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arXiv 1808.09149cond-mat.mes-hallcond-mat.str-el
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磁振子自旋霍尔系统的${\mathbb Z}_2$拓扑不变量

${\mathbb Z}_2$ Topological Invariant for Magnon Spin Hall Systems

Hiroki Kondo, Yutaka Akagi, Hosho Katsura

摘要:

我们提出了一个定义的${\mathbb Z}_2$拓扑不变量的磁振子自旋霍尔系统,这是玻色子模拟的二维拓扑绝缘体在类AII。在这些系统中,“Kramers对”的存在是由伪时间反演对称性保证的,伪时间反演对称性在某种幺正变换下与时间反演对称性相同。每对Kramers带的${\mathbb Z}_2$指数用Berry连接和曲率的玻色子对应物表示。我们构建明确的例子磁振子自旋霍尔系统,并证明我们的${\mathbb Z}_2$指数精确地表征螺旋边缘状态的存在或不存在。所提出的${\mathbb Z}_2$指数和所发展的形式不仅适用于磁振子系统,而且也适用于其他非相互作用玻色子系统。

英文摘要:

We propose a definition of a ${\mathbb Z}_2$ topological invariant for magnon spin Hall systems which are the bosonic analog of two-dimensional topological insulators in class AII. The existence of "Kramers pairs" in these systems is guaranteed by pseudo-time-reversal symmetry which is the same as time-reversal symmetry up to some unitary transformation. The ${\mathbb Z}_2$ index of each Kramers pair of bands is expressed in terms of the bosonic counterparts of the Berry connection and curvature. We construct explicit examples of magnon spin Hall systems and demonstrate that our ${\mathbb Z}_2$ index precisely characterizes the presence or absence of helical edge states. The proposed ${\mathbb Z}_2$ index and the formalism developed can be applied not only to magnonic systems but also to other non-interacting bosonic systems.

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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