Majorana bound states in a d-wave superconductor planar Josephson junction

Hamed Vakili; Moaz Ali; Mohamed Elekhtiar; Alexey A. Kovalev

doi:10.1103/PhysRevB.108.L140506

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Majorana bound states in a d-wave superconductor planar Josephson junction

Hamed Vakili, Moaz Ali, Mohamed Elekhtiar, Alexey A. Kovalev

DOI 10.1103/PhysRevB.108.L140506 · Physical Review B

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Abstract

We study phase-controlled planar Josephson junctions comprising a two-dimensional electron gas with strong spin-orbit coupling and d-wave superconductors, which have an advantage of a high critical temperature. We show that a region between the two superconductors can be tuned into a topological state by the in-plane Zeeman field, and can host Majorana bound states. The phase diagram as a function of the Zeeman field, chemical potential, and the phase difference between superconductors exhibits the appearance of Majorana bound states for a wide range of parameters. We further investigate the behavior of the topological gap and its dependence on the type of d-wave pairing, i.e., d, d+is, or d+id′, and note the difficulties that can arise due to the presence of gapless excitations in pure d-wave superconductors. On the other hand, the planar Josephson junctions based on superconductors with d+is and d+id′ pairings can potentially lead to realizations of Majorana bound states. Our proposal can be realized in cuprate superconductors, e.g., in a twisted bilayer, combined with the layered semiconductor Bi2O2Se.