Superconducting states in the tetrahedral compound ${\mathrm{PrOs}}_4{\mathrm{Sb}}_{12}$

We find possible superconducting states for tetrahedral $\left(T_h\right)$ symmetry crystals with strong spin-orbit coupling using Landau theory. Additional symmetry breaking within the superconducting state is considered. We discuss nodes of the gap functions for the different states, secondary superconducting order parameters, and coupling to the elastic strain. By comparing our results to experiments, we find that superconductivity in ${\mathrm{PrOs}}_4{\mathrm{Sb}}_{12}$ is best described by the three-dimensional representations of the point group $T_h$.

Figure 1

Second-order phase transitions among states of the $E_g$ and $E_u$ representations of $T_h$.

Figure 2

Second-order phase transitions among states of the $T_g$ and $T_u$ representations of $T_h$.