  We develop a microscopic theory of the single impurity Kondo effect on a
metallic surface. We calculate the hybridization energies for the Anderson
Hamiltonian of a magnetic impurity interacting with surface and bulk states and
show that, contrary to the Kondo effect of an impurity in the bulk, the
hybridization matrix elements are strongly dependent on the momentum around the
Fermi surface. Furthermore, by calculating the tunneling conductance of a
scanning tunneling microscope (STM), we show that when the magnetic impurity is
located at a surface the Kondo effect can occur with equal strength between
bulk and surface states. We compare our results with recent experiments of Co
impurities in Cu(111) and Cu(100) surfaces and find good quantitative
agreement.
