Low-frequency non-Gaussian conductance fluctuations in Si near the insulator-metal transition

In this work we review the investigations of conductance fluctuations in doped silicon at low temperatures (2K < T < 20K) as it is tuned through the metal-insulator transition by changing the carrier concentration n. Spectral power, S(f), of the conductance fluctuation retains a generic $1/f^\alpha$ dependence. In the metallic regime $(n>n_c)$ the doped Si is like a weakly-localized electron system and the conductance fluctuation is governed by the mechanism of Universal conductance fluctuations. The relative variance of fluctuation follows the temperature dependence $\alphaT-\beta,$ where $^\beta$ $\approx 1/2.$ However, the noise diverges by orders of magnitude as n decreases through the critical concentration $n_c$ and the fluctuation also becomes strongly temperature dependent with $\beta>> 1.$ At the transition $(n/n_c \approx1)$ the fluctuation becomes strongly non-Gaussian below 20K as observed through the second spectrum $S^{(2)}(f).$ At T=4.2K, we find that after subtracting the Gaussian background , $S^{(2)}(f)\alpha 1/f^p$ where p is small (< 0.5) for metallic samples $(n/n_c \geq 1.5)$ and it grows to > 1 for samples close to the transition $n/n_c \approx 1.$ The growth of non-Gaussianity is accompanied by a growth in low frequency spectral weight as seen through a significant enhancement of $\alpha$ from close to $1 (n>n_c)$ to nearly 1.4 for $n/n_c \approx 1.$ The growth of non-Gaussian fluctuation of extremely large magnitude with significant low frequency component points to a correlated low frequency dynamics of charge fluctuation near the insulator-metal transition. This has been interpreted as the onset of a glassy freezing of the electronic system across the transition