Waiting time distributions in quantum spin Hall based heterostructures

For the distinction of the Andreev bound states and Majorana bound states, we study the waiting time distributions (WTDs) for heterostructures, based on one dimensional edge states of a two dimensional topological insulators (TI) in combination with an proximitized s-wave superconductor (SC) and an applied magnetic field. We show for the time reversal symmetric (TRS) situation of a Josephson junction details of the WTD. This includes different transport processes, different numbers of Andreev bound states and the phase difference of the SC. We further consider a Zeeman field in the normal part of the junctions revealing novel features in the WTD along the phase transition between trivial bound states and Majorana bound states. We finally discuss clear signatures to discriminate between them.