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.
Similar content being viewed by others
REFERENCES
I. V. Lerner and Yu. E. Lozovik, J. Low Temp. Phys. 38, 333 (1980).
I. V. Lerner and Yu. E. Lozovik, Sov. Phys. JETP 53, 763 (1981).
A. B. Dzyubenko and Yu. E. Lozovik, Sov. Phys. Solid State 25, 874 (1983);
Sov. Phys. Solid State 26, 938 (1984).
E. V. Dumanov, I. V. Podlesny, S. A. Moskalenko, and M. A. Liberman, Phys. E (Amsterdam, Neth.) 88, 77 (2017).
D. Paquet, T. M. Rice, and K. Ueda, Phys. Rev. B 32, 5208 (1985).
S. A. Moskalenko et al., Phys. Rev. B 66, 245316 (2002).
A. Wojs et al., Can. J. Phys. 83, 1019 (2005).
M. A. Olivares-Robles and S. E. Ulloa, Phys. Rev B 64, 115302 (2001).
S. A. Moskalenko, P. I. Khadzhi, I. V. Podlesny, E. V. Dumanov, M. A. Liberman, and I. A. Zubac, Mold. J. Phys. Sci. 16, 149 (2017).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientist and Engineers (McGraw-Hill Book Company, New York, 1968).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Moscow, Nauka, 1971) [in Russian].
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series: Special Functions (CRC, Boca Ratono, FL, 1986).
P. W. Anderson, Phys. Rev. 110, 827 (1958).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Moskalenko, S.A., Khadzhi, P.I., Podlesny, I.V. et al. Metastable Bound States of the Two-Dimensional Bimagnetoexcitons in the Lowest Landau Levels Approximation. Semiconductors 52, 1801–1805 (2018). https://doi.org/10.1134/S1063782618140208
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063782618140208