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Topological Superconductivity in Two Dimensions with Mixed Chirality

We find a mixed chirality $d$-wave superconducting state in the coexistence region between antiferromagnetism and interaction-driven superconductivity in lightly doped honeycomb materials. This state has a topological chiral $d+id$-wave symmetry in one Dirac valley but $d-id$-wave symmetry in the other valley and hosts two counter-propagating edge states, protected in the absence of intervalley scattering. A first-order topological phase transition, with no bulk gap closing, separates the chiral $d$-wave state at small magnetic moments from the mixed chirality $d$-wave phase.