Geometric theory of the natural optical activity in noncentrosymmetric metals

TL;DR

This dissertation explores the geometric and topological origins of natural optical activity and the chiral magnetic effect in noncentrosymmetric metals, providing theoretical calculations and experimental implications for optical measurements.

Contribution

It introduces a unified semiclassical and Kubo formalism to calculate optical conductivity dispersion and distinguishes topological and geometric contributions to the chiral magnetic effect.

Findings

Static and dynamic chiral magnetic effects have different origins.

Faraday rotation can measure the dynamic chiral magnetic effect.

Macroscopic inhomogeneities affect optical polarization measurements.

Abstract

This is a PhD dissertation. Ignited by the chiral anomaly of recently discovered Weyl (semi-)metals, we study the chiral magnetic effect and the natural optical activity of noncentrosymmetric metals. Both phenomena are related to the linear-in-$\mathbf{q}$ spatial dispersion of the optical conductivity tensor, and can be calculated within the formalism of the semiclassical kinetic equation. Therefore, we calculate the dispersion of optical conductivity up to the linear order of the wave vector, in the low frequency regime, with both the semiclassical Boltzmann equation and the Kubo formula. The two different methods of calculation provide us the same result. In this result, the static and dynamic chiral magnetic effects are revealed to have different origin: one comes from topology, related to Berry monopoles, and the other has a geometric origin, which is determined by the orbital magnetic moment. The Faraday rotation of the polarization of light transmitted through a slab of the sample provides us the most direct way to measure the magnitude of dynamic chiral magnetic effect. We develop an effective medium theory for electromagnetic wave propagating through gapless nonuniform systems, to calculate macroscopic sample inhomogeneities induced corrections to the chiral magnetic conductivity. We show that, in metals with low carrier density, the way in which macroscopic fluctuations of the local conductivity affect the frequency dependent of the measured optical polarization rotation angle: by creating a sharp feature near the plasma edge, which can be detected by experiments. Then we narrow down our research a bit further to the current induced magnetization.