中国物理B ›› 2008, Vol. 17 ›› Issue (8): 3026-3034.doi: 10.1088/1674-1056/17/8/044

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Effect of electric field on the spectrum and the persistent current of a quantum ring with two electrons (II)---additional effect of a charged impurity

吴 洪   

  1. Department of Physics, School of Sciences, Jimei University, Xiamen 361021, China
  • 收稿日期:2007-10-08 修回日期:2008-01-03 出版日期:2008-08-20 发布日期:2008-08-20
  • 基金资助:
    Project supported by the Natural Science Foundation of Fujian Province of China (Grant No T0650010).

Effect of electric field on the spectrum and the persistent current of a quantum ring with two electrons (II)---additional effect of a charged impurity

Wu Hong(吴洪)†   

  1. Department of Physics, School of Sciences, Jimei University, Xiamen 361021, China
  • Received:2007-10-08 Revised:2008-01-03 Online:2008-08-20 Published:2008-08-20
  • Supported by:
    Project supported by the Natural Science Foundation of Fujian Province of China (Grant No T0650010).

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摘要： This paper studies the effect of a~charged~impurity together with or without an external homogeneous~electric field~on a~quantum~ring threaded by a magnetic field $B$ and containing two electrons. The potential caused by the impurity has been plotted which is helpful to the understanding of the electronic structures inside the ring. The deep valley appearing in the potential curve is the source of localization, which affects seriously the Aharonov--Bohm oscillation (ABO) of the energy and persistent current. It also causes the fluctuation of the total orbital angular momentum $L$ of the pair of electrons. It is found that the appearance of the impurity reduces the domain of the fractional ABO. During the increase of $B$, the domain of the integral ABO may appear earlier when $B$ is even quite small. The transition from the localized states to extended states has also been studied. Furthermore, it has deduced a set of related formulae for a transformation, by which an impurity with a charge $e_p$ placed at an arbitrary point ${\bm R}_p$ is equivalent to an impurity with a revised charge $\tilde {e}_p$ placed at the $X$-axis with a revised radial distance $\tilde {R}_p$. This transformation facilitates the calculation and make the analysis of the physical result clearer.

关键词: charged impurity, quantum ring, ABO, potential

Abstract: This paper studies the effect of a~charged~impurity together with or without an external homogeneous~electric field~on a~quantum~ring threaded by a magnetic field $B$ and containing two electrons. The potential caused by the impurity has been plotted which is helpful to the understanding of the electronic structures inside the ring. The deep valley appearing in the potential curve is the source of localization, which affects seriously the Aharonov--Bohm oscillation (ABO) of the energy and persistent current. It also causes the fluctuation of the total orbital angular momentum $L$ of the pair of electrons. It is found that the appearance of the impurity reduces the domain of the fractional ABO. During the increase of $B$, the domain of the integral ABO may appear earlier when $B$ is even quite small. The transition from the localized states to extended states has also been studied. Furthermore, it has deduced a set of related formulae for a transformation, by which an impurity with a charge $e_p$ placed at an arbitrary point Rp is equivalent to an impurity with a revised charge $\tilde {e}_p$ placed at the $X$-axis with a revised radial distance $\tilde {R}_p$. This transformation facilitates the calculation and make the analysis of the physical result clearer.

Key words: charged impurity, quantum ring, ABO, potential

中图分类号:  (Persistent currents)

  • 73.23.Ra
73.20.Jc (Delocalization processes) 73.21.-b (Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems)