Temperature-Frequency Scaling in Amorphous Niobium-Silicon near the Metal-Insulator Transition

Millimeter-wave transmission measurements have been performed in amorphous niobium-silicon alloy samples where the dc conductivity follows the critical temperature dependence σdc∝T1/2. The real part of the conductivity is obtained at eight frequencies in the range 87--1040 GHz for temperatures 2.6 K and above. In the quantum regime (ω>kBT) the real part of the high-frequency conductivity has a power-law frequency dependence Reσ(ω)∝ω1/2. For temperatures 16 K and below the data exhibit temperature-frequency scaling predicted by theories of dynamics near quantum-critical points.