Metastable Bound States of the Two-Dimensional Bimagnetoexcitons in the Lowest Landau Levels Approximation
- Authors: Moskalenko S.A.1, Khadzhi P.I.1, Podlesny I.V.1, Dumanov E.V.1, Liberman M.A.2, Zubac I.A.1
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Affiliations:
- Institute of Applied Physics
- Nordic Institute for Theoretical Physics (NORDITA) KTH and Stockholm University
- Issue: Vol 52, No 14 (2018)
- Pages: 1801-1805
- Section: Excitons in Nanostructures
- URL: https://journals.rcsi.science/1063-7826/article/view/204992
- DOI: https://doi.org/10.1134/S1063782618140208
- ID: 204992
Cite item
Abstract
The possible existence of the bound states of the interacting two-dimensional (2D) magnetoexcitons in the lowest Landau levels (LLLs) approximation was investigated using the Landau gauge description. The magnetoexcitons taking part in the formation of the bound state with resultant wave vector \({\mathbf{k}} = 0\) have opposite in-plane wave vectors \({\mathbf{k}}\) and \( - {\mathbf{k}}\) and look as two electric dipoles with the arms oriented in-plane perpendicularly to the corresponding wave vectors. The bound state of two antiparallel dipoles moving with equal probability in any direction of the plane with equal but antiparallel wave vectors is characterized by the variational wave function of the relative motion \({{\varphi }_{n}}({\mathbf{k}})\) depending on the modulus \({\text{|}}{\mathbf{k}}{\text{|}}\). The spins of two electrons and the effective spins of two holes forming the bound states were combined separately in the symmetric or in the antisymmetric forms \(( \uparrow \downarrow \, + \eta \, \downarrow \uparrow )\) with the same parameter \(\eta = \pm 1\) for electrons and holes. In the case of the variational wave function \({{\varphi }_{2}}(k) = {{(8{{\alpha }^{3}})}^{{1/2}}}{{k}^{2}}l_{0}^{2}\exp [ - \alpha {{k}^{2}}l_{0}^{2}]\) the maximum density of the magnetoexcitons in the momentum space representation is concentrated on the in-plane ring with the radius \({{k}_{r}} = 1{\text{/}}(\sqrt \alpha {{l}_{0}}).\) The stable bound states of the bimagnetoexciton molecule do not exist for both spin orientations. Instead of them, a deep metastable bound state with the activation barrier comparable with the ionization potential \({{I}_{l}}\) of the magnetoexciton with \({\mathbf{k}} = 0\) was revealed in the case \(\eta = 1\) and \(\alpha = 0.5\). In the case \(\eta = - 1\) and \(\alpha = 3.4\) only a shallow metastable bound state can appear.
About the authors
S. A. Moskalenko
Institute of Applied Physics
Author for correspondence.
Email: exciton@phys.asm.md
Moldova, Republic of, Chisinau, MD-2028
P. I. Khadzhi
Institute of Applied Physics
Email: exciton@phys.asm.md
Moldova, Republic of, Chisinau, MD-2028
I. V. Podlesny
Institute of Applied Physics
Email: exciton@phys.asm.md
Moldova, Republic of, Chisinau, MD-2028
E. V. Dumanov
Institute of Applied Physics
Email: exciton@phys.asm.md
Moldova, Republic of, Chisinau, MD-2028
M. A. Liberman
Nordic Institute for Theoretical Physics (NORDITA) KTH and Stockholm University
Email: exciton@phys.asm.md
Sweden, Stockholm, SE-106 91
I. A. Zubac
Institute of Applied Physics
Email: exciton@phys.asm.md
Moldova, Republic of, Chisinau, MD-2028