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Hybrid superconductor-semiconductor nanowires with Rashba spin-orbit couplingare arguably becoming the leading platform for the search of Majorana boundstates (MBSs) in engineered topological superconductors. We perform asystematic numerical study of the low-energy Andreev spectrum and supercurrentsin short and long superconductor-normal-superconductor junctions made ofnanowires with strong Rashba spin-orbit coupling, where an external Zeemanfield is applied perpendicular to the spin-orbit axis. In particular, weinvestigate the detailed evolution of the Andreev bound states from the trivialinto the topological phase and their relation with the emergence of MBSs. Dueto finite length, the system hosts four MBSs, two at the inner part of thejunction and two at the outer one. They hybridize and give rise to a finiteenergy splitting at superconducting phase difference $\phi=\pi$, a well-visibleeffect that can be traced back to the evolution of the energy spectrum with theZeeman field: from the trivial phase with Andreev bound states into thetopological phase with MBSs. Similarly, we carry out a detailed study ofsupercurrents for short and long junctions from the trivial to the topologicalphases. The supercurrent, calculated from the Andreev spectrum, is$2\pi$-periodic in the trivial and topological phases. In the latter itexhibits a clear \emph{sawtooth} profile at phase difference of $\pi$ when theenergy splitting is negligible, signalling a strong dependence of current-phasecurves on the length of the superconducting regions. Effects of temperature,scalar disorder and reduction of normal transmission on supercurrents are alsodiscussed. Further, we identify the individual contribution of MBSs. In shortjunctions the MBSs determine the current-phase curves, while in long junctionsthe spectrum above the gap (quasi-continuum) introduces an importantcontribution.

Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states