Josephson effect in multiterminal topological junctions

Abstract

We study the Josephson effect in a trijunction formed by two topological superconductor (TS) wires and a conventional s-wave superconductor. Using a boundary Green's function formalism, analytical results for the current-phase relation are obtained in various limiting cases by modeling the TS wires via the low-energy limit of a Kitaev chain. We show that Josephson transport critically depends on the spin canting angle θ between the boundary spin polarizations of the TS wires, which in turn suggests that the spin structure of Majorana states can be accessed through supercurrent measurements. We also extend the boundary Green's function approach to a more microscopic spinful wire model and thereby compute the dependence of θ on experimentally accessible parameters such as the Zeeman field and/or the chemical potential. Furthermore, we show that the equilibrium current-phase relation between both TS wires exhibits a robust 4π-periodicity since the conventional superconducting lead effectively locks the fermion parity of the trijunction.

Spin-Orbit Splitting of Andreev States Revealed by Microwave Spectroscopy

“…Spectroscopy experiments on carbon nanotubes [6], atomic contacts [7][8][9] and semiconducting nanowires [10][11][12] have clearly revealed these fermionic states, each of which can be occupied at most by two quasiparticles. The role of spin in these excitations is a topical issue in the rapidly growing fields of hybrid superconducting devices [13][14][15] and of topological superconductivity [16][17][18][19]. It has been predicted that for finite-length weak links the combination of a phase difference, which breaks time-reversal symmetry, and of spinorbit coupling, which breaks spin-rotation symmetry, is enough to lift the spin degeneracy, giving therefore rise to spin-dependent Josephson supercurrents even in the absence of an external magnetic field [20][21][22][23].…”

Finite length effect on supercurrents between trivial and topological superconductors

“…More importantly though, I(φ) undergoes an enhancement due to the reduction of the MBSs energy splitting when L R increases. We have verified that for very large magnetic fields B B c , the overall supercurrent is reduced and eventually completely suppressed due to the different pairing symmetries in the trivial and topological superconducting regions [93,55]. This can be understood as follows: the superconducting correlations in the left S have spin singlet s-wave symmetry and also mixed spin triplet p-wave due to finite SOC both with m z = 0 for the Cooper pairs [94,95], while in the right S there is a coexistence of correlations with spin-singlet (m z = 0) s-wave, equal spin-triplet (m z = ±1) p-wave, and mixed spin-triplet (m z = 0) p-wave due to the finite magnetic field in such region.…”

“…(4)(c). This is due to the incompatibility between the superconducting correlation symmetries in the trivial region and in the topological region at extremely large magnetic fields, as explained before [93,55]. However, much before that, the critical current captures the splitting of MBSs through noticeable oscillations as function of the magnetic field.…”

Transport signatures of Majorana bound states in superconducting hybrid structures

“…In the model discussed in the previous section the focus has been placed on a superconducting JJ between a topological superconductor and a non topological superconductor [158,159,162]. In such a JJ, the current phase relation features a 2π periodicity like the traditional Josephson effect.…”