Optical absorption in quantum dots: Coupling to longitudinal optical phonons treated exactly

TL;DR

This paper provides an exact theoretical analysis of optical absorption in quantum dots considering excitonic effects and coupling to longitudinal optical phonons, highlighting the importance of phonon dispersion assumptions.

Contribution

It introduces an exact solution method for modeling phonon-electron coupling in quantum dots with finite levels, improving accuracy over common approximations.

Findings

Exact solution for phonon-electron coupling in quantum dots

Comparison shows approximation overestimates phonon effects

Numerical results for CdSe quantum dots with specific energy levels

Abstract

Optical transitions in a semiconductor quantum dot are theoretically investigated, with emphasis on the coupling to longitudinal optical phonons, and including excitonic effects. When limiting to a finite number of $m$ electron and $n$ hole levels in the dot, the model can be solved exactly within numerical accuracy. Crucial for this to work is the absence of dispersion of the phonons. A suitable orthogonalization procedure leaves only $m(m+1)/2+n(n+1)/2-2$ phonon modes to be coupled to the electronic system. We calculate the linear optical polarization following a delta pulse excitation, and by a subsequent Fourier transformation the resulting optical absorption. This strict result is compared with a frequently used approximation modeling the absorption as a convolution between spectral functions of electron and hole, which tends to overestimate the effect of the phonon coupling. Numerical results are given for two electron and three hole states in a quantum dot made from the polar material CdSe. Parameter values are chosen such that a quantum dot with a resonant sublevel distance can be compared with a nonresonant one.