High-field hopping magnetotransport in kesterites

Transport properties of the kesterite-like single crystals of Cu2ZnSnS4, Cu2ZnSnxGe1−xSe4 and Cu2ZnGeS4 are investigated in pulsed magnetic fields up to B = 20 T. The Mott variable-range hopping (VRH) conduction is established by investigations of the resistivity, ρ (T), in all the materials mentioned above within broad temperature intervals of ΔTv4 ∼ 50-150 K, 50-250 K and 100-200 K, respectively. In addition, the Shklovskii-Efros VRH conductivity below Tv2 ∼ 3-4 K, the nearest-neighbour hopping (NNH) charge transfer between T ∼ 250-320 K and the conductivity by activation of holes on the mobility threshold at temperatures outside ΔTv4, respectively, are observed in these materials. In Cu2ZnSnS4, magnetoresistance (MR) contains only a positive contribution, connected mainly to a shrinkage of impurity wave functions by the magnetic field. At the same time, a negative contribution to MR, attributable to interference effects in VRH, is observed in Cu2ZnSnxGe1−xSe4 and, especially, in Cu2ZnGeS4. The joint analysis of the MR and ρ (T) data has yielded important electronic parameters of the materials. This includes widths of the acceptor band W and of the Coulomb gap Δ, the NNH activation energy En, the localization radius a, the acceptor concentration NA and the density of the localized states at the Fermi level, g (μ). A dramatic increase of a in Cu2ZnSnS4 with decreasing T is observed, whereas in Cu2ZnSnxGe1−xSe4 all the parameter W, En, g (μ), a and NA are non-monotonic functions of x. Finally, in Cu2ZnGeS4 the Hall coefficient RH (T) is negative (despite of the p-type conduction), exhibiting the dependence close to that of ρ (T) in the Mott VRH interval.