# Quantum plasmons and intraband excitons in doped nanoparticles: Failure of the Tamm-Dancoff approximation and importance of electron-hole attraction

## TL;DR

This study investigates the electronic excitations in doped semiconductor nanoparticles, highlighting the failure of the Tamm-Dancoff approximation and emphasizing the importance of electron-hole attraction for accurate modeling of plasmons and excitons.

## Contribution

It demonstrates the limitations of common single-excitation theories and introduces a schematic model that accurately reproduces numerical and experimental results for doped nanoparticles.

## Key findings

- Time-dependent Hartree-Fock best describes excitation character.
- Excitations transition from confinement to excitonic to plasmonic with increasing electrons.
- Electron-hole attraction and de-excitations are crucial for accurate descriptions.

## Abstract

We use excited-state quantum chemistry techniques to investigate the intraband absorption of doped semiconductor nanoparticles as a function of doping density, nanoparticle radius, and material properties. The excess electrons are modeled as interacting particles confined in a sphere. We compare the predictions of various single-excitation theories, including time-dependent Hartree-Fock, the random-phase approximation, and configuration interaction with single excitations. We find that time-dependent Hartree-Fock most accurately describes the character of the excitation, as compared to equation-of-motion coupled-cluster theory with single and double excitations. The excitation evolves from confinement-dominated, to excitonic, to plasmonic with increasing number of electrons at fixed density, and the threshold number of electrons to produce a plasmon increases with density due to quantum confinement. Exchange integrals (attractive electron-hole interactions) are essential to properly describe excitons, and de-excitations (i.e.~avoidance of the Tamm-Dancoff approximation) are essential to properly describe plasmons. We propose a schematic model whose analytic solutions closely reproduce our numerical calculations. Our results are in good agreement with experimental spectra of doped ZnO nanoparticles at a doping density of $1.4\times 10^{20}$ cm$^{-3}$.