Theory of Electronic Response to Electromagnetic Fields in Crystalline Solids

In a classical theory of light-matter interactions, the introduction of macroscopic polarization and magnetization fields, and free charge and current densities, provides physical insight into the distribution and the dynamics of the charges that constitute a material medium. Here we consider a semi-classical theory of such interactions in crystalline materials and introduce microscopic polarization and magnetization fields, and free charge and current densities, from which the macroscopic analogues can be found. We do so by identifying "sites" in an extended system with respect to which spatially localized portions of the charge and current densities can be associated, and define "site" polarization and magnetization fields from them. The sum of these "site quantities" are taken to constitute the microscopic polarization and magnetization fields. The identification of such site quantities employs a set of spatially localized basis functions, which additionally allow the identification of free charge and current densities that are here associated with charge movement from site to site. In the beginning chapters of this thesis we present the formalism and consider various limiting cases. We consider the "molecular crystal limit" of the more general expressions and recover the expected results. We also consider the linear response of an insulator in the "long-wavelength limit", and find the well-known electrical conductivity tensor. Finally, we consider the macroscopic ground state polarization and magnetization of an "ordinary" insulator, and find agreement with the expressions of the "modern theories of polarization and magnetization". In the chapters that follow we implement this formalism to study various phenomena in a class of insulators, including the orbital magnetoelectric effect and optical activity. The linear response of such systems is captured by that of the microscopic polarization and magnetization fields; from the multipole moments of the macroscopic analogues of these fields, we identify the relevant susceptibility tensors. At various levels of approximation, we show that these general tensors reduce to known results. We also consider the optical response of metallic systems, for which the induced free charge and current densities play a nontrivial role. We derive the usual conductivity tensor, which involves both "Drude" and "anomalous Hall" contributions.

Department dc:contributor.department

Physics

Year dc:date.issued

2021

Author dc:creator

• Mahon, Perry

Advisor dc:contributor.advisor

• Sipe, John E

• Condensed matter physics
• Optical properties of solids
• Theoretical physics

Handle dc:identifier.uri

http://hdl.handle.net/1807/108821

OAI identifier oai:identifier

oai:utoronto.scholaris.ca:1807/108821