论文标题

拓扑阶段和谐振光学响应的​​单数连接方法

Singular connection approach to topological phases and resonant optical responses

论文作者

Mera, Bruno, Ozawa, Tomoki

论文摘要

我们引入了一类单数连接,以替代在参数空间上定义的任何量子状态的浆果连接。我们发现在两个频段之间的过渡偶极子的背景下,奇异连接的自然应用。我们发现,移位矢量不过是奇异连接与涉及带的浆果连接引起的连接之间的差异。偏移载体的量规不变性与该表达式是透明的。我们使用单数连接表明,通过这种连接,可以通过对涉及两个频段的过渡偶极矩阵的零基因座的点来计算与两个频段之间的光学跃迁相关的两个维度的拓扑不变。因此,这种不变式在布里渊区的动量数量上提供了自然拓扑的下限,通过吸收光子,可以从一个bloch频段到另一个bloch频段激发电子的动量数量。

We introduce a class of singular connections as an alternative to the Berry connection for any family of quantum states defined over a parameter space. We find a natural application of the singular connection in the context of transition dipoles between two bands. We find that the shift vector is nothing but the difference between the singular connection and the connection induced from the Berry connections of involved bands; the gauge invariance of the shift vector is transparent from this expression. We show, using singular connections, that the topological invariant in two dimensions associated with optical transitions between the two bands can be computed, by means of this connection, by algebraically counting the points in the zero locus of a transition dipole matrix element of the two bands involved. It follows that this invariant provides a natural topological lower bound on the number of momenta in the Brillouin zone for which an electron cannot be excited from one Bloch band to the other by absorbing a photon.

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