Electrical field effects near the metal-insulator transition

A detailed study of the nonlinear conductivity of two disordered alloys, ${\mathrm{Ge}}_{\mathrm{x}}$ ${\mathrm{Au}}_{1\mathrm{-}\mathrm{x}}$ and ${\mathrm{C}}_{\mathrm{x}}$ ${\mathrm{Cu}}_{1\mathrm{-}\mathrm{x}}$, is carried out near their metal-insulator transition on the metallic side for 1.3 K<T<4.2 K and for electric fields E up to 500 V/cm. Analyzing the σ(E) data in the context of an electron-gas–heating model yields unacceptably long electron relaxation times. Alternatively, the electric field can limit renormalization by pumping the electrons’ energy above the disordered potential. The system then changes from quantum-mechanical scaling to classically diffusive behavior beyond a certain length scale. The temperature and electric field data can then give the characteristic lengths and prefactors for the metal-insulator transition.