Quantum-critical conductivity scaling for a metal-insulator transition

Temperature (T)- and frequency (omega)-dependent conductivity measurements are reported here in amorphous niobium-silicon alloys with compositions (x) near the zero-temperature metal-insulator transition. There is a one-to-one correspondence between the frequency- and temperature-dependent conductivity on both sides of the critical concentration, thus establishing the quantum-critical nature of the transition. The analysis of the conductivity leads to a universal scaling function and establishes the critical exponents. This scaling can be described by an x-, T-, and omega-dependent characteristic length, the form of which is derived by experiment.