We perform microscopic numerical simulations of the Josephson effect through short junctions between two full-shell hybrid nanowires, comprised of a semiconductor core fully wrapped by a thin superconductor shell, both in the trivial and topological regimes. We explore the behavior of the current-phase relation and the critical current $I_c$ as a function of a threading flux for different models of the semiconductor core and different transparencies of the weak link. We find that $I_c$ is modulated with flux due to the Little-Parks (LP) effect and displays a characteristic skewness towards large fluxes within nonzero LP lobes, which is inherited from the skewness of a peculiar kind of subgap states known as Caroli-de Gennes-Matricon (CdGM) analogs. The appearance of Majorana zero modes at the junction in the topological phase is revealed in $I_c$ as fin-shaped peaks that stand out from the background at low junction transparencies. The competition between CdGMs of opposite electron- and holelike character produces steps and dips in $I_c$. A rich phenomenology results, which includes 0-, $\pi$-, and $\varphi$-junction behaviors depending on the charge distribution across the wire core and the junction transparency.

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• Josephson effect
• Majorana bound states
• Josephson junctions
• Nanowires
• Topological superconductors