Electrical properties of isotopically enriched neutron-transmutation-doped70Ge:Ganear the metal-insulator transition

We report low-temperature carrier transport properties of a series of nominally uncompensated neutron-transmutation-doped ${}^{70}\mathrm{G}\mathrm{e}:\mathrm{G}\mathrm{a}$ samples very close to the critical concentration $N_c$ for the metal-insulator transition. The nine samples closest to $N_c$ have Ga concentrations $N$ in the range ${0.99N}_c<N<\mathrm{}{1.01N}_c.$ The electrical conductivity σ has been measured in the temperature range $T=0.02\mathrm{}–1\mathrm{K}.$ On the metallic side of the transition the standard $\sigma {\mathrm{}\left(T\right)=a+bT}^q$ with $q=1/2\mathrm{}$ was observed for all the samples except for the two that are closest to $N_c$ with $N$ between $N_c$ and ${1.0015N}_c.$ These samples clearly show $q=1/3.\mathrm{}$ An extrapolation technique has been developed in order to obtain the zero-temperature conductivity σ(0) from $\sigma \mathrm{}\left(T\right)\mathrm{}$ with different dependence on $T.\mathrm{}$ Based on the analysis, $\nu \approx 0.5$ in the familiar form of $\sigma \mathrm{}\left(0\right)\mathrm{}\propto {(N/N}_c-{1)}^{\nu }$ has been found. On the insulating side of the transition, variable range hopping resistivity $\rho \mathrm{}\left(T\right)\mathrm{}\propto \exp {(T}_0{/T)}^p$ with $p=1/2\mathrm{}$ has been observed for all the samples having $N<\mathrm{}{0.991N}_c.$ In this regime $T_0\propto (1\mathrm{}-{N/N}_c{)}^{\alpha }$ with $\alpha \approx 1$ as $\overrightarrow{N}{N}_c.$ The values of $T_0$ agree very well with theoretical estimates based on the modified Efros and Shklovskii relation