Geometrically induced electric polarization in conical topological insulators

TL;DR

This paper investigates how the geometry of a conical topological insulator induces electric polarization and topological effects, revealing a net Hall current and phase differences related to the cone's shape, with potential experimental detection.

Contribution

It introduces a novel analysis of topological magnetoelectric effects and gravitational Aharonov-Bohm phenomena in conical topological insulators, linking geometry to observable quantum effects.

Findings

Net Hall current flows towards the cone apex, indicating electric polarization.

The phase difference in wavefunctions depends on the cone's aperture angle.

Potential detection via accumulated Hall charge near the apex.

Abstract

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.