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Recently, much research has been dedicated to understanding topologicalsuperconductivity and Majorana zero modes induced by a magnetic field in hybridproximity structures. This paper proposes a realization of topologicalsuperconductivity in a short Josephson junction at an edge of a 2D topologicalinsulator subject to a perpendicular magnetic field. The magnetic field effectis entirely orbital, coming from a gradient of the order parameter phase at theedge, which results in a soliton defect at the junction with a pair of gaplessAndreev bound states. The latter are reducible to Majorana zero modes by aunitary rotation and protected by a chiral symmetry. Furthermore, both groundstate and excitations are quasiperiodic in the magnetic flux enclosed in thejunction, with the period equal to the double flux quantum $2\Phi_0 = h/e$.This behaviour follows from the gauge invariance of the $4\pi$ - phaseperiodicity of the Majorana states and manifests itself as $2\Phi_0$ - spacedmagnetic oscillations of the critical current. Another proposed observable is apersistent current occurring in the absence of an external phase bias. Besidethe oscillations, it shows a sign reversal prompted by the neutral Majoranazero modes. These findings offer the possibility to access topologicalsuperconductivity through low-field dc magnetotransport measurements.

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