Resonance line shapes in quasi-one-dimensional scattering

Abstract

In various recent model calculations on the transport properties of microstructures, transmission resonances have been found that exhibit the asymmetric Fano line shape. In particular, one often encounters points of vanishing transmission or reflection as a resonance is crossed. The interference effects that cause this phenomenon are identified in this paper using first a coupled-channel theory that starts from the full scattering Hamiltonian and second a more general S-matrix approach. The latter is model independent and thus yields predictions for the possible line shapes in a wide variety of systems. Model-independent results are desirable because knowledge of the microstructure potentials is often incomplete. We show for the most general multiprobe, multisubband structure that the total transmission never varies by more than unity on resonance, generalizing a result previously known only for resonant tunneling structures. The role of symmetry is investigated to clarify which features (e.g., reflection zeros) are a consequence of special invariance properties and which are robust in the unsymmetric case. The effect of a resonance is found to decrease with an increasing number of leads in a rotationally symmetric structure. Only in a two-probe geometry can zeros in transmission and reflection occur together for a single resonance. The known result that resonances in symmetric resonant tunneling devices always display exactly unit variation of the transmission is shown to be violated in structures where the nonresonant transmission exceeds 1. Time reversal invariance is not required in the present treatment. Two model systems displaying asymmetric resonances are discussed. Their advantage is that the resonance lifetime can be tuned externally, making it possible to test a scaling property of the Fano line shape that we derive below.