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arXiv 1010.0071cond-mat.mes-hall
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Dirac费米子的谷自旋和规则:拓扑论证

Valley Spin Sum Rule for Dirac Fermions: Topological Argument

Jun Goryo

摘要:

我们考虑一个二维二分格系统。在这样的系统中,布洛赫带谱可能有一些谷点,狄拉克费米子出现在这些谷点周围作为低能激发。每个谷点具有谷自旋+1或-1。在这样的系统中,有两个拓扑数分别计算布里渊区中的涡旋和merons。这些数字是等价的,这一事实导致了一个求和规则,该规则指出,即使在没有时间反演和宇称对称的系统中,谷自旋的总和也是不存在的。我们可以在奇维空间中的Nielsen-Ninomiya no-go定理中看到谷自旋和手征之间的一些相似之处。

英文摘要:

We consider a two-dimensional bipartite lattice system. In such a system, the Bloch band spectrum can have some valley points, around which Dirac fermions appear as the low-energy excitations. Each valley point has a valley spin +1 or -1. In such a system, there are two topological numbers counting vortices and merons in the Brillouin zone, respectively. These numbers are equivalent, and this fact leads to a sum rule which states that the total sum of the valley spins is absent even in a system without time-reversal and parity symmetries. We can see some similarity between the valley spin and chirality in the Nielsen-Ninomiya no-go theorem in odd-spatial dimensions.

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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