Effect of an applied electric field upon one-dimensional localization

The transmission coefficient of an electron interacting with a one-dimensional chain of variable length $L$ is calculated using a variation of standard transfer-matrix techniques. The potential energy with which the electron interacts consists of a random potential and a fixed static electric field. In this study, the random potential is modeled as a potential step on a lattice. Using the zero-temperature Landauer formula, the dimensionless resistance and, hence, the localization length are obtained. It is found that the presence of the electric field causes delocalization of the electron for all applied fields $F$.