Abstract
Quantum crystallization of electrons in a quantum dot (QD) subjected to an external magnetic field is considered. Two-electron QDs with two-dimensional (2D) parabolic confining potential in an external transverse magnetic field are calculated. The Hamiltonian is numerically diagonalized in the basis of one-particle functions to find the energy spectra and wave functions for the relative motion of electrons with inclusion of electron-electron interaction for a broad range of the confining-potential steepness (α) and external magnetic fields (B). The region of the external parameters (α, B) within which a gradual transition to quantum crystalline order occurs is numerically determined. In contrast to a 2D unbounded system, a magnetic field acts nonmonotonically on “crystallization” in a quantum dot with several electrons because of a competition between two effects taking place with increasing B, namely, decreasing spread of the electron wave functions and increasing effective steepness of the confining potential, which reduces the average separation between electrons.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. Geerinckx, F. M. Peeters, and J. T. Devreese, J. Appl. Phys. 68, 3435 (1990).
W. Hansen, M. Horst, J. P. Kotthaus, U. Merkt, Ch. Sikorski, and K. Ploog, Phys. Rev. Lett. 58, 2586 (1987).
Ch. Sikorski and U. Merkt, Phys. Rev. Lett. 62, 2164 (1989).
C. T. Liu, K. Nakamura, D. C. Tsui, K. Ismail, D. A. Antoniadis, and H. I. Smith, Appl. Phys. Lett. 55, 168 (1989).
T. Demel, D. Heitmann, P. Grambow, and K. Ploog, Phys. Rev. Lett. 64, 788 (1990).
J. Dempsey, N. F. Johnson, L. Brey, and B. I. Halperin, Phys. Rev. B 42, 11708 (1990).
P. Hawrylak, Phys. Rev. Lett. 71, 3347 (1993).
A. Kumar, S. E. Laux, and F. Stern, Phys. Rev. B 42, 5166 (1990).
Al. A. Andreev, Ya. M. Blanter, and Yu. E. Lozovik, Solid State Commun. 91, 581 (1994); Int. J. Mod. Phys. B 9, 1843 (1995).
E. P. Wigner, Phys. Rev. 46, 1002 (1934); Trans. Faraday Soc. 34, 678 (1938).
R. S. Crandall and R. Williams, Phys. Lett. A 7, 678 (1971).
A. V. Chaplik, Zh. Éksp. Teor. Fiz. 62, 746 (1972) [JETP 35, 395 (1972)].
Yu. E. Lozovik and V. I. Yudson, JETP Lett. 22, 11 (1975); Yu. E. Lozovik and D. R. Musin, Fiz. Tverd. Tela (Leningrad) 21, 1974 (1979) [Sov. Phys. Solid State 21, 1132 (1979)]; B. Abdullaev and Yu. E. Lozovik, ibid. 24, 2663 (1982) [Sov. Phys. Solid State 24, 1510 (1982)].
H. Fukuyama, Solid State Commun. 19, 551 (1976).
Yu. E. Lozovik and V. M. Farztdinov, Solid State Commun. 54, 725 (1985); Yu. E. Lozovik, V. M. Farztdinov, and B. Abdullaev, J. Phys. C 18, L807 (1985).
T. Ando, A. B. Fowler, and F. Stern, Rev. Mod. Phys. 54, 1 (1982).
V. B. Shikin and Yu. P. Monarkha, Two-Dimensional Charged Systems in Helium [in Russian], Nauka, Moscow, 1989.
M. Shaegan, Perspectives in Quantum Hall Effects, edited by S. Das Sarma and A. Pinchuk (John Wiley Publ., New York, 1997).
R. H. Morf, Phys. Rev. Lett. 43, 931 (1979).
V. M. Bedanov, G. V. Gagiyak, and Yu. E. Lozovik, Zh. Éksp. Teor. Fiz. 88, 1622 (1985) [JETP 61, 967 (1985)].
C. G. Crimes and G. Adams, Phys. Rev. Lett. 42, 795 (1979).
Yu. E. Lozovik, Usp. Fiz. Nauk 153, 356 (1987) [Sov. Phys. Usp. 30, 912 (1987)]; Yu. E. Lozovik and V. A. Mandelshtam, Phys. Lett. A 145, 269 (1990).
Yu. E. Lozovik and V. A. Mandelshtam, Phys. Lett. A 165, 469 (1992).
Yu. E. Lozovik and E. A. Rakoch, JETP Lett. 65, 282 (1997); Phys. Lett. A 235, 55 (1997).
Author information
Authors and Affiliations
Additional information
Fiz. Tverd. Tela (St. Petersburg) 40, 1753–1759 (September 1998)
Rights and permissions
About this article
Cite this article
Kaputkina, N.E., Lozovik, Y.E. Energy spectra and quantum crystallization in two-electron quantum dots in a magnetic field. Phys. Solid State 40, 1594–1599 (1998). https://doi.org/10.1134/1.1130607
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1134/1.1130607