We report on our recent progress regarding classes of materials which exhibit chiral triplet and singlet superconductivity, where topologically nontrivial pairing phenomena can emerge. Specifically, motivated by recent experimental advances, we show that graphene doped to the van Hove regime can give rise to a plethora of interesting ordering instabilities such as spin density wave and superconductivity. As a function of system parameters such as doping and range of Coulomb interaction, we explain which instability is favored by the system, and analyze the effect of long-range interactions on superconductivity giving rise to a competition between singlet d+id and triplet f wave. We further report on our investigations of Cobaltate superconductors where we believe the experimental evidence can be reconciled by an anisotropic d+id superconducting gap. We also outline our work in progress for other compounds such as strontium ruthenate and SrPtAs which we believe are promising to stabilize such interesting topological superconducting states of matter.
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