Localized electron states in the continuous spectrum of the Cu(001) monolayer

The results of the calculation of electron bands of bound states that cross the edge of the continuous spectrum for the (001) fcc copper monolayer are presented for the first time. The calculations are performed in the local approximation for the exchange and correlations using the film variant of the Green's function technique. Symmetry of electron states near the edge of the continuous spectrum is explored. It is found that there are bound states along the $\bar\Sigma$ direction of the two-dimensional Brillouin zone of the Cu(001) monolayer that are embedded in the continuum of delocalized states of the continuous spectrum. Along the $\bar\Delta$ and $\bar{Y}$ directions, bands of bound states turn into resonance states after crossing the edge of the continuous spectrum.