Metal-insulator Transition in \({}^{70}\)Ge: Ga Semiconductor by Applying the Scaling Laws

Abstract

In this article, we focus on the scaling theory of Abraham et al. without and with a magnetic field on the metallic side of the Metal-Insulator Transition (MIT) for the three-dimensional system \({}^{70}\)Ge: Ga, at very low temperatures. In particular, we have determined the zero temperature conductivity critical exponent when the MIT transition occurs with the variation of the impurity concentration \((\upsilon=0.503)\) and with the application of a magnetic field \((\upsilon=1.06)\). We have also estimated the critical magnetic field \(B_C\) that separates the metallic behavior \((B<B_C)\) from the variable-range hopping regime \((B>B_C)\). The data are for a \({}^{70}\)Ge: Ga sample prepared and reported by Itoh et al., Physical Review Letters 77 (1996), 4058 and Watanabe et al., Physical Review B 60 (1999), 15817.