Microscopic derivation of Frenkel excitons in second quantization

TL;DR

This paper derives the microscopic Hamiltonian for Frenkel excitons from the fundamental electron-lattice interactions, emphasizing their atomic basis and composite nature, to facilitate future many-body studies.

Contribution

It introduces a new grouping of terms in the Hamiltonian to derive Frenkel excitons in second quantization, highlighting their atomic basis and non-bosonic commutation relations.

Findings

Derived Frenkel exciton creation operators.

Established commutation relations highlighting their composite nature.

Provided a framework for future many-body effects analysis.

Abstract

Starting from the microscopic hamiltonian describing free electrons in a periodic lattice, we derive the hamiltonian appropriate to Frenkel excitons. This is done through a grouping of terms different from the one leading to Wannier excitons. This grouping makes appearing the atomic states as a relevant basis to describe Frenkel excitons in the second quantization. Using them, we derive the Frenkel exciton creation operators as well as the commutators which rule these operators and which make the Frenkel excitons differing from elementary bosons. The main goal of the present paper is to provide the necessary grounds for future works on Frenkel exciton many-body effects, with the composite nature of these particles treated exactly through a procedure similar to the one we have recently developed for Wannier excitons.