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 ${\sigma }_{\mathrm{dc}}\propto T^{1/2}$. 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 $(ħ\omega >k_{B}T)$ the real part of the high-frequency conductivity has a power-law frequency dependence $\mathrm{Re}\sigma \left(\omega \right)\propto {\omega }^{1/2}$. For temperatures 16 K and below the data exhibit temperature-frequency scaling predicted by theories of dynamics near quantum-critical points.