Signature of electronic correlations in the optical conductivity of the doped semiconductor Si:P

Electronic transport in highly doped but still insulating silicon at low temperatures is dominated by hopping between localized states; it serves as a model system of a disordered solid for which the electronic interaction can be investigated. We have studied the frequency-dependent conductivity of phosphorus-doped silicon in the terahertz frequency range (30 GHz-3 THz) at low temperatures T >= 1.8 K. The crossover in the optical conductivity from a linear to a quadratic frequency dependence as predicted by Efros and Shklovskii [Sov. Phys. JETP 54, 218 (1982)] is observed qualitatively; however, the simple model does not lead to a quantitative agreement. Covering a large range of donor concentration, our temperature- and frequency-dependent investigations reveal that electronic correlation effects between the localized states play an important and complex role at low temperatures. In particular, we find a superlinear frequency dependence of the conductivity that highlights the influence of the density of states, i.e., the Coulomb gap, on the optical conductivity. When approaching the metal-to-insulator transition by increasing doping concentration, the dielectric constant and the localization length exhibit critical behavior.