We present an infrared magneto-optical study of the highly thermoelectric narrow-gap semiconductor Bi$_2$Se$_3$. Far-infrared and mid-infrared (IR) reflectance and transmission measurements have been performed in magnetic fields oriented both paralle
l 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 in the absorption edge due to direct electronic transitions. Magnetic fields $H parallel c$ dramatically renormalize and asymmetrically broaden the strongest far-IR optical phonon, indicating interaction of the phonon with the continuum free-carrier spectrum and significant magnetoelectric coupling. For the perpendicular field orientation, electronic absorption is enhanced, and the plasma edge is slightly shifted to higher energies. In both cases the direct transition energy is softened in magnetic field.
