Feynman paradox in a spherical axion insulator

TL;DR

This paper demonstrates that a small charged probe near a spherical topological insulator induces a rotation of the insulator due to axion electrodynamics, with the rotation frequency depending on charge position and material properties.

Contribution

It provides a theoretical analysis of the Feynman paradox in a spherical axion insulator, deriving explicit formulas for induced rotation and surface currents based on axion electrodynamics.

Findings

The insulator rotates when the charge position changes.

Rotation frequency depends on charge, dielectric constant, and geometry.

Surface Hall currents induce angular momentum and surface velocities.

Abstract

We show that a small charged probe near a spherical topological insulator causes the latter to rotate around a symmetry axis defined by the center of the sphere and the position of the charge outside the latter. The rotation occurs when the distance from the charge to the center of the sphere is changed. This phenomenon occurs due to induced static fields and is a consequence of the axion electrodynamics underlying the electromagnetic response of a topological insulator. Assuming a regime where the charged probe can be regarded as a point charge $q=Ne$, where $N$ is a positive integer and $e$ is the elementary electric charge, we obtain that the rotation frequency is given by $\omega=(N\alpha)^2\Upsilon(\epsilon,d/a)/I$, where $I$ is the moment of inertia, $\alpha$ is the fine-structure constant, and the function $\Upsilon$ depends on the dielectric constant $\epsilon$ and the relative distance $d/a$ of the charge from the center of the sphere of radius $a$. Since the point charge also induces Hall currents on the surface, we compute also their associated angular momentum. This allows us to derive an exact expression for the electronic velocity on the surface as a function of $a/d$.