Validity of the transfer Hamiltonian approach : application to the STM spectroscopic mode

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Abstract
Starting from a non-perturbative one electron Green's function method, we rederive Bardeen's perturbative expression for the tunneling current. We discuss its range of validity in terms of barrier thickness and reflection coefficients at the surfaces of the electrodes. At special energies corresponding to localized states, these latter may become large enough to invalidate the perturbative approach, and the question of the observability of such states in the spectroscopic mode of the Scanning Tunneling Microscope (STM) is raised