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arXiv 1104.0369cond-mat.mes-hallquant-ph
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石墨烯环中的Aharonov-Bohm-Coulomb问题

Aharonov-Bohm-Coulomb Problem in Graphene Ring

Eylee Jung, Mi-Ra Hwang, ChangSoo Park, DaeKil Park

摘要:

研究了石墨烯环中的Aharonov-Bohm-Coulomb问题。我们调查,特别是,一个库仑型势的形式$ξ/r$上的狄拉克电子的能谱的石墨烯环在两种不同的方式:一个为标量耦合和其他的矢量耦合。研究发现,由于标量耦合势打破了两个谷之间的时间反演对称性以及单个谷的有效时间反演对称性,一个谷的能谱与另一个谷的能谱分离,表现出谷极化。然而,在矢量耦合中,势并不破坏这两种对称性中的任何一种,它的作用只表现为Aharonov-Bohm势谱的附加常数。相应的持续电流,破缺能谱的可观测量,被证明是不对称的零磁通量在标量耦合,而对称的矢量耦合。

英文摘要:

We study the Aharonov-Bohm-Coulomb problem in a graphene ring. We investigate, in particular, the effects of a Coulomb type potential of the form $ξ/r$ on the energy spectrum of Dirac electrons in the graphene ring in two different ways: one for the scalar coupling and the other for the vector coupling. It is found that, since the potential in the scalar coupling breaks the time-reversal symmetry between the two valleys as well as the effective time-reversal symmetry in a single valley, the energy spectrum of one valley is separated from that of the other valley, demonstrating a valley polarization. In the vector coupling, however, the potential does not break either of the two symmetries and its effect appears only as an additive constant to the spectrum of Aharonov-Bohm potential. The corresponding persistent currents, the observable quantities of the symmetry-breaking energy spectra, are shown to be asymmetric about zero magnetic flux in the scalar coupling, while symmetric in the vector coupling.

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