Inequivalent Berry Phases for the Bulk Polarization
Inequivalent Berry Phases for the Bulk Polarization
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DOI：
10.1103/physrevx.8.021065
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发表时间：
2018-02
影响因子：
12.5
通讯作者：
Haruki Watanabe;M. Oshikawa
中科院分区：
文献类型：
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作者：
Haruki Watanabe;M. Oshikawa
我们解决了普遍存在的混乱，在表征极化的绝缘体的周期性边界条件下的贝里相位。对于带绝缘体，Berry相可以用Bloch函数和晶格动量来表示。更一般地说，在存在相互作用或无序的情况下，人们可以使用多体基态作为穿透环的通量的函数。然而，Bloch函数的定义和描述通量的方式并不唯一。因此，极化的值及其行为取决于如何精确地定义它。我们通过根据贝瑞相制定极化的不同定义并阐明它们的相互关系来证明这一点。在无源泵浦过程中传输的总电荷与定义无关，反映了其拓扑性质。
We address the widespread confusion in characterizing the polarization for insulators under the periodic boundary condition in terms of the Berry phase. The Berry phase can be formulated in terms of the Bloch function and the the lattice momentum for band insulators. More generally, in the presence of interactions or disorders, one can instead use the many-body ground state as a function of the flux piercing the ring. However, the definition of the Bloch function and the way describing the flux are not unique. As a result, the value of the polarization and its behavior depend on how precisely it is defined. We demonstrate this by formulating different definitions of the polarization in terms of Berry phases, and elucidating their mutual relations. The total charge transported during a Thouless pumping process is independent of the definition, reflecting its topological nature.