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 $T^{1/2}$. 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 ($\hbar \omega > k_B T$) the real part of the high-frequency conductivity has a power-law frequency dependence $Re~\sigma(\omega) \propto \omega^{1/2}$. For temperatures 16 K and below the data exhibits temperature-frequency scaling predicted by theories of dynamics near quantum-critical points.