# Half-Spectrum Suppression in Dynamic Resonant Tunneling
## 6 Half-Spectrum Suppression Leads to 100% Reflection and Fano Resonance  
In Figure 5, the currents in the suppression scenarios are not much different between the different types of suppressions, and the differences between the spectra do not have much influence on the current. However, in the case where the incoming particle's energy is lower than the oscillations' frequency \(\Omega<\omega\), then in the case of suppression of the upper half of the spectrum all the positive spectral components vanish, and the transmission reaches zero. These zero-transmissions/Fano-resonances are marked by black arrows in Figure 9 for the case \(\Omega<\omega\). The spectral components at these resonances consist of only negative energies (see, for example, the black spectrum in Figure 10). Figure 8: Same parameters as in Figure 5, for the amplitude \(\beta U^{-1/2}=0.0471\). Both Equations (48) and (49) are valid simultaneously (with opposite signs); these points are seen in the intersection of the red and blue lines in Figure 5. On the upper panel, **(a)**, the incoming energy is \(\Omega=\langle\Omega_{R}\rangle-\omega/2\) and the high energies’ spectral components are suppressed, and on the bottom panel, **(b)**, \(\Omega=\langle\Omega_{R}\rangle+\omega/2\) and the lower spectral components are suppressed. Figure 7: The same parameters as in Figure 5 but with the amplitude \(\beta U^{-1/2}=0.04516\). The output spectrum is presented for different incoming energies. **(a)** and **(c)**: The activation criterion: Equation (49) for \(\Omega=\langle\Omega_{R}\rangle\pm\omega\) (the crossing point between the blue curves in Figure 5b). **(b)** The current suppression criterion: Equation (48) for \(\Omega=\langle\Omega_{R}\rangle\) (the crossing point between the red curves in Figure 5b). **(d)** is an enlargement of **(b)**. Note the resemblance between the two cases: \(\Omega=\langle\Omega_{R}\rangle\pm\omega\). Figure 10: Here, (**b**) is an enlargement of (**a**). The parameters are as in Figure 9 for the case of \(\alpha U^{-1/2}=-2.04\). This scenario is represented by the left-most black arrow in Figure 9. The high-energies part of the spectrum is suppressed for both incoming energies, but although both spectra are very similar, they lead to fundamentally different scenarios. For the case of \(\Omega/\omega<1\) (black curve in Figures 9 and 10), there are no positive spectral components; in that case, 100% reflection occurs, as can be seen in Figure 9. On the other hand, for the case \(\Omega/\omega>1\) (dotted red curve in Figures 9 and 10), there is a single spectral component with positive energy (**b**). This minor difference is sufficient to prevent a total reflection since this positive spectral component has a finite probability of escaping from the varying well out through the barrier. In Figure 9, the current is presented as a function of \(\alpha\) for two adjacent incoming energies, \(\Omega<\omega\) (black curve) and \(\Omega>\omega\) (dotted red curves). Around the blue arrows, there is not much difference between suppressions in both cases (\(\Omega<\omega\), \(\Omega>\omega\)); the  
Figure 9: The current as a function of \(\alpha\) for adjacent incoming energy. In the black curve, the incoming energy is slightly lower than the oscillations’ frequency \(\Omega<\omega\). The black arrows represent the cases when the higher energies of the spectrum (i.e., \(\Omega_{out}\geq\Omega\)) are suppressed, and since there are no positive energies that can propagate, a 100% reflection appears. The blue arrows represent the case when the lower part of the spectrum (i.e., \(\Omega_{out}<\Omega\)) is suppressed; in that case, there are positive energies with a finite probability to escape from the well out through the barrier, and therefore the suppression is not complete. The dotted red curve represents the case where the incoming energy is slightly higher than the frequency \(\Omega>\omega\); in this case, there is always a spectral component with positive energy, and therefore a total reflection cannot exist.