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arXiv 0712.2571cond-mat.mes-hall
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非阿贝尔“磁场”中的超冷原子气体:量子霍尔效应的优越性

Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy

N. Goldman, A. Kubasiak, P. Gaspard, M. Lewenstein

摘要:

现在,在实验上可以为囚禁在光晶格中的超冷原子建立人工的,特别是非阿贝尔的规范势。基于这一事实,我们研究了非阿贝尔U(2)规范势中超冷费米气体的基本性质,该规范势具有\emph{constant}威尔逊圈的特征。在此特定条件下,能谱表现出一个具有大禁带的稳健能带结构,并揭示了一个新的分形图形。横向电导率与拓扑不变量有关,并且当费米能量位于光谱的间隙内时,横向电导率被量子化。我们证明了中性原子的整数量子霍尔效应的类似物在非阿贝尔耦合下仍然存在,并导致了一个引人注目的分形相图。此外,这种耦合诱导了如在石墨烯中观察到的异常霍尔效应。

英文摘要:

Nowadays it is experimentally feasible to create artificial, and in particular, non-Abelian gauge potentials for ultracold atoms trapped in optical lattices. Motivated by this fact, we investigate the fundamental properties of an ultracold Fermi gas in a non-Abelian U(2) gauge potential characterized by a \emph{constant} Wilson loop. Under this specific condition, the energy spectrum exhibits a robust band structure with large gaps and reveals a new fractal figure. The transverse conductivity is related to topological invariants and is shown to be quantized when the Fermi energy lies inside a gap of the spectrum. We demonstrate that the analogue of the integer quantum Hall effect for neutral atoms survives the non-Abelian coupling and leads to a striking fractal phase diagram. Moreover, this coupling induces an anomalous Hall effect as observed in graphene.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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