Topological Magneto-Electric Effect Decay

TL;DR

This paper investigates how realistic disorder affects the decay of the topological magneto-electric effect, showing that the effective magnetic monopole near a topological insulator surface retreats at a speed proportional to conductivity, with specific results for massive Dirac surface states.

Contribution

It provides a detailed analysis of the decay dynamics of the topological magneto-electric effect considering disorder and conductivity effects, including the monopole retreat speed and surface state behavior.

Findings

Magnetic monopole retreats at speed v_M = α c g due to conductivity.

Hall currents vanish at T=0 once surface charge screens the external potential.

Disorder influences the decay rate of the topological magneto-electric effect.

Abstract

We address the influence of realistic disorder on the effective magnetic monopole that is induced near the surface of an ideal topological insulator (TI) by azimuthal currents which flow in response to a suddenly introduced external electric charge. We show that when the longitudinal conductivity $\sigma_{xx} = g (e^2/h)$ is accounted for, the apparent position of a magnetic monopole initially retreats from the TI surface at speed $v_{M} = \alpha c g$, where $\alpha$ is the fine structure constant and $c$ is the speed of light. For the particular case of TI surface states described by a massive Dirac model, we further find that the temperature T=0 Hall currents vanish once the surface charge has been redistributed to screen the external potential.