Embedding on to a one-dimensional crystal

Details Embedding on to a one-dimensional crystal Embedding on to a one-dimensional crystal

2010-03-11

arxiv.org/abs/1003.2282v1

Physics

Computational Physics

15 pages, 5 figures

Scientific paper

A simple expression is derived for the band structure of a one-dimensional periodic potential in terms of two solutions of the Schroedinger equation within the unit cell, one with a zero-derivative boundary condition on the left-hand end of the cell and the other with zero derivative on the right-hand end. From this starting point, a new expression is derived for the embedding potential - this can be added to the Hamiltonian for the surface region of a crystal to replace the semi-infinite substrate, in a one-dimensional approximation. The results are demonstrated in calculations of the band structure and embedding potential for Al in the [001] direction, and the surface electronic structure of the Al(001) surface.

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