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arXiv 1302.6535cond-mat.str-el
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三维玻色拓扑绝缘体与统计Witten效应

Bosonic topological insulator in three dimensions and the statistical Witten effect

Max A. Metlitski, C. L. Kane, Matthew P. A. Fisher

摘要:

众所周知,三维电子拓扑绝缘体的一个特征是威滕效应:如果系统耦合到一个紧凑的电磁规范场,则体中的一个拓扑绝缘体获得半奇整数极化电荷。在目前的工作中,我们提出了一个相应的现象的拓扑绝缘体的玻色子在三维粒子数守恒和时间反演对称性的保护。我们认为,尽管玻色子的拓扑绝缘体中的电子能保持电中性,但它的统计性质从玻色子转变为费米子。我们证明,这种"统计威滕效应"直接意味着,如果拓扑绝缘体的表面既不是无间隙的,也不是自发打破对称性,它必然支持一个内在的二维拓扑秩序。此外,在纯2D系统中不能完全实现表面特性。我们还证实,由Vishwanath和Senthil(arXiv:1209.3058)提出的玻色子拓扑绝缘体的表面相提供了一个一致的散装表现出统计威滕效应的终止。在另一篇论文中,我们将提供一个明确的场论,晶格正则化,玻色子的三维拓扑绝缘体的建设,采用部分子分解和随后的凝聚的部分子-半导体复合材料。

英文摘要:

It is well-known that one signature of the three-dimensional electron topological insulator is the Witten effect: if the system is coupled to a compact electromagnetic gauge field, a monopole in the bulk acquires a half-odd-integer polarization charge. In the present work, we propose a corresponding phenomenon for the topological insulator of bosons in 3d protected by particle number conservation and time-reversal symmetry. We claim that although a monopole inside a topological insulator of bosons can remain electrically neutral, its statistics are transmuted from bosonic to fermionic. We demonstrate that this ``statistical Witten effect" directly implies that if the surface of the topological insulator is neither gapless, nor spontaneously breaks the symmetry, it necessarily supports an intrinsic two-dimensional topological order. Moreover, the surface properties cannot be fully realized in a purely 2d system. We also confirm that the surface phases of the bosonic topological insulator proposed by Vishwanath and Senthil (arXiv:1209.3058) provide a consistent termination of a bulk exhibiting the statistical Witten effect. In a companion paper, we will provide an explicit field-theoretic, lattice-regularized, construction of the 3d topological insulator of bosons, employing a parton decomposition and subsequent condensation of parton-monopole composites.

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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