Fundamentals of Electron-Photon Interaction in Nanostructures

TL;DR

This paper reviews the fundamental equations governing electron-photon interactions in nanostructures, building on bulk crystal theory, and discusses optical phenomena, quantum optics, and the importance of envelope and Wannier functions.

Contribution

It provides a comprehensive derivation of the fundamental equations for electron-photon interactions in nanostructures, integrating bulk crystal theory with nanostructure specifics.

Findings

Highlights the importance of envelope and Wannier functions in optical phenomena

Extends bulk crystal theory to nanostructures for electron-photon interactions

Briefly discusses quantum optics in nanostructures

Abstract

We describe the fundamental equations for description of electron-photon interactions in insulating nanostructures. Since the theory for the nanostructures are based on the theory for the bulk crystals, we shall describe elements of the theory for the bulk crystals \cite{knox}-\cite{b2} in the first three subsections. It is important in discussions on optical phenomena that both the envelope function and the Wannier functions (or, equivalently, cell-periodic parts of the Bloch functions) should be taken into account. The theory for the nanostructure is discussed in the fourth subsection. In the final subsection, we briefly mention quantum optics in nanostructures.