2010/03/11 by Inglesfield, J. E.
#Computational Physics (physics.comp-ph) #FOS: Physical sciences #Other Condensed Matter (cond-mat.other)
paper · doi:10.48550/arxiv.1003.2282
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.