Topological Magnetoelectric Effect Decay

We address the influence of realistic disorder and finite doping on the effective magnetic monopole induced near the surface of an ideal topological insulator (TI) by currents that flow in response to a suddenly introduced external electric charge. We show that when the longitudinal conductivity sigma(xx) = g(e(2)/h) not equal 0, the apparent position of a magnetic monopole initially retreats from the TI surface at speed v(M) = alpha cg, 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 when the external potential is screened.