中国物理B ›› 2009, Vol. 18 ›› Issue (4): 1578-1585.doi: 10.1088/1674-1056/18/4/048

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Ground state energy of excitons in quantum dot treated variationally via Hylleraas-like wavefunction

  

  • 收稿日期:2008-07-23 修回日期:2008-10-27 出版日期:2009-04-20 发布日期:2009-04-20

Ground state energy of excitons in quantum dot treated variationally via Hylleraas-like wavefunction

S. Şakiroĝlua)†, ü. Doĝana), A. Yildiza), K. Akgüngöra), H. Epika), Y. Ergünb), H. Saric), and ì. Sökmena)   

  1. a Physics Department, Dokuz Eyl¨ul University, ˙Izmir 35160, Turkey; b Physics Department, Anadolu University, Eski¸sehir 26470, Turkey; c Physics Department, Cumhuriyet University, Sivas 58140, Turkey
  • Received:2008-07-23 Revised:2008-10-27 Online:2009-04-20 Published:2009-04-20

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摘要： In this work, the effects of quantum confinement on the ground state energy of a correlated electron--hole pair in a spherical and in a disc-like quantum dot have been investigated as a function of quantum dot size. Under parabolic confinement potential and within effective mass approximation Ritz's variational method is applied to Hylleraas-like trial wavefunction. An efficient method for reducing the main effort of the calculation of terms like $r^k_{\rm eh}\exp(-\lambda r_{\rm eh})$ is introduced. The main contribution of the present work is the introduction of integral transforms which provide the calculation of expectation value of energy and the related matrix elements to be done analytically over single-particle coordinates instead of Hylleraas coordinates.

关键词: exciton, parabolic confinement, variational method, Hylleraas coordinates

Abstract: In this work, the effects of quantum confinement on the ground state energy of a correlated electron--hole pair in a spherical and in a disc-like quantum dot have been investigated as a function of quantum dot size. Under parabolic confinement potential and within effective mass approximation Ritz's variational method is applied to Hylleraas-like trial wavefunction. An efficient method for reducing the main effort of the calculation of terms like $r^k_{\rm eh}\exp(-\lambda r_{\rm eh})$ is introduced. The main contribution of the present work is the introduction of integral transforms which provide the calculation of expectation value of energy and the related matrix elements to be done analytically over single-particle coordinates instead of Hylleraas coordinates.

Key words: exciton, parabolic confinement, variational method, Hylleraas coordinates

中图分类号:  (Excitons and related phenomena)

  • 71.35.-y
73.21.La (Quantum dots) 71.18.+y (Fermi surface: calculations and measurements; effective mass, g factor)