Soliton defects and topological $4π$-periodic superconductivity from an orbital magnetic field effect in edge Josephson junctions

Abstract: Recently, much research has been dedicated to understanding topological superconductivity and Majorana zero modes induced by a magnetic field in hybrid proximity structures. This paper proposes a realization of topological superconductivity in a short Josephson junction at an edge of a 2D topological insulator subject to a perpendicular magnetic field. The magnetic field effect is entirely orbital, coming from a gradient of the order parameter phase at the edge, which results in a soliton defect at the junction with a pair of gapless Andreev bound states. The latter are reducible to Majorana zero modes by a unitary rotation and protected by a chiral symmetry. Furthermore, both ground state and excitations are quasiperiodic in the magnetic flux enclosed in the junction, with the period equal to the double flux quantum $2\Phi_0 = h/e$. This behaviour follows from the gauge invariance of the $4\pi$ - phase periodicity of the Majorana states and manifests itself as $2\Phi_0$ - spaced magnetic oscillations of the critical current. Another proposed observable is a persistent current occurring in the absence of an external phase bias. Beside the oscillations, it shows a sign reversal prompted by the neutral Majorana zero modes. These findings offer the possibility to access topological superconductivity through low-field dc magnetotransport measurements.