Surface properties of solids using a semi-infinite approach and the tight-binding approximation

A semi-infinite approach (rather than a slab method or finite number of layers) is used to treat surface properties such as wave functions, energy levels, and Fermi surfaces of semi-infinite solids within the tight-binding (TB) approximation. Previous single-band results for the face-centered cubic lattice with a (111) surface and for the simple cubic lattice with a (001) surface are extended to semi-infinite layers, while the extension to calculations of other surfaces is straightforward. Treatment of more complicated systems is illustrated in the calculation of the graphite (0001) surface. Four interacting bands are considered in the determination of the wave functions, energies, and Fermi surface of the graphite (0001) surface. For the TB model used, the matrix elements in the secular determinants for the semi-infinite solid and for the infinite bulk solid obey the same expressions, and the wave functions are closely related. Accordingly, the results for the bulk system can then be directly applied to the semi-infinite one. The main purpose of the present paper is to provide wave functions and other properties used elsewhere to treat phenomena such as scanning tunneling microscopy and electron transfer rates at electrodes.