Theory of nonlinear quantum tunneling resistance in one-dimensional disordered systems

A novel generalized Landauer formula is derived and used to study the voltage-dependent resistance in a one-dimensional (1D) disordered system. A finite voltage difference introduces energy integration and gives the system self-averaging behavior to a certain extent. The quantum resistance of a 1D system generally shows a rich structure in its dependence on applied voltage and length. Resistance fluctuations are shown to decrease with increasing voltage. In spite of the self-averaging, the mean resistance at large voltage turns out to scale superlinearly with length.