A solvable model for excitonic complexes in one dimension

Anders J. Markvardsen, Neil F Johnson

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

It is known experimentally that stable few-body clusters containing negatively-charged electrons (e) and positively-charged holes (h) can exist in low-dimensional semiconductor nanostructures. In addition to the familiar exciton (e+h), three-body "charged excitons" (2e+h and 2h+e) have also been observed. Much less is known about the properties of such charged excitons since three-body problems are generally very difficult to solve, even numerically. Here we introduce a simple model, which can be considered as an extended Calogero model, to calculate analytically the energy spectra for both a charged exciton and a neutral exciton in a one-dimensional nanostructure, such as a finite-length quantum wire. Apart from its physical motivation, the model is of mathematical interest in that it can be related to the Heun (or Heine) equation and, as shown explicitly, highly accurate, closed form solutions can be obtained.

Original languageEnglish (US)
Pages (from-to)4013-4022
Number of pages10
JournalJournal of Mathematical Physics
Volume38
Issue number8
StatePublished - Aug 1997
Externally publishedYes

Fingerprint

Solvable Models
Exciton
One Dimension
excitons
Nanostructures
Quantum Wires
Three-body Problem
three body problem
Energy Spectrum
quantum wires
Closed-form Solution
Semiconductors
energy spectra
Model
Electron
Calculate
electrons

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Markvardsen, A. J., & Johnson, N. F. (1997). A solvable model for excitonic complexes in one dimension. Journal of Mathematical Physics, 38(8), 4013-4022.

A solvable model for excitonic complexes in one dimension. / Markvardsen, Anders J.; Johnson, Neil F.

In: Journal of Mathematical Physics, Vol. 38, No. 8, 08.1997, p. 4013-4022.

Research output: Contribution to journalArticle

Markvardsen, AJ & Johnson, NF 1997, 'A solvable model for excitonic complexes in one dimension', Journal of Mathematical Physics, vol. 38, no. 8, pp. 4013-4022.
Markvardsen, Anders J. ; Johnson, Neil F. / A solvable model for excitonic complexes in one dimension. In: Journal of Mathematical Physics. 1997 ; Vol. 38, No. 8. pp. 4013-4022.
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