Abstract
An eigenvalue problem of a finite linear chain (representing a thin film in the direction perpendicular to its surface) is formulated and solved exactly for the case when the first three boundary atoms located near the ends of the chain (the first three surface/subsurface monolayers of the film) are perturbed. The perturbation consists in a change of the diagonal (self-energies) as well as the off-diagonal (hopping) matrix elements of the respective tight-binding Hamiltonian. Exact solutions of this eigenproblem are obtained for the first time and analytic conditions for the existence of localized (surface and subsurface) states are determined and discussed in terms of the perturbation parameters involved.
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