Geometrically induced electric polarization in conical topological insulators

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.

4 pages revtex style, 2 figures

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Cited by in corpus (9)

• Comment on: "Interaction of the magnetic quadrupole moment of a non-relativistic particle with an electric field in a rotating frame. Ann. Phys. 412 (2020) 168040''
• Electron-polaron--electron-polaron bound states in mass-gap graphene-like planar quantum electrodynamics: $s$-wave bipolarons
• On the electron-polaron--electron-polaron scattering and Landau levels in pristine graphene-like quantum electrodynamics
• Geometrically induced reversion of Hall current in a topological insulator cavity
• The quantum scale invariance in graphene-like quantum electrodynamics
• Quantum parity conservation in planar quantum electrodynamics
• Berry phases and zero-modes in toroidal topological insulator
• Bound-states and polarized charged zero modes in three-dimensional topological insulators induced by a magnetic vortex
• The spectrum consistency of fractional quantum Hall effect model