Metal-Insulator Transition in Neutron Transmutation Doped Ge

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We report on the scaling analysis of the low temperature (T=0.02-1 K) electronic conductivity σ with and without magnetic fields in order to determine the critical exponents μ, μ', s, and ν of the conductivity without magnetic fields, conductivity with magnetic fields, dielectric constant, and localization length, respectively. Two series of Ge : Ga samples, one that is nominally uncompensated and the other with the compensation ratio 0.32, have been employed. For the uncompensated series of samples, Ga concentration N of the range 0.90N_c<N<1.40N_c with the special focus on the region 0.99N_c<N<1.01N_c where N_c is the critical concentration for MIT has been studied in detail.We have obtained for the uncompensated series μ【approximately equal】0.5 for N>1.01N_c μ【approximately equal】1.1 for 0.99N_c<N<1.01N_c, and μ'【approximately equal】1.1 for all N and for applied fields B>4T using the finite temperature scaling of the forms σ (N,T) ∝ T^xf (N-N_c/T^y), σ (N, T, B=const.) ∝ T^<x'>f (N-N_c/T^y) and σ (N=const., T, B) ∝ T^<x'>f (B_c-B/T^y) with μ=x/y and μ'=x'/y'. The resistivity ρ of the insulating samples has been analyzed in the framework of Efros-Shklovskii's variable range hopping theory and the relation ρ^∝T^<1/3>exp(T_0/T)^<1/2> has been found for all samples. A further analysis with magnetic fields has lead to determination of critical exponents ν【approximately equal】0.33 and s【approximately equal】0.62 for N<0.99N_c, and ν【approximately equal】1.2 and s【approximately equal】2.3 for 0.99N_c<N<N_c, i.e., Wegner's scaling law μ【approximately equal】ν holds only for the small region ±1% of N_c. Comparison of these results with that of the compensated series demonstrates unambiguously that the special features of the small region, ±1% of N_c in nominally uncompensated series appear due to an extremely small level of compensation (less than 0.1%) that unavoidably presents in the samples, i.e., the width of the critical region changes as a function of the compensation.