Manifestation of Majorana modes overlap in the Aharonov–Bohm effect

Abstract

One of the key features of the Majorana bound states emerging in topological superconducting (SC) wires is increasing oscillations of their energy under the growth of magnetic field or chemical potential due to concomitant enhancement of hybridization of the Majorana mode wave functions initially localized at the opposite edges of the structure. In this study we found that the other consequence of it is a shift of Aharonov-Bohm (AB) oscillations of linear-response conductance in an interference device where two ends of the SC wire connected with a normal contact via non-SC wires (arms). In addition, it is accompanied by an oscillation period doubling. The numerical calculations for the spinful system are supported by the analytical results for different spinless models allowing to track the conductance evolution as the hybridization of the Majorana modes increases. It is shown that since the coupling between the different arms and normal contact is implemented only via the different-type Majoranas the AB oscillations acquire a fundamental π/2 shift in comparison with the effect for an analogous system of zero-energy quantum dots.

Probing Majorana bound states through an inhomogeneous Andreev double dot interferometer

“…However, as we also mentioned above, at the high magnetic, when M 1 (M 2 ) penetrates sufficiently into the bottom (top), the bulk ABS emerges (formally in the nontrivial phase) and the AB period, in general, is 2π even though A ≈ 0. The latter takes place since each Majorana mode couples with the normal contact via both arms [52]. Such a situation at h = 2, near the upper border (h = h c2 ) of the S-segment topological phase, is depicted by dash-dotted curve in Fig.…”

“…According to (19), immediately after the topological phase transition, the conductance can be amplified by the magnetic flux and reaches a 4G 0 -height plateau at φ = π/2 (see Fig. 2b) [52,58]. Then, as the Zeeman energy grows the conductance starts to oscillate with the increasing amplitude due to the overlap of MC wave functions.…”

“…topo equals 4G 0 for any B, τ iσ [52]. In general, the different periodicities can imply that both inhomogeneous ABSs are needed to generate the AB oscillations in the trivial phase while the single nonlocal excitation (i.e.…”

“…a bulk ABS). It can emerge, for example, if the topological gap collapses at the high magnetic fields [52] or due to the presence of random disorder in the trivial phase [27]. In the framework of the above-formulated model, both MCs of such an excitation interact with the normal contact via both arms.…”

Majorana modes and Fano resonances in Aharonov-Bohm ring with topologically nontrivial superconducting bridge

“…Finally, let us consider a limiting case of the above transport scheme by leaving only the left half of the system. In other words, in this section we turn to a Π-shaped device consisting of the LT and LB normal wires separated by the SW [35,36].…”