Charge d-wave topological insulator

Formation of a condensate of singlet electron-hole pairs in a two-dimensional metal lattice with the nesting of the Fermi contour is investigated. A numerical solution is obtained for the self-consistency equation for the insulating order parameter depending on the ratio of the coupling constants in the s- and d-wave channels of electron-hole pairing. Solutions with the pure orbital symmetry of s- and d-type are found, as well as solutions with the mixed s + d-symmetry. It is shown that in a wide range of values of the s- and d-wave coupling constants, the two-dimensional insulating order with the orbital symmetry $d_{x^2-y^2}$ can compete with pure ordered s- and d_xy-states and mixed s + d-states. Time reversal symmetry breaking under an established real order with $d_{x^2-y^2}$-wave symmetry may generate the imaginary component of the order parameter with symmetry d_xy and cause a rise in topologically nontrivial d + id-wave ordering similar to the quantum Hall state in the absence of external magnetic field.