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

We study phase-controlled planar Josephson junction comprising a two-dimensional electron gas with strong spin-orbit coupling and d-wave superconductors, which have an advantage of high critical temperature. We show that a region between the two superconductors can be tuned into topological state by the in-plane Zeeman field, and can host Majorana bound states. 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. In case of d + is pairing, we have demonstrated realizations of MBS for a wide range of parameters. In the case of d + id′ pairing there are no gapless states in the bulk of 2DEG; however, the even Chern number associated with the bulk leads to appearance of gapless chiral edge modes, which can hybridize with MBS. To realize MBS with d + id′ pairing, we have proposed a modified JJ in which the chiral edge modes are gapped and do not hybridize with MBS. Our proposal can be realized in cuprate superconductors, e.g., in a twisted bilayer, combined with the layered semiconductor Bi2O2Se.