The surface-state of the topological insulator Bi$_2$Se$_3$ revealed by cyclotron resonance

To date transport measurements of topological insulators have been dominated by the conductivity of the bulk, leading to substantial difficulties in resolving the properties of the surface. To this end, we use high magnetic field, rf- and microwave-spectroscopy to selectively couple to the surface conductivity of Bi$_2$Se$_3$ at high frequency. In the frequency range of a few GHz we observe a crossover from quantum oscillations indicative of a small 3D Fermi surface, to cyclotron resonance indicative of a 2D surface state.