Excitonic Bloch equations from first principles

TL;DR

This paper derives excitonic Bloch equations from first principles, providing a rigorous framework for exciton dynamics that avoids overscreening issues present in model Hamiltonian approaches, applicable beyond linear regimes.

Contribution

It introduces a first-principles derivation of excitonic Bloch equations, incorporating an auxiliary exciton concept to eliminate overscreening effects in exciton dynamics modeling.

Findings

Derivation of excitonic Bloch equations from ab initio Hamiltonians.

Identification of overscreening effects in model Hamiltonian approaches.

Prediction of exciton number conservation after external field removal.

Abstract

The ultrafast conversion of coherent excitons into incoherent excitons, as well as the subsequent exciton diffusion and thermalization, are central topics in current scientific research due to their relevance in optoelectronics, photovoltaics and photocatalysis. Current approaches to the exciton dynamics rely on {\em model} Hamiltonians that depend on already screened electron-electron and electron-phonon couplings. In this work, we subject the state-of-the-art methods to scrutiny using the {\em ab initio} Hamiltonian for electrons and phonons. We offer a rigorous and intuitive proof demonstrating that the exciton dynamics governed by model Hamiltonians is affected by an overscreening of the electron-phonon interaction. The introduction of an auxiliary exciton species, termed the irreducible exciton, enables us to formulate a theory free from overscreening and derive the excitonic Bloch equations. These equations describe the time-evolution of coherent, irreducible, and incoherent excitons during and after the optical excitation. They are applicable beyond the linear regime, and predict that the total number of excitons is preserved when the external fields are switched off.