Majorana bound states in d-wave superconductor planar Josephson junction

TL;DR

This paper proposes a method to realize Majorana bound states in phase-controlled planar Josephson junctions with d-wave superconductors, using a 2D electron gas with strong spin-orbit coupling, tunable via Zeeman field and phase difference.

Contribution

It introduces a new platform for Majorana states using d-wave superconductors in Josephson junctions, analyzing the effects of different pairing symmetries and practical material considerations.

Findings

Majorana states can be induced by tuning Zeeman field and phase difference.

Topological gap depends on the type of d-wave pairing, with challenges in pure d-wave.

d+is and d+id' pairings are promising for Majorana realization.

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 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.