Green-function study of electrified solids

Abstract

When a tight-binding chain of atoms is subjected to an electric field, its electronic energy spectrum takes on the form of the Wannier-Stark ladder. For such a system, successive use of the Dyson equation enables the recursive Green function to be derived analytically as a continued fraction, which can be expressed as a ratio of Bessel functions. The site representation of the Green function provides access to the local density of states. The versatility of this technique is illustrated via its application to infinite, semi-infinite and finite chains, as well as systems constructed piecewise from these components. In particular, the Wannier-Stark effect on surface states, hydrogen chemisorption on electrified substrates and electron transmission of molecular switches are investigated.