The conventional way of writing down the gap in a superconducting material $\Delta(k) = \langle \hat{c}_\alpha({\bf k}) \hat{c}_\beta({\bf -k}) \rangle$ is
$$\Delta(k) = (\Delta_0(k) + {\bf d(k) \sigma}) (i \sigma_2)_{\alpha\beta}$$
where $\Delta({\bf k}) = \Delta({\bf -k})$ is the spin-singlet contribution and ${\bf d(k)} = {\bf - d(-k)}$ is the spin-triplet contribution. For more details I refer to this well written post by FraSchelle.
My question refers to the spin part $i \sigma_2$. Why is there an $i$ in front of this term? To me it seems that the intention is to make it symmetric with respect to time-reversal. (Which I think in this case would be complex conjugation)
Even if it is only convention, was there a certain history that led to it?
