High-field hopping magnetotransport in kesterites

Abstract Transport properties of the kesterite-like single crystals of Cu 2 ZnSnS 4 , Cu 2 ZnSn x Ge 1−x Se 4 and Cu 2 ZnGeS 4 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 Δ T v4  ∼ 50–150 K, 50–250 K and 100–200 K, respectively. In addition, the Shklovskii-Efros VRH conductivity below T v2  ∼ 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 Δ T v4 , respectively, are observed in these materials. In Cu 2 ZnSnS 4 , 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 Cu 2 ZnSn x Ge 1−x Se 4 and, especially, in Cu 2 ZnGeS 4 . 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 E n , the localization radius a , the acceptor concentration N A and the density of the localized states at the Fermi level, g (μ). A dramatic increase of a in Cu 2 ZnSnS 4 with decreasing T is observed, whereas in Cu 2 ZnSn x Ge 1−x Se 4 all the parameter W , E n , g (μ), a and N A are non-monotonic functions of x . Finally, in Cu 2 ZnGeS 4 the Hall coefficient R H ( T ) is negative (despite of the p -type conduction), exhibiting the dependence close to that of ρ ( T ) in the Mott VRH interval.