[PDF]    http://dx.doi.org/10.3952/lithjphys.50405

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 50, 377–394 (2010)

Review

QUASICLASSICAL THEORY OF QUANTUM DOTS
E. Anisimovas a and A. Matulis b
a Department of Theoretical Physics, Vilnius University, Saulėtekio 9, LT-10222 Vilnius, Lithuania
E-mail: egidijus.anisimovas@ff.vu.lt
b Semiconductor Physics Institute, Center for Physical Sciences and Technology, A. Goštauto 11, LT-01108 Vilnius, Lithuania
E-mail: amatulis@takas.lt

Received 30 November 2010; accepted 15 December 2010

We review the quasiclassical theory of quantum dots. The starting point of the developed approximate approaches is the observation that in large (in comparison to the effective Bohr radius) quantum dots the energy of the classical Coulomb interactions dominates over the quantum-mechanical kinetic energy. This dominance is further enhanced by application of a perpendicular magnetic field. The classical regime is marked by the formation of structures (the Wigner crystal) and structural transitions. The nature of these phenomena is indeed classical, and they can be successfully tackled using classical approaches which are transparent and easy to understand. In this way heavy calculations typical of quantum-mechanical schemes are avoided and the quantum effects are included in an perturbative manner. We discus, in particular, the application of the renormalized perturbation series to the energy spectra, the structural transitions, the power law behaviour of the critical fields, the global (persistent) and local currents in quantum dots, and dissipation in mixed systems with both quantum and classical degerees of freedom.
Keywords: quantum dots, quasiclassical approximation, Wigner crystal
PACS: 73.21.La, 03.65.Sq


KVAZIKLASIKINĖ KVANTINIŲ TAŠKŲ TEORIJA
E. Anisimovas a, A. Matulis b
a Vilniaus universitetas, Vilnius, Lietuva
b Fizinių ir technologijos mokslų centro Puslaidininkių fizikos institutas, Vilnius, Lietuva

Kvantiniai taškai yra dariniai, kuriuose elektrono judėjimas yra apribotas visomis trimis erdvės kryptimis, o energijos spektras diskretus. Taigi, kvantiniai taškai yra dirbtiniai atomai: valdomų parametrų natūralių atomų analogai. Dideliųmatmenų (lyginant su efektiniu Boro spinduliu) kvantiniuose taškuose klasikinė kuloninės stūmos energija žymiai viršija kvantinę kinetinę energiją. Elektrostatinės sąveikos santykinę svarbą dar labiau išryškina stiprus taško plokštumai statmenas magnetinis laukas. Todėl, viena vertus, šiuose kvantiniuose taškuose yra stebimi kolektyviniai reiškiniai (Vignerio kristalizacija), antra vertus, jų fizika yra iš esmės klasikinė. Straipsnyje apžvelgiama kvaziklasikinė kvantinių taškų teorija, išplėtota pasinaudojus šiais pastebėjimais. Taikomi klasikiniai metodai leidžia išvengti sudėtingų ir nevaizdžių kvantinių mechaninių skaičiavimų. Klasikiniais metodais gauti rezultatai yra lengvai suprantami ir interpretuojami, o į kvantines pataisas atsižvelgiama kaip į mažus trikdžius. Aptariamas renormalizuotos trikdžių eilutės taikymas energijų spektrams skaičiuoti, struktūrų susidarymas ir virsmai kvantiniuose taškuose, laipsniniai dėsniai, nusakantys kritinių parametrų elgesį, ir disipacija mišriose sistemose, pasižyminčiose klasikinių ir kvantinių laisvės laipsnių sąveika.


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