Fano resonances in transport across a quantum well in a tilted magnetic field.

Asymmetric Fano resonances are predicted to occur in the linear electronic conductance across a shallow quantum well in a high magnetic field. The Fano lineshape results from the interference between direct transmission and transmission via a quasi-bound state in the well which is weakly mixed with the continuum by tilting the field. The resonance width increases with tilt angle but general S-matrix theory predicts that the lineshapes remain approximately unchanged upon rescaling of the field. This reflects a general property of Fano resonances which may be tested for the first time experimentally. Resonances in electronic transport are of great interest in microstructures both as a basis for new device concepts and for characterization of heterostructures. Resonant tunneling devices operating at room temperature have become possible since three-dimensional heterostructures can be grown with atomic precision [1]. However recently a number of theoretical studies [2, 3, 4, 5, 6, 7, 8, 9, 10] have addressed resonances in quantum wire structures without large tunnel barriers. Typically these systems are calculated to exhibit asymmetric Fano resonances as opposed to the familiar symmetric Breit-Wigner (BW) lineshape. However no experiment has unambiguously observed asymmetric resonances in quantum wire devices (although there is some evidence for asymmetric resonances mediated by impurities [11] in the measurements of McEuen et al. [12]). It is likely that the quantum wire devices fail to demonstrate clear Fano resonances because of the lack of imperfections arising from the lack of a true epitaxial fabrication procedure for these devices[13]. Since the Fano lineshape represents the most general form for an isolated resonance it would be interesting to find such resonances experimentally in electronic transport and test aspects of scattering theory inaccessible in standard scattering experiments on atoms and nuclei. To this end we will show below that a certain type of 3D heterostructure in a tilted magnetic field should exhibit Fano resonances just as in the ideal quantum wire systems. However given the precision of heteroepitaxy it is much more likely that the experiments on such heterostructures will yield results consistent with the theory for the ideal structure.