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arXiv 0901.2326cond-mat.mes-hallcond-mat.mtrl-scicond-mat.str-elnucl-thquant-ph
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石墨烯量子点中的边缘态:零磁场下分数量子霍尔效应的类比和差异

Edge states in graphene quantum dots: Fractional quantum Hall effect analogies and differences at zero magnetic field

Igor Romanovsky, Constantine Yannouleas, Uzi Landman

摘要:

我们研究了在自由磁场条件下,具有锯齿形边界的准圆形石墨烯量子点中的中间带隙边缘态的简并流形支持类似于分数量子霍尔效应(Fractional磁场中半导体异质结构的情况下所熟悉的强关联多体行为的方式。本文首次对5 <= N <= 8的全自旋极化电子和N(N-1)/2 <= L <= 150的总角动量进行了系统的精确对角化(EXD)数值研究。本文在前面介绍的方法的基础上推导了一个双电子分子(REM)型波函数。Yannouleas和U. Landman,Phys.Rev.B66,115315(2002)]中的方法。将EXD波函数与Laughlin型和REM型试函数进行了比较。结果发现,REM的变分扩展提供了一个更好的描述所有分数填充相比,劳克林功能(包括总能量和重叠),一个事实,反映了强大的方位角定位的边缘电子。与圆形半导体量子点中电子的多环排列相反,石墨烯REM在所有情况下都表现出单(0,N)双环分子(晶体)结构,所有电子都位于边缘上。沿着圆形边缘的锯齿形边界条件中的中断有效地充当钉扎电子分子的杂质,产生具有破坏的旋转对称性的单粒子密度,其直接描绘边缘电子的方位角定位。

英文摘要:

We investigate the way that the degenerate manifold of midgap edge states in quasicircular graphene quantum dots with zig-zag boundaries supports, under free-magnetic-field conditions, strongly correlated many-body behavior analogous to the fractional quantum Hall effect (FQHE), familiar from the case of semiconductor heterostructures in high magnetic fields. Systematic exact-diagonalization (EXD) numerical studies are presented for the first time for 5 <= N <= 8 fully spin-polarized electrons and for total angular momenta in the range of N(N-1)/2 <= L <= 150. We present a derivation of a rotating-electron-molecule (REM) type wave function based on the methodology introduced earlier [C. Yannouleas and U. Landman, Phys. Rev. B 66, 115315 (2002)] in the context of the FQHE in two-dimensional semiconductor quantum dots. The EXD wave functions are compared with FQHE trial functions of the Laughlin and the derived REM types. It is found that a variational extension of the REM offers a better description for all fractional fillings compared with that of the Laughlin functions (including total energies and overlaps), a fact that reflects the strong azimuthal localization of the edge electrons. In contrast with the multiring arrangements of electrons in circular semiconductor quantum dots, the graphene REMs exhibit in all instances a single (0,N) polygonal-ring molecular (crystalline) structure, with all the electrons localized on the edge. Disruptions in the zig-zag boundary condition along the circular edge act effectively as impurities that pin the electron molecule, yielding single-particle densities with broken rotational symmetry that portray directly the azimuthal localization of the edge electrons.

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