Topological $d$-wave superconductor

Hypothetical topologically nontrivial superconducting state of two-dimensional electron system is discussed in connection with the problem of high-temperature superconductivity of cuprates. Direct numerical solution of the self-consistency equation exhibits two nearly degenerate order parameters which can be formally referred to $d^{}_{x^2-y^2}$ and $d^{}_{xy}$ orbital symmetry. Spontaneous breaking of the time-reversal symmetry can mix these states and form fully gapped chiral $d+id$ superconducting state.