Spin Fano Resonances and Control in Two-Dimensional Mesoscopic Transport

In electronic transport through mesoscopic systems, the various resonances in quantities such as conductance and scattering cross sections are characterized by the universal Fano formula. Does a similar formula exist for spin transport? We provide an affirmative answer by deriving a Fano formula to characterize the resonances associated with two fundamental quantities underlying spin transport: Spin-resolved transmission and the spin polarization vector. In particular, we generalize the conventional Green's function formalism to spin transport and use the Fisher-Lee relation to obtain the spin-resolved transmission matrix, which enables the spin polarization vector to be calculated, leading to a universal Fano formula for spin resonances. Particularly, the theoretically obtained resonance width depends on the nature of the classical dynamics as determined by the geometric shape of the dot. We explicitly demonstrate this fact and argue that it can be used to smooth out or even eliminate Fano spin resonances by manipulating the classical dynamics, which can be realized by applying or withdrawing a properly designed local gate potential. Likewise, modulating the classical dynamics in a different way can enhance the resonance. This is of particular importance in the design of electronic switches that can control the spin orientation of the electrons associated with the output current through weakening or enhancement of a Fano resonance, which are a key component in spintronics.