Transport through an AC-driven impurity: Fano interference and bound states in the continuum

Abstract

Using the Floquet formalism we study transport through an AC-driven impurity in a tight binding chain. The results obtained are exact and valid for all frequencies and barrier amplitudes. At frequencies comparable to the bulk bandwidth we observe a breakdown of the transmission T=0 which is related to the phenomenon of Fano resonances associated to AC-driven bound states in the continuum. We also demonstrate that the location and width of these resonances can be modified by tuning the frequency and amplitude of the driving field. At high frequencies there is a close relation between the resonances and the phenomenon of coherent destruction of tunneling. As the frequency is lowered no more resonances are possible below a critical value and the results approach a simple time average of the static transmission. J n j J J n New J. Phys. 19 (2017) 043029 S A Reyes et al 4.3. Inhomogeneous coupling to the impurity site ¢ ¹ J J Let us now go back to the tight binding model in order to explore what happens when we consider a different coupling to the impurity site ( ¢ ¹ J J ) corresponding to physical realizations where the coupling to the driven impurity may also differ from the ones along the chain.In figure 5 we show results for the transmission for a weaker hopping amplitude ¢ = J J 0.9 . While there are similarities to the homogeneous case discussed above, the resonances now start at a finite value of m > 0 according to equation (17). As can clearly be seen in the bottom part of figure 5 for w = J 3 accordingly there is a dip but no resonance for m = J , while the resonance at m = J 3 is relatively sharp. As shown in figure 6 (top) for larger hopping amplitude ¢ = J J 2 we observe a general increase in transmission across the parameter space and the resonances move to higher frequencies for a given energy of the incoming wave following equation (16). Correspondingly, the resonances are also displaced in energy at fixed frequency w = J 3 as shown in figure 6 (bottom). These features can be interpreted nicely by using the Fano resonances due to the 'side-attached' systems explained above and depicted in figure 2. It turns out that the two resonances we observe in figures 5 and 6 are Figure 4. Transmission coefficient in the limit of vanishing lattice spacing for  ¢ = 1 in units of 1/2m, i.e. for a quadratic dispersion relation with a local driving in form of a delta-function. 6 New J. Phys. 19 (2017) 043029 S A Reyes et alFigure 5. Transmission coefficient for modified coupling ¢ = J J 0.9 . Top: for a fixed energy  = -J 0.5 as a function of μ and ω. The dashed lines depict the analytic approximations for the location of the resonances at high frequencies (green), and close to where they emerge (red) from equation (15). Bottom: for fixed frequency w = J 3 .Figure 6. Transmission coefficient for modified coupling ¢ = J J 2 . Top: for a fixed energy  = -J 0.5 as a function of μ and ω. The red dashed lines depict the analytic approximations for the location of the resonances close to where they emerge from equation ...

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