Abstract
We theoretically investigate the evolution of the peak height of energy-resolved electronic wave-packets ballistically propagating along integer quantum Hall edge channels at filling factor equal to two. This is ultimately related to the elastic scattering amplitude for the fermionic excitations evaluated at different injection energies. We investigate this quantity assuming a short-range capacitive coupling between the edges. Moreover, we also phenomenologically take into account the possibility of energy dissipation towards additional degrees of freedom—both linear and quadratic—in the injection energy. Through a comparison with recent experimental data, we rule out the non-dissipative case as well as a quadratic dependence of the dissipation, indicating a linear energy loss rate as the best candidate for describing the behavior of the quasi-particle peak at short enough propagation lengths.
Highlights
The possibility to prepare, manipulate, and measure individual electronic wavepackets propagating along mesoscopic quantum channels opened the way to so-called electron quantum optics (EQO) [1,2,3,4,5,6,7]
We have investigated the evolution of the relative peak height of electronic wave-packets well resolved in energy and ballistically propagating along quantum Hall (QH) edge channels at ν = 2 as a function of the injection energy
According to what has been discussed in the literature, together with the conventional non-dissipative case, we considered a dissipation that is both linear and quadratic in the energy
Summary
The possibility to prepare, manipulate, and measure individual electronic wavepackets propagating along mesoscopic quantum channels opened the way to so-called electron quantum optics (EQO) [1,2,3,4,5,6,7]. The preliminary steps in the study of dissipative effects involved the investigation of the evolution of a non-equilibrium electronic distribution as a function of the interaction length [38,39], where experiments showed that the signature of important energy losses towards external degrees of freedom was only included effectively in the theoretical models [40,41,42] Such dissipation effects are crucial in order to properly describe both the dynamics of integer QH states [43] and the evolution of the peak height of energy-resolved wave-packets injected into them [44].
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