Multi-continuum Fano resonance in coupled quantum point contacts: A manifestation of the "integral" Fano formula

We discuss how a pair of quantum point contacts (QPCs), which are coupled to each other via their mutual wavefunction overlap with a common continuum, can be used to provide a realization of a multi-continuum Fano resonance. This behavior arises from the multi-subband character of the QPCs, each of whose transverse subbands may be viewed as providing a unique continuum. Reminiscent of the original analysis of Fano, we show that the resonance exhibited by this system can be defined in terms of an asymmetry parameter (q) and characteristic level broadenings (Γ Γ₀), although these parameters now determine the resonance lineshape through their inclusion in energy integrals, a result that we refer to as the integral Fano formula. We also demonstrate how, dependent upon the effective dimensionality of the detector QPC that exhibits the Fano resonance, the resonance amplitude can significantly exceed the one-dimensional conductance quantum (2e²/h). Our experimental and theoretical results, therefore, provide further support for the scenario of spontaneous bound-state formation in QPCs near pinch-off and suggest that this bound state may be used to study new aspects of Fano-resonance phenomenology.