Canal states in bilayer thin films of zero-range potentials

Canal (discrete, 2D-localized) states embedded in continuum are studied for a particle interacting with thin 3D layer of 2D-periodic zero-range potentials. General analysis is presented for a “molecular monolayer” obtained by 2D periodic mapping of N different zero-range scatterers. Numerical calculations of canal states are performed for the case of an atomic bilayer on a square lattice. For particle scattering on this system we demonstrate the manifestations of canal states in impact-energy and impact-angles dependence of total reflection/transmission probabilities. Special cases when energy eigenvalues of the canal states tend to scattering thresholds are also analyzed. Graphical abstract