Fractional charge bound to a vortex in two-dimensional topological crystalline insulators
Fractional charge bound to a vortex in two-dimensional topological crystalline insulators
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DOI：
10.1103/physrevb.101.241109
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发表时间：
2019-03
影响因子：
3.7
通讯作者：
Eunwoo Lee;A. Furusaki;Bohm-Jung Yang
中科院分区：
文献类型：
--
作者：
Eunwoo Lee;A. Furusaki;Bohm-Jung Yang
我们建立的分数电荷之间的对应关系绑定到一个涡旋的纹理晶格和相关的体带拓扑结构在二维（2D）拓扑晶体绝缘体。作为一个代表性的例子，我们考虑的凯库勒织构石墨烯的体带拓扑结构的特点是由一个2D $\mathbb{Z}_{2}$拓扑不变量$\nu_{\rm 2D}$的反转对称性保护。局部化在凯库勒纹理中的涡旋的分数电荷被示出为与涡旋周围的体积拓扑不变量$\nu_{\rm 2D}$的变化有关，如在苏-Schriefer-Heeger模型的情况下，其中局部化在畴壁的分数电荷与简并基态之间的体积电荷极化的变化有关。我们表明，有效的三维（3D）的哈密顿，其中的角度$\θ $周围的一个漩涡在凯库勒织构石墨烯是第三个坐标，描述了一个三维的轴子绝缘体与量子化的磁电极化。在绝热变化的$\theta$对应的手征铰链模式的轴子绝缘体，并确定了累积的电荷定位在涡，这是半量子化时，手征对称性存在的频谱流。当手征对称性不存在时，位于涡旋的电荷不再量子化，但只要反转对称性存在，涡旋总是携带半量子化的Wannier电荷。对于磁电极化由于对称性的存在而被量子化的情况，我们对所有可能的拓扑晶体绝缘体进行分类，其涡旋缺陷携带分数电荷。
We establish the correspondence between the fractional charge bound to a vortex in a textured lattice and the relevant bulk band topology in two-dimensional (2D) topological crystalline insulators. As a representative example, we consider the Kekule textured graphene whose bulk band topology is characterized by a 2D $\mathbb{Z}_{2}$ topological invariant $\nu_{\rm 2D}$ protected by inversion symmetry. The fractional charge localized at a vortex in the Kekule texture is shown to be related to the change in the bulk topological invariant $\nu_{\rm 2D}$ around the vortex, as in the case of the Su-Schriefer-Heeger model in which the fractional charge localized at a domain wall is related to the change in the bulk charge polarization between degenerate ground states. We show that the effective three-dimensional (3D) Hamiltonian, where the angle $\theta$ around a vortex in Kekule-textured graphene is a third coordinate, describes a 3D axion insulator with a quantized magnetoelectric polarization. The spectral flow during the adiabatic variation of $\theta$ corresponds to the chiral hinge modes of an axion insulator and determines the accumulated charge localized at the vortex, which is half-quantized when chiral symmetry exists. When chiral symmetry is absent, electric charge localized at the vortex is no longer quantized, but the vortex always carries a half-quantized Wannier charge as long as inversion symmetry exists. For the cases when magnetoelectric polarization is quantized due to the presence of symmetry that reverses the space-time orientation, we classify all possible topological crystalline insulators whose vortex defect carries a fractional charge.