How a Fano Resonance Crosses the Mobility Edge in Quantum Waveguides

Abstract

new scenario for the occurrence of a Fano resonance in the transmission probability of electron waveguides is investigated using a coupled-channel theory. Both a quantum dot and an antidot with either short- or finite-range interaction are embedded in the electron waveguide. Particularly, when the Fano resonance occurs close to the mobility edge (channel threshold), it is shown that Γ~U₁₂^4/3, where Γ is the resonance width and U₁₂ is the coupling strength between bound state and continuum. This is in contrast to the usual result Γ ~U₁₂², which is valid when the resonance occurs far from the mobility edge. Furthermore, it is shown that increasing the size of both dot and antidot leads to larger resonance width.