Topological d-wave superconductivity in two dimensions

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 supercon-ductivity 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 super-conducting 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.