Year: 2001
Type: article
Abstract: A perturbation theory of the static response of insulating crystals to homogeneous electric fields that combines the modern theory of polarization (MTP) with the variation-perturbation framework is developed at unrestricted order of perturbation. First, we address conceptual issues related to the definition of such a perturbative approach. In particular, in our definition of an electric-field-dependent energy functional for periodic systems, the position operator appearing in the perturbation term is replaced by a Berry-phase expression, along the lines of the MTP. Moreover, due to the unbound nature of the perturbation, a regularization of the Berry-phase expression for the polarization is needed in order to define a numerically stable variational procedure. Regularization is achieved by means of discretization, which can be performed either before or after the perturbation expansion. We compare the two possibilities and apply them to a model tight-binding Hamiltonian. Lowest-order as well as generic formulas are presented for the derivatives of the total energy, the normalization condition, the eigenequation, and the Lagrange parameters.
Authors: R. W. Nunes, Xavier Gonze
Institutions: Universidade Federal de Minas Gerais, UCLouvain, KU Leuven
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2036208941