Majorana bound states in hybrid 2D Josephson junctions with ferromagnetic insulators

Abstract

We consider a Josephson junction consisting of superconductor/ferromagnetic insulator (S/FI) bilayers as electrodes which proximizes a nearby 2D electron gas. By starting from a generic Josephson hybrid planar setup we present an exhaustive analysis of the the interplay between the superconducting and magnetic proximity effects and the conditions under which the structure undergoes transitions to a non-trivial topological phase. We address the 2D bound state problem using a general transfer matrix approach that reduces the problem to an effective 1D Hamiltonian. This allows for straightforward study of topological properties in different symmetry classes. As an example we consider a narrow channel coupled with multiple ferromagnetic superconducting fingers, and discuss how the Majorana bound states can be spatially controlled by tuning the superconducting phases. Following our approach we also show the energy spectrum, the free energy and finally the multiterminal Josephson current of the setup.

8 pages; 5 figures

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• Reconstruction-Induced ${\phi }_0$ Josephson Effect in Quantum Spin Hall Constrictions
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• Topological superconductivity in a magnetic-texture coupled Josephson junction
• Beyond the standard model of topological Josephson junctions: From crystalline anisotropy to finite-size and diode effects
• Multiple Majorana bound states and their resilience against disorder in planar Josephson junctions