Discrete levels in the continuum and tunneling

We investigate electron localization and tunneling in a quasi-one-dimensional nanochannel with two attracting impurities. We solve the one-electron problem for a short-range interaction with the impurity and obtain expressions for the scattering amplitude, the wave function, and the electron spectrum. We show that coherent interaction of the Fano resonances leads to a new phase-coherent effect, the collapse of the resonance–antiresonance pairs and the disappearance of resonances. Consequently, the system acquires discrete levels in the continuum for certain critical parameters. We analyze electron tunneling through the discrete levels in detail and show that a certain type of degeneration, with one of the states belonging to the discrete spectrum and the other propagating, can occur in this case.