Fano resonances for tilted linear and quadratic band touching dispersions in a harmonically driven potential well

TL;DR

This paper investigates how tilt in linear and quadratic band touching dispersions affects Fano resonances and shot noise in a harmonically driven potential well, revealing tunable signatures and potential experimental observables.

Contribution

It introduces a Floquet scattering matrix approach to analyze tilt effects on Fano resonances and shot noise, highlighting their dependence on transverse momentum and tilt strength.

Findings

Fano resonance energy shifts with transverse momentum and tilt sign.

Tilt allows tuning of Fano resonance energies.

Shot noise spectra show characteristic inflections near Fano resonances.

Abstract

Considering models with tilted linear and quadratic band touching dispersions, we analyze the effect of the transverse linear tilt on the transmission spectra through a harmonically driven potential well oriented longitudinally. Employing the Floquet scattering matrix formalism, we find Fano resonances as an outcome of matching between the Floquet sidebands and quasi-bound states, where the tilt renormalizes their energies and wave vectors. We find that the Fano resonance energy decreases (increases) for linear (quadratic) band touchings as the magnitude of the transverse momentum increases, indicating a distinct signature of the underlying band dispersion in the transmission profile. The sign of the product of the transverse momentum and the tilt also determines the relative shift in the Fano resonance energy with respect to the untilted case for both band dispersions, suggesting a possible tunability of the Fano resonance for tilted systems. Importantly, the tilt strength can also be directly determined by measuring the Fano resonance energy as function of the transverse momenta direction. We furthermore study the shot noise spectra and their differential property where we find an inflection region and undulation, respectively, around the Fano resonance energy. Interestingly, differential shot noise and transmission spectra both qualitatively behave in a similar fashion and might thus serve as important observables for future experiments on driven solid-state systems.