Analytically determined topological phase diagram of the proximity-induced gap in diffusive n-terminal Josephson junctions

Morten Amundsen,Jacob Linder,Jabir Ali Ouassou

doi:10.1038/srep40578

Morten Amundsen, Jacob Linder + Show 1 more

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https://doi.org/10.1038/srep40578

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Abstract

Multiterminal Josephson junctions have recently been proposed as a route to artificially mimic topological matter with the distinct advantage that its properties can be controlled via the superconducting phase difference, giving rise to Weyl points in 4-terminal geometries. A key goal is to accurately determine when the system makes a transition from a gapped to non-gapped state as a function of the phase differences in the system, the latter effectively playing the role of quasiparticle momenta in conventional topological matter. We here determine the proximity gap phase diagram of diffusive n-terminal Josephson junctions (), both numerically and analytically, by identifying a class of solutions to the Usadel equation at zero energy in the full proximity effect regime. We present an analytical equation which provides the phase diagram for an arbitrary number of terminals n. After briefly demonstrating the validity of the analytical approach in the previously studied 2- and 3-terminal cases, we focus on the 4-terminal case and map out the regimes where the electronic excitations in the system are gapped and non-gapped, respectively, demonstrating also in this case full agreement between the analytical and numerical approach.

Highlights

Multiterminal Josephson junctions have recently been proposed as a route to artificially mimic topological matter with the distinct advantage that its properties can be controlled via the superconducting phase difference, giving rise to Weyl points in 4-terminal geometries
In multiterminal Josephson junctions hosting well-defined Andreev bound states, the crossing of these states with the Fermi level has been shown to be analogous to Weyl points in 3D solids with the Andreev bound state taking on the role of energy bands and the superconducting phase differences corresponding to quasiparticle momenta
A considerable advantage in utilizing multiterminal Josephson junctions rather than 3D solids to study exotic phenomena such as Weyl singularities and topologically different phases is that the phase differences are much more controlled experimentally than the quasiparticle momenta

Summary

Josephson junctions

Multiterminal Josephson junctions have recently been proposed as a route to artificially mimic topological matter with the distinct advantage that its properties can be controlled via the superconducting phase difference, giving rise to Weyl points in 4-terminal geometries. We here determine the proximity gap phase diagram of diffusive n-terminal Josephson junctions (n ∈ N), both numerically and analytically, by identifying a class of solutions to the Usadel equation at zero energy in the full proximity effect regime. We here determine the proximity gap phase diagram of diffusive n-terminal Josephson junctions (n ∈ ), both numerically and analytically, by identifying a class of solutions to the Usadel equation[10] at zero energy in the full proximity effect regime. (x = 0, y = 0) = 0000...,888666666,,, if (φL, φR) if (φL, φR) if (φL, φR) if (φL, φR) These solutions may be compared with the numerical solution of the full proximity-gap phase diagram, where it can be seen that the analytically determined transition curves of Fig. 2(b) trace out exactly the regions where the density of states is non-zero. The gapped region at 0

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