A magnetic monopole in topological insulator: exact solution

TL;DR

This paper provides an exact solution for a magnetic monopole in a topological insulator, revealing the presence of bound states and discussing implications for the Witten effect, with results showing robustness and size-dependent degeneracy lifting.

Contribution

It offers the first exact analytical solution of a magnetic monopole in a topological insulator, clarifying the conditions for the Witten effect in such systems.

Findings

A magnetic monopole induces a zero energy bound state and a surface state.

External fields can lift the degeneracy of these states.

Energy differences decay exponentially with system size.

Abstract

The Witten effect tells that a unit magnetic monopole can bind a half elementary charge in an axion media. We present an exact solution of a magnetic monopole in a topological insulator that was proposed to be an axion media recently. It is found that a magnetic monopole can induce one zero energy state bound to it and one surface state of zero energy. The two states are quite robust, but the degeneracy can be removed by external fields. For a finite size system, the interference of two states may lift the degeneracy, and the resulting states have one half near the origin and another half around the surface, which realizes the Witten effect. However, the energy difference decays exponentially with the size of the system. The exact solution does not fully support the realization of the Witten effect in a topological insulator.