Spin Fano Resonances and Control in Two-Dimensional Mesoscopic Transport

Abstract

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 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 exploited 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 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.

A Chirality-Based Quantum Leap

“…The idea originates from recent studies to control spin polarization by exploiting classical chaotic dynamics 370 , 371 and spin Fano resonances. 372 …”

“… 373 Recently, a Fano formula was discovered to characterize the resonances associated with two fundamental quantities underlying spin transport: the spin-resolved transmission and the spin polarization vector. 372 A Green’s function formalism was generalized to describe spin transport and the Fisher-Lee relation was used to compute the spin-resolved transmission matrix, enabling the spin polarization vector to be calculated and leading to a universal Fano formula for spin resonances. The resonance width depends on the nature of the classical dynamics, as defined by the geometric shape of the dot, and this property could be exploited for control.…”

Spin Fano Resonances in Chiral Molecules: An Alternative Mechanism for the CISS Effect and Experimental Implications

“…Using chiral polyacetylene molecules of different number of carbon atoms, we find the occurrences of various resonance peaks in the curve of spin polarization versus the electron energy. Extending the recently derived formula of spin Fano resonances for transport through a two-dimensional mesoscopic quantum dot to complex molecules, we obtain a general formula for spin Fano resonances, which can be important to quantum biology. Our formula is more general than previous formulas in electronic transport through solid-state devices, because it includes multiple energy levels.…”

“…In electronic transport through mesoscopic, solid-state systems, various resonances in experimental quantities such as conductance and scattering cross sections can arise and are described by the universal Fano formula. , In terms of spin transport, resonances in the spin polarization arising from the edge of a zigzag graphene nanoribbon were studied using the nonequilibrium Green’s function formalism within the framework of density functional theory . Quite recently, a Fano formula characterizing the resonances associated with spin transport was derived . In quantum biology, there were studies of Fano resonances in molecular charge transport. , For example, control of electronic transport through Fano resonances in molecular wires was investigated using a first-principle approach, where the resonances are induced and can be controlled by the side groups attached to the molecule .…”

Electronic transport in three-terminal chaotic systems with a tunnel barrier

“…Interest in the mesoscopic regime stems from to the fact that electrons can maintain phase coherence throughout the process, leading to observable quantum effects. One of the most important examples of ballistic mesoscopic sample are the chaotic semiconductor billiards, one of the platforms for studying quantum chaos [6,7,8,9,10], the interplay between quantum properties and chaotic dynamics [11,12,13].…”