Highly convergent schemes for the calculation of bulk and surface Green functions

The surface and bulk densities of states of a solid described by the stacking of principal layers are obtained by means of an iterative procedure which allows (i) the inclusion of 2n layers after n iterations, (ii) the simultaneous calculation of the Green functions for both the 'right' and 'left' surfaces as well as for the bulk (or central) principal layer, and (iii) the use of imaginary parts eta as small as one wishes in the energy without any large increase in computing time, so that the limit eta to 0 can really be obtained. As a by-product the authors obtain (i) the 'right' and 'left' transfer matrices of the 'effective field' or continuous fraction approach and (ii) a factorisation theorem which relates the Green functions of both surfaces to the Green functions of both surfaces to the Green functions of the bulk and the free metal atom.