Josephson critical currents in annular superconductors with Pearl vortices

We investigate the influence of Pearl vortices in the vicinity of an edge-type Josephson junction for a superconducting thin-film loop in the form of an annulus, under uniform magnetic field. Specifically, we obtain the exact analytic formulation that allows to describe the circulating current density and the gauge invariant phase increment $\Delta\phi$ across the junction. The main properties of $\Delta\phi$ and their influence on the critical current pattern $I_c(B)$ are described quantitatively in terms of the loop's width to radius ratio $W/R$ and of the vortex position within the loop ${\bf r}_v$. It is shown that narrow loops ($W/R < 0.3$) may be well described by the straight geometry limit. However, such approximation fails to predict a number of distinctive features captured by our formulation, as the node lifting effect of the $I_c(B)$ pattern in wide loops or the actual influence of a vortex pinned at different positions.