Optical characterization of Bi$_2$Se$_3$ in magnetic field: evidence for magneto-electric coupling

We present an infrared magneto-optical study of Bi$_2$Se$_3$, one of a class of materials recently shown to exhibit topological surface states due to spin-orbit coupling. Far- and mid-infrared (IR) reflectance and transmission measurements have been performed in magnetic fields oriented both parallel and perpendicular to the trigonal $c$ axis of this layered material, and supplemented with UV-visible ellipsometry to obtain the optical conductivity $\sigma_1(\omega)$. With lowering of temperature we observe narrowing of the Drude conductivity due to reduced quasiparticle scattering, as well as the increase of the band gap absorption edge. Magnetic fields $H \parallel c$ produce dramatic effects in the far-IR, revealing significant magneto-electric coupling. For the perpendicular field orientation, a new feature is observed in the far-IR, and the plasma edge is slightly shifted to higher energies. In both cases the band gap edge is softened in magnetic field.