Abstract

Three-dimensional topological insulators possess surface-conducting states in the bulk energy gap, which are topologically protected and can be well described as helical 2 + 1 Dirac fermions. The electromagnetic response is given by axion electrodynamics in the bulk, leading to a Maxwell-Chern-Simons theory at the boundary, which is the source of the Hall conductivity. In this paper, we extend the formulation of axion electrodynamics such that it captures higher-derivative corrections to the Hall conductivity. Using the underlying 2 + 1 quantum field theory at the boundary, we employ thermal field theory techniques to compute the vacuum polarization tensor at finite chemical potential in the zero-temperature limit. Applying the derivative expansion method, we obtain higher-order derivative corrections to the Chern-Simons term in 2 + 1 dimensions. To first order the corrections, we find that the Hall conductivity receives contributions proportional to omega 2 and k2 from the higher-derivative Chern-Simons term. Finally, we discuss the electrodynamic consequences of these terms on the topological Faraday and Kerr rotations of light, as well as on the image monopole effect.