Full proximity treatment of topological superconductors in Josephson-junction architectures

Abstract

Experiments on planar Josephson-junction architectures have recently been shown to provide an alternative way of creating topological superconductors hosting accessible Majorana modes. These zero-energy modes can be found at the ends of a one-dimensional channel in the junction of a twodimensional electron gas (2DEG) proximitized by two spatially separated superconductors. The channel, which is below the break between the superconductors, is not in direct contact with the superconducting leads, so that proximity coupling is expected to be weaker and less well controlled than in the simple nanowire configuration widely discussed in the literature. This provides a strong incentive for this paper which investigates the nature of proximitization in these Josephson junction architectures. At a microscopic level we demonstrate how and when it can lead to topological phases. We do so by going beyond simple tunneling models through solving self-consistently the Bogoliubov-de Gennes equations of a heterostructure multicomponent system involving two spatially separated s-wave superconductors in contact with a normal Rashba spin-orbit-coupled 2DEG. Importantly, within our self-consistent theory we present ways of maximizing the proximity-induced superconducting gap by studying the effect of the Rashba spin-orbit coupling, chemical potential mismatch between the superconductor and 2DEG, and sample geometry on the gap. Finally, we note (as in experiment) a Fulde-Ferrell-Larkin-Ovchinnikov phase is also found to appear in the 2DEG channel, albeit under circumstances which are not ideal for the topological superconducting phase.

Anisotropic topological superconductivity in Josephson junctions

“…Previous investigations 37,39,42 have shown the im- portance of properly tuning the chemical potential, magnetic field strength, and superconducting phase difference for driving the JJ into the TS state. However, the strong dependence of the TS state and the ground-state phase on the spin-orbit angle (θ so ), the magnetic field orientation (ϕ B ), and the supercurrent direction (θ c ), shown in Fig.…”

“…In a more general scenario, there are situations in which the topological transition occurs without the current having a local minimum. 39,100 Figure 2(a) reveals that the topological gap is sizable only on a reduced part of the topological region. The topological gap is crucial for ensuring the practical protection of the MBS.…”

Fragility of surface states in topological superfluid 3He

“…Current strategies explore the manipulation of Majorana zero modes (MZMs) in devices which rely on 1-D topological superconductivity [16][17][18][19] induced by the proximity effect in topological insulators or semiconductors with strong spin-orbit coupling, or via planar Josephson Junctions 20,21 . However, MZMs may be corrupted by non-topological low energy Andreev bound states (ABS) 22 , which can be present as a result of details of interfaces and materials properties in such systems 23 . Here we report the fragility of surface ABS in superfluid 3 He at an ideal non-transparent interface, exploiting the ability to tune in situ the scattering of quasiparticles by the surface through adjustment of the isotopic composition of the helium surface boundary layer.…”

Signatures of Topological Transitions in the Spin Susceptibility of Josephson Junctions

“…Furthermore, it has also been shown that the presence of critical current minima may not necessarily be associated to transitions between the trivial and TS states [45] and a further analysis of magnetic and crystalline anisotropies of the TS state [46,47] may be needed to better understand the physical origin of the critical current minima [36]. In spite of the challenges, planar JJs continue to attract attention due to their experimental feasibility, versatility, and enhanced region of system parameters supporting the TS state [41,[46][47][48][49][50][51][52][53][54][55][56][57][58][59][60].…”

“…Therefore, although in some cases the ground-state phase jumps appear to occur at the same Zeeman energy at which the critical current minima occur, this is, in general, not necessarily true. Further, the existence of ground-state jumps may not even be accompanied by critical current minima (nor vice versa), especially for junctions with narrow S regions [49]. In such cases, the existence of current minima does not necessarily represent a signature of topological phase transition.…”