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Auteurs principaux: Belov, Pavel A., Morawetz, Florian, Krüger, Sjard Ole, Scheuler, Niklas, Rommel, Patric, Main, Jörg, Giessen, Harald, Scheel, Stefan
Format: Preprint
Publié: 2023
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Accès en ligne:https://arxiv.org/abs/2310.19746
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author Belov, Pavel A.
Morawetz, Florian
Krüger, Sjard Ole
Scheuler, Niklas
Rommel, Patric
Main, Jörg
Giessen, Harald
Scheel, Stefan
author_facet Belov, Pavel A.
Morawetz, Florian
Krüger, Sjard Ole
Scheuler, Niklas
Rommel, Patric
Main, Jörg
Giessen, Harald
Scheel, Stefan
contents Due to quantum confinement, excitons in finite-sized crystals behave rather differently than in bulk materials. We investigate the dependence of energies of Rydberg excitons on the strengths of parabolic as well as rectangular confinement potentials in finite-sized crystals. The evolution of the energy levels of hydrogen-like excitons in the crossover region from weak to strong parabolic confinement is analyzed for different quantum numbers by numerical solution of the two-dimensional Schrödinger equation. The energy spectrum of hydrogen-like excitons in Cu$_{2}$O-based rectangular quantum wells is, in turn, obtained numerically from the solution of the three-dimensional Schrödinger equation as a function of the quantum well width. Various crossings and avoided crossings of Rydberg energy levels are observed and categorized based on the symmetry properties of the exciton wave function. Particular attention is paid to the two limiting cases of narrow and wide quantum wells attributed to strong and weak confinement, respectively. The energies obtained with the pure Coulomb interaction are compared with the results originating from the Rytova-Keldysh potential, i.e., by taking into account the dielectric contrast in the quantum well and in the barrier.
format Preprint
id arxiv_https___arxiv_org_abs_2310_19746
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Energy states of Rydberg excitons in finite crystals: From weak to strong confinement
Belov, Pavel A.
Morawetz, Florian
Krüger, Sjard Ole
Scheuler, Niklas
Rommel, Patric
Main, Jörg
Giessen, Harald
Scheel, Stefan
Mesoscale and Nanoscale Physics
Computational Physics
Due to quantum confinement, excitons in finite-sized crystals behave rather differently than in bulk materials. We investigate the dependence of energies of Rydberg excitons on the strengths of parabolic as well as rectangular confinement potentials in finite-sized crystals. The evolution of the energy levels of hydrogen-like excitons in the crossover region from weak to strong parabolic confinement is analyzed for different quantum numbers by numerical solution of the two-dimensional Schrödinger equation. The energy spectrum of hydrogen-like excitons in Cu$_{2}$O-based rectangular quantum wells is, in turn, obtained numerically from the solution of the three-dimensional Schrödinger equation as a function of the quantum well width. Various crossings and avoided crossings of Rydberg energy levels are observed and categorized based on the symmetry properties of the exciton wave function. Particular attention is paid to the two limiting cases of narrow and wide quantum wells attributed to strong and weak confinement, respectively. The energies obtained with the pure Coulomb interaction are compared with the results originating from the Rytova-Keldysh potential, i.e., by taking into account the dielectric contrast in the quantum well and in the barrier.
title Energy states of Rydberg excitons in finite crystals: From weak to strong confinement
topic Mesoscale and Nanoscale Physics
Computational Physics
url https://arxiv.org/abs/2310.19746