Chern-Simons orbital magnetoelectric coupling in generic insulators

Abstract

We present a Wannier-based method to calculate the Chern-Simons orbital magnetoelectric coupling in the framework of first-principles density-functional theory. In view of recent developments in connection with strong ${\mathbb{Z}}_{2}$ topological insulators, we anticipate that the Chern-Simons contribution to the magnetoelectric coupling could, in special cases, be as large or larger than the total magnetoelectric coupling in known magnetoelectrics, such as Cr${}_{2}$O${}_{3}$. The results of our calculations for the ordinary magnetoelectrics Cr${}_{2}$O${}_{3}$, BiFeO${}_{3}$, and GdAlO${}_{3}$ confirm that the Chern-Simons contribution is quite small in these cases. On the other hand, we show that, if the spatial-inversion and time-reversal symmetries of the ${\mathbb{Z}}_{2}$ topological insulator Bi${}_{2}$Se${}_{3}$ are broken by hand, large induced changes appear in the Chern-Simons magnetoelectric coupling.