MODIFIED LANCZOS PROCEDURE FOR WANNIER-STARK RESONANCES IN SOLIDS

We present a real-space analysis of Wannier-Stark resonances based on an extension of the Lanczos iterative procedure. Our method is well su ited for multiband structures also in the presence of Zener tunneling. It can be applied to systems of very large dimensions with superimpos ed uniform electric fields of arbitrary strength and provides a valuab le tool for the study of the degree of localization of the wave functi ons at the Wannier-Stark energies. As an example, the method is applie d to one-dimensional single- and two-band tight-binding Hamiltonians.