Josephson junctions of multiple superconducting wires

Abstract

We study the spectrum of Andreev bound states and Josephson currents across a junction of $N$ superconducting wires which may have $s$- or $p$-wave pairing symmetries and develop a scattering matrix based formalism which allows us to address transport across such junctions. For $N\ge 3$, it is well known that Berry curvature terms contribute to the Josephson currents; we chart out situations where such terms can have relatively large effects. For a system of three $s$- or three $p$-wave superconductors, we provide analytic expressions for the Andreev bound state energies and study the Josephson currents in response to a constant voltage applied across one of the wires; we find that the integrated transconductance at zero temperature is quantized to integer multiples of $4e^2/h$, where $e$ is the electron charge and $h=2\pi \hslash$ is Planck's constant. For a sinusoidal current with frequency $\omega$ applied across one of the wires in the junction, we find that Shapiro plateaus appear in the time-averaged voltage $⟨V_1⟩$ across that wire for any rational fractional multiple (in contrast to only integer multiples in junctions of two wires) of $2e⟨V_1⟩/(\hslash \omega )$. We also use our formalism to study junctions of two $p$- and one $s$-wave wires. We find that the corresponding Andreev bound state energies depend on the spin of the Bogoliubov quasiparticles; this produces a net magnetic moment in such junctions. The time variation of these magnetic moments may be controlled by an external applied voltage across the junction. We discuss experiments which may test our theory.

21 pages, 15 figures; made some corrections and added several references; this is the published version

References in corpus (7)

• The electronic properties of graphene
• Topological Andreev bands in three-terminal Josephson junctions
• Non-trivial Chern numbers in three-terminal Josephson junctions
• Weyl nodes in Andreev spectra of multiterminal Josephson junctions: Chern numbers, conductances and supercurrents
• Voltage-induced Shapiro steps in a superconducting multi-terminal structure
• Josephson effect in multiterminal topological junctions
• Spontaneous spin accumulation in singlet-triplet Josephson junctions

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