Electric-field-dependent resistance moments in one-dimensional disordered systems.

Abstract

We study analytically the effect of a finite electric field on the ensemble-averaged resistance (\ensuremath{\rho}) and on its fluctuations for a one-dimensional disordered conductor of length L. We use an invariant-imbedding approach, properly generalized to include the effect of a constant electric field. From this approach we derive differential recursion relations for the resistance moments, using the Landauer formula and assuming, as usual, that the modulus and phase of the reflection amplitude of the conductor are distributed independently. The length scale dependence of the average resistance crosses over from an exponential to a power-law (${L}^{\ensuremath{\alpha}}$) behavior with increasing field strength. F. We find \ensuremath{\alpha}\ensuremath{\approxeq}1/F when the distribution of phases is uniform and \ensuremath{\alpha}\ensuremath{\approxeq}const when it is nonuniform. Other effects of the applied field, as well as comparison with previous work of Vijayagovindan, Jayannavar, and Kumar [Phys. Rev. B 35, 2029 (1987)], are also discussed.