Fano Resonances for Tilted Linear and Quadratic Band Touching Dispersions in a Harmonically Driven Potential Well

Abstract

Considering models with tilted linear and quadratic band touching dispersions, the effect of the transverse linear tilt on the transmission spectra is analyzed through a harmonically driven potential well oriented longitudinally. Employing the Floquet scattering matrix formalism, Fano resonances are found as an outcome of matching between the Floquet sidebands and quasi‐bound states, where the tilt renormalizes their energies and wave vectors. It is found 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. The shot noise spectra and their differential property are further studied where an inflection region and undulation, respectively, is found 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.

Fano resonances in tilted Weyl semimetals in an oscillating quantum well

“…The momenta k y,z are considered in units of 10 −9 m −1 . The length of the potential barrier L is in units of 10 −9 m. One can increase L and consider it in units of L −6 m but the transmission spectra remain qualitatively unaltered [60,61,63]. The above choices of the parameters restrict the low-energy model, described in equation ( 1), to have energy in the meV regime.…”

“…We now choose to subject this system to a harmonically driven quantum well of width L in the x-direction. The potential V(t) for the well is defined as [59,63,64],…”

“…Hence, we only work with n = 0 case. From the S matrix, we can define the total transmission coefficient T as [59,63,64]…”

“…Previous literature has dealt with the Fano resonance structure of Dirac [60] and Weyl systems [62] employing Floquet theory in the presence of a harmonically driven potential well. However, there is not much commentary on the consequences of tilt in the energy dispersion on Fano resonances in these cases [63]. Considering the fact that tilt appears to be a key factor in manipulating the transport properties of WSMs as described previously [22][23][24], and motivated by the intricacies of Fano resonances, we examine the role of tilting on Fano resonances in three-dimensional WSMs in this work.…”