锥形拓扑绝缘体中的几何诱导电极化的强度
Geometrically induced electric polarization in conical topological insulators
摘要：
研究了当点电荷$q$位于锥顶附近时，锥拓扑绝缘体上的拓扑磁电效应。确定了在锥面上感应的霍尔电流和镜像电荷组态。我们还研究了这种几何中的一种引力Aharonov-Bohm效应，并实现了在（奇异）锥尖附近闭合平行输运时波函数（旋量）分量之间的相位差。具体地说，出现了一个流向锥顶（或锥底）的净电流，从而产生了锥形拓扑绝缘体的电极化的强度。这种效应可以例如借助于顶点附近的净累积霍尔电荷来检测。一旦它只依赖于材料的几何形状（本质上是锥孔角），这可能是（2+1）维爱因斯坦引力的微观尺度实现。
英文摘要：
We study the topological magnetoelectric effect on a conical topological insulator when a point charge $q$ is near the cone apex. The Hall current induced on the cone surface and the image charge configuration are determined. We also study a kind of gravitational Aharonov-Bohm effect in this geometry and realize a phase diference betwen the components of the wavefunctions (spinors) upon closed parallel transport around the (singular) cone tip. Concretely, a net current flowing towards cone apex (or botton) shows up, yielding electric polarization of the conical topological insulator. Such an effect may be detected, for instance, by means of the net accumulated Hall charge near the apex. Once it depends only on the geometry of the material (essetially, the cone apperture angle) this may be faced as a microscopic scale realization of (2+1)-dimensional Einstein gravity.
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