Metal-Insulator Transition in Neutron Transmutation Doped Ge

本文对低温（T=0.02-1 K）电子电导率σ在有磁场和无磁场情况下的标度分析，以确定无磁场电导率、有磁场电导率、介电常数和定域长度的临界指数μ、UNF '、s和ν。两个系列的Ge：Ga样品，一个是名义上未补偿的，另一个补偿比为0.32，已被采用。对于未补偿的样本系列，本文详细研究了0.90N_c<N<1.40N_c范围内的Ga浓度N，特别是0.99N_c<N<1.01N_c范围内的Ga浓度N，其中N_c是MIT的临界浓度，我们得到了未补偿系列μ[约等于]0.5（N>1.01N_c）μ[约等于]1.1（0.99N_c<N<1.01N_c）1.01N_c，且对于所有N和外加场B> 4 T，使用形式为σ（N，T）B=常数.τ T ^x '> f（N-N_c/T^y）和σ（N=常数，T，B）= T^x '> f（B_c-B/T^y），其中μ=x/y且INF'= x '/y'。在Efros-Shklovskii的变程跳跃理论框架下分析了绝缘样品的电阻率ρ，发现所有样品的电阻率ρ均与exp（T_0/T）^<1/2>有关系。对磁场的进一步分析导致确定临界指数ν[约等于]0.33和s[约等于]0.62（N<0.99N_c），以及ν[约等于]1.2和s[约等于]2.3（0.99N_c<N<N_c），即，Wegner标度律μ[近似等于]ν仅对N_c的±1%的小区域成立。将这些结果与补偿系列的结果进行比较，明确地表明，标称未补偿系列中N_c的±1%的小区域的特殊性是由于样品中可解释地存在的极小的补偿水平（小于0.1%），即，临界区域的宽度作为补偿的函数而改变。

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.