Possible triplet superconductivity in thin films and layered compounds in a strong, parallel magnetic field

We consider a model of both singlet and triplet superconductivity in thin films and intercalated layered compounds in which the attractive electron-electron interaction has both $s$- and $p$-wave form in the layers and interlayer pairing is also possible for the layered materials. We include the effects of intralayer $s$- and $p$-wave impurity scattering. As expected, we find that the intralayer singlet state is not suppressed by scattering, but the interlayer state is suppressed by $s$-wave scattering and the intralayer $p$-wave state is suppressed by transport scattering. For thin films in a parallel magnetic field the $p$-wave state is dominant below the transition temperature $T_i$ at fields exceeding the $s$-wave Pauli limit $H_p$. For the layered compounds with interlayer tunneling matrix element $J$, there is a temperature $T^{*}>0\mathrm{}$ below which $H_{c2,\parallel }$ for one of the triplet states is divergent, provided that $J<\mathrm{}\frac{2\pi T_{I0\mathrm{}}}{\gamma \sqrt{e}}$ or $J<\mathrm{}\frac{2\pi T_{i0\mathrm{}}f\left(\frac{{\tau }_s}{{\tau }_{\mathrm{tr}}}\right)}{\gamma }$, where $f\left(z\right)\mathrm{}\ge 1$ and $T_{i0\mathrm{}}$ and $T_{I0\mathrm{}}$ are the intra- and interlayer triplet transition temperatures in the absence of impurities, respectively. We also examine the behavior of the triplet states in small magnetic fields, and discuss the possibilities of observing the phenomenon in real materials.