  As the fundamental quantum mechanical theory predicts, it is believed that
electronic states can be bound only to potential wells and not to potential
barriers in any dimension and their energies should be below the background
potential. However, with the help of atomic lattice potentials with a flat
electron band in momentum space in the background, an atomically thin 1D
potential barrier can possess barrier-centered bound states above the
background potential. Here we provide a theoretical proof using Green function
pole analysis with Dyson equation that shows the existence of
barrier-bound-states whose energy is elevated from the flat band energy nearly
by the barrier height. The phenomenon is believed to be independently confirmed
in a system of Pd monolayer on a flat oxide substrate with Stoner
ferromagnetism using spin-polarized STM technique and through comparison with
real-space QPI simulations using realistic 2D Pd band structure.
