First-principles calculation of dynamical properties of insulators in finite electric fields and anomalous Hall conductivity of ferromagnets based on Berry phase approach

Abstract

OF THE DISSERTATION First-principles calculation of dynamical properties of insulators in finite electric fields and anomalous Hall conductivity of ferromagnets based on Berry phase approach by Xinjie Wang Dissertation Director: Professor David Vanderbilt We present first-principles methods for calculating two distinct types of physical quantities within the framework of density functional theory: the response properties of an insulator to finite electric fields, and the anomalous Hall conductivity of a ferromagnet. Both of the methods are closely related to the same ingredient, namely the Berry phase, a geometric phase acquired by a quantum system transporting in parameter space. We develop gauge-invariant formulations in which the random phases of Bloch functions produced by numerical subroutines are irrelevant. First, we provide linear-response methods for calculating phonon frequencies, Born effective charge tensors and dielectric tensors for insulators in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded with respect to both small atomic displacements and electric fields within the framework of density-functional perturbation theory. The linear responses of field-polarized Bloch functions to atomic displacements and electric fields are obtained by minimizing the second-order derivatives of the total-energy functional. The