New Methods of Characterizing Fractional Josephson Junctions and Majorana Excitations

Abstract

In this thesis we propose and discuss new ways to probe and characterize fractional Josephson junctions and Majorana excitations forming inside of such junctions. First we propose a Josephson junction based on silicene. By using the buckled structure of silicene, topological edge states can be defined using electric fields. When mediating the Josephson effect with such edge states, the resulting Josephson junction can be tuned electrically between a fractional junction hosting two Majorana excitations and a nonfractional junction hosting no Majorana excitations. An experimental setup to use this effect as an indicator for the topology of the junction is proposed and discussed. Such signatures will typically only be visible in measurements if the quasiparticle poisoning is slow in these junctions. We analyze the effects that such poisoning events have on the dynamics of fractional Josephson junctions. Experimental schemes to measure the poisoning rate through voltage measurements are proposed for different parameter regimes. Many of the proposed setups use the fact that the Josephson junction is in the long junction regime. We propose a setup in which the topological edge states mediating the fractional Josephson effect are coupled to additional states. As an example we consider the cases where the edge states either couple to an additional nondispersive channel or to a single level quantum dot. Due to this coupling, the electrons and holes forming the Andreev bound states pick up an additional phase during one round trip, which alters their energy phase relation. The resulting setups mimic junctions with an effective length that is longer than the physical length of the junction. We characterize these junctions including coupling to additional states by an effective junction length and consider multiple limiting cases. By employing such coupling short junctions can potentially be tuned to the long junction regime, which would make many of the proposed measurements possible even in junctions that are physically in the short junction regime. This thesis also contains a brief overview of the current experimental situation surrounding this field of study as well as a short review of the Kane-Mele model as an example model featuring a quantum spin Hall insulating phase including spin-helical topological edge states.