Time-resolved energy dynamics after single electron injection into an interacting helical liquid

The possibility of injecting a single electron into ballistic conductors is at the basis of the new field of electron quantum optics. Here, we consider a single electron injection into the helical edge channels of a topological insulator. Their counterpropagating nature and the unavoidable presence of electron-electron interactions dramatically affect the time evolution of the single wave packet. Modeling the injection process from a mesoscopic capacitor in the presence of nonlocal tunneling, we focus on the time-resolved charge and energy packet dynamics. Both quantities split up into counterpropagating contributions whose profiles are strongly affected by the interaction strength. In addition, stronger signatures are found for the injected energy, which is also affected by the finite width of the tunneling region, in contrast to what happens for the charge. Indeed, the energy flow can be controlled by tuning the injection parameters, and we demonstrate that, in the presence of nonlocal tunneling, it is possible to achieve a situation in which charge and energy flow in opposite directions