Charge oscillations in quantum spin Hall constrictions

Constrictions between 1D helical edge states represent a useful tool for the realization of devices based on topological materials. Indeed, they complement superconductivity and magnetic barriers as gaps allowing to enlarge the functionalities of topological nanostructures. Recent experiments point to the direction that electronic interactions are not negligible in such systems. Herein, the interaction-induced oscillations of the local electronic density at constrictions between helical edges are theoretically inspected. The system is in the quantum dot configuration thanks to magnetic barriers. By means of bosonization, it is shown that the fractional charge oscillations, predicted for single edges, can persist. On top of that, oscillations involving both edges and with different wave vectors can appear. It is argued that the dominant oscillation can be discriminated by varying the angle of magnetization of the barriers, thus providing information about the dominant interaction mechanisms.