Topological d-wave superconductivity in two dimensions

Abstract

Despite intensive searches for topological superconductors, the realization of topological superconductivity remains under debate. Previous proposals for the topological $s$-wave, $p$-wave, and chiral $d$-wave superconductivity have both advantages and disadvantages. In this review, we discuss two-dimensional topological superconductivity based on the non-chiral $d$-wave superconductors. It is shown that the noncentrosymmetric $d$-wave superconductors become topological superconductors under an infinitesimal Zeeman field without fine-tuning of parameters. Floquet engineering for introducing the Zeeman field in a controllable way is also proposed. When the two-dimensional noncentrosymmetric superconductors are stacked to recover the global inversion symmetry, the field-induced parity transition may occur, and the high-field odd-parity superconducting state realizes various topological phases depending on the stacking structures. Two-dimensional heterostructures of strongly correlated electron systems, which have been developed by recent experiments, are proposed as a platform of the high-temperature topological superconductivity and the interplay of topology and strong correlations in superconductors.

31 pages, 17 figures. Submitted to Physica E as an invited review paper

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• Majorana bound states in d-wave superconductor planar Josephson junction
• Reciprocal and nonreciprocal paraconductivity in bilayer multiphase superconductors
• Fermions in $(1+2)$-dimensions modified by nonminimal coupling and its applications to condensed matter physics
• Quasiclassical theory of vortex states in locally non-centrosymmetric superconductors: application to CeRh${}_2$As${}_2$