We present here extensive numerical simulations on electron transport in an impurity-band model for a doped semiconductor in the presence of site-diagonal disorder and long-range Coulomb interactions. The primary question we address is, what is the role of the finite-temperature particle-hole distribution on the conductance? At T=0, we find a soft Coulomb gap of the form ρ(${\mathit{E}}_{\mathit{F}}$)∼‖E-${\mathit{E}}_{\mathit{F}}$${\mathrm{\Vert }}^{1.17}$ for d=2 and ρ(${\mathit{E}}_{\mathit{F}}$)∼‖E-${\mathit{E}}_{\mathit{F}}$${\mathrm{\Vert }}^{2.38}$ for d=3. An analysis of the distribution of particles and holes at T=0 reveals that sites with small excitation energies in the ground state are segregated into particle and hole clusters of varying radii. The role of such clusters in the transport process is examined. It is observed that the conductance calculated within single-particle transport theory obeys the expected granular metal law of σ=${\mathrm{\sigma }}_0$ exp[-(${\mathit{T}}_0$/T${)}^{1/2}$] in d=2,3 when the T=0 ground-state configuration of the particles and holes is used to compute the conductance. At finite temperature, we find that the Coulomb gap fills in as ρ(${\mathit{E}}_{\mathit{F}}$)∼${\mathit{T}}^{\mathit{d}\mathrm{-}1}$. However, we observe that the conductance is activated, σ=${\mathrm{\sigma }}_0$ exp(-${\mathit{T}}_{\mathit{a}}$/T), even at very low temperatures when the finite-temperature distribution of particles and holes is used to compute the conductance in d=3. Only slight deviations from ${\mathit{T}}^{\mathrm{-}1/2}$ were observed in d=2. Our results suggest then that the precise origin of the σ=${\mathrm{\sigma }}_0$ exp[-(${\mathit{T}}_0$/T${)}^{1/2}$] law for the conductance in strongly correlated systems is unclear. The relevance of our findings to experiments on doped magnetic semiconductors which observe activated as opposed to ${\mathit{T}}^{\mathrm{-}1/2}$ transport is discussed.

• Received 14 October 1993

DOI:https://doi.org/10.1103/PhysRevB.49.10269