Unconventional singlet-triplet superconductivity

Have you been lying awake wondering what symmetries determine whether a superconductor is spin singlet, triplet, or both? We show that if BCS theory is supplied with additional degrees of freedom, spin singlet can coexist with spin triplet superconductivity. In the first part, we didactically guide the reader to the most general superconducting state using symmetry arguments. If both singlet and triplet pairing channels are present, a magnetic field can convert between spin singlet and triplet states. In the second part, we discuss two possible singlet-triplet superconductors: CeRh$_2$As$_2$ and bilayer-NbSe$_2$.