Quantum resonance catastrophe for conductance through a periodically driven barrier

Thuberg, Daniel; Reyes, Sebastian; Eggert, Sebastian

doi:10.1103/physrevb.93.180301

Cited by 24 publications

(38 citation statements)

References 45 publications

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“…For any given energy ϵ σ it is possible to find a frequency ω so that there are always zero transmission points given by Equation . Equation is valid for

J^{'} \geq J

true(β \leq 0 true)

, i.e., the strong coupling regime.…”

Section: Resultsmentioning

confidence: 99%

Berry‐Phase in a Periodically Driven Single Molecule Magnet Transistor

González

2019

Physica Status Solidi (b)

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The electron transport through a single molecule magnet transistor in the presence of a local transverse magnetic field and ac‐driven gate voltage has been considered. The conductance has been calculated as a function of the electron energy and transverse magnetic field by using the Floquet and Landauer formalism. It is shown that the time periodic potential causes zero transmission resonances that oscillate as a function of the transverse magnetic field due to the Berry phase interference associated with two quantum tunneling paths. It has been found that these Berry phase oscillations can be detected in the conductance as a function of the transverse magnetic field for an incoming electron with a specific energy.

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“…For any given energy ϵ σ it is possible to find a frequency ω so that there are always zero transmission points given by Equation . Equation is valid for

J^{'} \geq J

true(β \leq 0 true)

, i.e., the strong coupling regime.…”

Section: Resultsmentioning

confidence: 99%

Berry‐Phase in a Periodically Driven Single Molecule Magnet Transistor

González

2019

Physica Status Solidi (b)

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“…4.1. Homogeneous chains ¢ = J J The homogeneous chain has been explored before, but only in the high frequency region [25]. Resonances occur even for small values of μ if the frequency is tuned just above the critical frequencies w c1 2 .…”

Section: Results and Analysismentioning

confidence: 99%

“…Periodically driven tunneling has been studied before by several authors [19][20][21][22][23]. Interestingly, recent works have highlighted the possibility of observing AC-driven bound states in the continuum (BIC's) in transport experiments [15,[24][25][26]. First proposed by von Neumann and Wigner [27], BIC's consist of spatially localized states embedded in the spectrum of scattering states.…”

Section: Introductionmentioning

confidence: 99%

“…From previous works it is known that the driven impurity problem shows remarkable features such as tunability to perfect transmission or to a complete blockade at higher frequencies [20,25,32]. Such a quantum resonance catastrophe [25] can even occur at infinitesimally small driving amplitude, if the frequency ω is slightly larger than the energy of the incoming particle relative to the upper or lower band edge. It is also known that at very high frequencies a driven chemical potential can generally be mapped to a static effective model involving Bessel functions [33,34].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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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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“…Further, it would be interesting to the effect of such a localized periodic kicking on the transmission across the site; a similar analysis for localized harmonic driving has been carried out in Refs. 75,76. One can also study what happens if there is both a time-independent on-site potential (which can produce a bound state and affect the transmission on its own) and periodic kicking at the same site.…”

Section: Introductionmentioning

confidence: 99%

Effects of local periodic driving on transport and generation of bound states

Agarwala

Sen

2017

Phys. Rev. B

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We periodically kick a local region in a one-dimensional lattice and demonstrate, by studying wave packet dynamics, that the strength and the time period of the kicking can be used as tuning parameters to control the transmission probability across the region. Interestingly, we can tune the transmission to zero which is otherwise impossible to do in a time-independent system. We adapt the non-equilibrium Green's function method to take into account the effects of periodic driving; the results obtained by this method agree with those found by wave packet dynamics if the time period is small. We discover that Floquet bound states can exist in certain ranges of parameters; when the driving frequency is decreased, these states get delocalized and turn into resonances by mixing with the Floquet bulk states. We extend these results to incorporate the effects of local interactions at the driven site, and we find some interesting features in the transmission and the bound states.

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Quantum resonance catastrophe for conductance through a periodically driven barrier

Cited by 24 publications

References 45 publications

Berry‐Phase in a Periodically Driven Single Molecule Magnet Transistor

Berry‐Phase in a Periodically Driven Single Molecule Magnet Transistor

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

Effects of local periodic driving on transport and generation of bound states

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