Internal field-assisted thermally activated hopping and tunnelling in insulators and composite materials

Abstract

A description of transport hopping processes at the Fermi surface in insulators is presented in which the role of internal fields is emphasized. Taking account of these fields up to the quadrupole term, we find that the conductivity σ at low applied fields obeys a ln(σ/σ 0 ) ≈ −(T 0 /T ) β law, with β varying from 1/2 to 1/4 as the temperature is raised. Typical orders of magnitude L ≈ 10 5 V cm −1 , Q ≈ 100 A 2 and d ≈ 3 √ Q for the field, the quadrupole moment and the dipole length respectively can be obtained from experimental data in the β = 1/2 and β = 1/4 regimes.

QUANTUM PERCOLATION AND CHARGE TRANSPORT IN HIGH Tc SUPERCONDUCTORS

“…where the exponent takes on the values 1/2, 1/3, 1/4 according to whether C[ , p or Q dominates [14].…”

“…Recently we have found that both cases are limiting cases of a single mechanism, i.e coulomb repulsion, with due care of the finite extension of the charge distribution on the sites, producing then a multipolar expansion, the Efros-Shklovskii law being the result of the leading coulomb term and the Mott's law the result of the quadrupolar term of the internal field experienced by carriers during hops [14] .…”