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

TL;DR

This paper investigates how single electron injection into helical edge channels of topological insulators affects charge and energy dynamics, revealing interaction-dependent splitting and controllable energy flow directions.

Contribution

It models the time-resolved charge and energy dynamics considering electron-electron interactions and non-local tunneling in helical liquids, highlighting new control mechanisms.

Findings

Charge and energy packets split into counterpropagating contributions.

Energy flow can be reversed by tuning injection parameters.

Stronger signatures observed in energy dynamics.

Abstract

The possibility to inject 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 wavepacket. Modeling the injection process from a mesoscopic capacitor in presence of non-local 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 interactions strength. In addition, stronger signatures are found for the injected energy, which is also affected by the finite width of the tunneling region. Indeed, the energy flow can be controlled by tuning the injection parameters and we demonstrate that, in presence of non-local tunneling, it is possible to achieve situation in which charge and energy flow in opposite directions.