Theory of orbital do-vector in a two-band spin-singlet superconductor: application to nematic superconductivity

We study even-parity spin-singlet orbital-triplet pairing states in a two-band superconductor. An orbital d_o(k)-vector is introduced to characterize such pairings. Naively, one might think the double degeneracy of orbitals would be lifted by orbital hybridizations due to the crystal field splitting or electron- electron interactions, then spin-singlet orbital-dependent pairings may be severely suppressed. However, we demonstrate that these pairings are not excluded in real materials and a corresponding orbital do-vector could be stabilized along certain axis in orbital subspace. Even more remarkably, the interplay between the many-body interaction induced nematic order and the superconducting order leads to the establishment of a nematic orbital do-vector, which gives rise to the coexistence of nematicity and superconductivity. The generalization to a single-band superconductor with two valleys (e.g. honeycomb lattice with two sublattices) is also discussed. The nematic superconductivity in both FeSe and magic-angle twisted bilayer graphene might be interpreted within our theory framework. Moreover, the complex orbital d_o-vector spontaneously breaks time-reversal symmetry (TRS), which may induce the TRS-breaking orbital-polarization, analogous to the spin magnetism.