We consider the flow of polarization current J=dP/dt produced by a homogeneous electric field ℰ(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 Schrödinger 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 ℰ. 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 ℰ(t), displaying the Franz-Keldysh effect.
|Original language||English (US)|
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - 2004|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics