorge Íñiguez, Jorge Iniguez +1 · 1 citation
Chemistry · Physics and Astronomy · #Acoustics #Advanced Chemical Physics Studies #Berry #Biology #Botany #Chemistry #Condensed matter physics #Dynamics (music) #Electric field #Geometric phase #Physics #Polarization (electrochemistry) #Quantum and electron transport phenomena #Quantum mechanics #Topological Materials and Phenomena #cond-mat.mtrl-sci
paper · pdf · doi:10.1103/physrevb.69.085106
Significant changes in the section containing the numerical results
arxiv created 2003/11/26 · openalex publication_date 2004/02/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the flow of polarization current J=dP/dt produced by a homogeneous electric field \mathscE(t) or by rapidly varying some other parameter in the Hamiltonian of a solid. For an initially insulating system and a collisionless time evolution, the dynamic polarization P(t) is given by a nonadiabatic version of the King-Smith--Vanderbilt geometric-phase formula. This leads to a computationally convenient form for the Schr"odinger equation where the electric field is described by a linear scalar potential handled on a discrete mesh in reciprocal space. Stationary solutions in sufficiently weak static fields are local minima of the energy functional of Nunes and Gonze. Such solutions only exist below a critical field that depends inversely on the density of k points. For higher fields they become long-lived resonances, which can be accessed dynamically by gradually increasing \mathscE. As an illustration the dielectric function in the presence of a dc bias field is computed for a tight-binding model from the polarization response to a step-function discontinuity in \mathscE(t), displaying the Franz-Keldysh effect.