Determination of the Critical Conductivity Exponent for the Metal-Insulator Transition at Nonzero Temperatures: Universality of the Transition

Abstract

A new approach has been developed for the determination of the critical conductivity exponent \ensuremath{\mu} and the critical concentration ${N}_{c}$ of the metal-insulator transition without extrapolation of the temperature dependence of the conductivity $\ensuremath{\sigma}(T)$ to $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$. We propose to replace $\ensuremath{\sigma}(0)$ by $\ensuremath{\Delta}\ensuremath{\sigma}({T}^{*})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\sigma}}_{N}({T}^{*})\ensuremath{-}{\ensuremath{\sigma}}_{{N}_{c}}({T}^{*})$ at low ${T}^{*}$, where $\ensuremath{\sigma}(T){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}a+bT}^{p},p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ or 1/3 is observed. Two series of samples of Ge:As and Ge:Sb were investigated. It is shown that $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ for both series. The normalized values of $\ensuremath{\Delta}\ensuremath{\sigma}({T}^{*})/\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\sigma}}$ merge for Ge:As, Ge:Sb, Si:P, and Si:Sb into a universal line.