Low-field negative magnetoresistance in the variable-range-hopping regime in copper indium diselenide

Study of the temperature and magnetic-field dependence of the negative magnetoresistance in the Mott variable-range-hopping regime is made on n-type ${\mathrm{CuInSe}}_2$. The relative magnetoresistance Δρ/ρ(0) is found to be proportional to ${\mathit{T}}^{\mathrm{-}\mathrm{\alpha }}$ ${\mathit{B}}^2$ in the low-field region below about 0.35 T. Below 4 K, where ${\mathit{R}}_{\mathrm{hop}}$/ξ≥1.5, it is observed that α=3/4. This confirms, to our knowledge for the first time, the theories based on quantum interferences for the negative magnetoresistance in the variable-range-hopping regime. However, α=1.22 above 4 K where ${\mathit{R}}_{\mathrm{hop}}$/ξ