Spin-triplet p-wave pairing ($S=1,L=1$)

Spin-triplet p-wave pairing has pair spin $S=1$ and orbital angular momentum $L=1$, allowing multiple order parameters beyond conventional BCS theory with zero orbital angular momentum. ^[ref]

Specifying this symmetry does not determine its microscopic attraction mechanism. A short exchange-symmetry check explains why these quantum numbers fit fermions. The spin-one-half triplet states $|\uparrow \uparrow ⟩$, $(|\uparrow \downarrow ⟩+|\downarrow \uparrow ⟩)/\sqrt{2}$ and $|\downarrow \downarrow ⟩$ are symmetric under exchange. A stipulated orbital factor proportional to relative momentum $k_x$ changes sign under $\mathbf{k}\mapsto -\mathbf{k}$. Multiplying any symmetric spin function by that odd orbital factor gives an antisymmetric pair wave function, as required by Fermi-Dirac statistics. By comparison, an even s-wave orbital factor needs the antisymmetric spin singlet state. This checks compatibility with exchange statistics; it neither selects a stable phase nor derives its transition temperature.