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Majorana bound states in d-wave superconductor-based hybrid systems

For the search of Majorana fermions, we propose to employ a ramp-type Josephson edge junction between a normal metal such as Au, Ag or alloys of heavy metals and a topologically-trivial dx2-y2 wave high-Tc superconductor YBa2Cu3O7. The success in forming the elusive zero-energy Majorana bound states (MBS) at the junction relies crucially upon the strength of the Rashba spin-orbit coupling (RSOC) at the metal/superconductor interface, the tunneling direction, and the interface quality which includes a near zero tunnel barrier height. When these junction conditions are collectively satisfied, definitive signatures of Majorana fermions will emerge. After inspecting a vast amount of published data of junctions that are close to what we have proposed, we were able to find: 1) angular resonant Andreev reflection, and 2) quantized zero bias normalized differential conductance peak (ZBCP), as possible evidence for MBS formed at the junction interface. Encouraged by these findings, we have designed a MBS-supporting d-wave superconductor based pi-loop heterostructure as a qubit platform. Such pi-loops are characterized by a doubly degenerate half flux quantum vortex (HQV) and are topologically protected by a parity effect arising from an odd number of sign changes of the supercurrent circulating in the loop. The topological protection is further enhanced by the formation of RSOC induced Majorana bound states at the Josephson junction interface. The proposed MBS-plus-HQV qubit platform will be useful for demonstrating non-Abelian exchange statistics and for building a prototype topological quantum computer.