Using Ginzburg-Landau formalism, we investigate the effect of confinement on the ground state of mesoscopic chiral $p$-wave superconductors in the absence of magnetic field. We reveal stable multichiral states with domain walls separating the regions with different chiralities, as well as monochiral states with spontaneous currents flowing along the edges. We show that multichiral states can exhibit identifying signatures in the spatial profile of the magnetic field if those are not screened by edge currents in the case of strong confinement. Such magnetic detection of domain walls in topological superconductors can serve as long-sought evidence of broken time-reversal symmetry. Furthermore, when applying electric current to mesoscopic $p$-wave samples, we found a hysteretic behavior in the current-voltage characteristic that distinguishes states with and without domain walls, thereby providing another useful hallmark for indirect confirmation of chiral $p$-wave superconductivity.

• Received 29 July 2016
• Revised 21 October 2016

DOI:https://doi.org/10.1103/PhysRevB.94.184517