Tailoring $T_c$ by symmetry principles: The concept of Superconducting Fitness.

We propose a generalization of the concept of superconducting fitness, which allows us to make statements analogous to Anderson's theorems concerning the stability of different superconducting states. This concept can be applied to complex materials with several orbital, layer, sublattice or valley degrees of freedom. The superconducting fitness parameters $F_A(\bf{k})$ and $F_C(\bf{k})$ give a direct measure of the robustness of the weak coupling instability and of the presence of detrimental terms in the Hamiltonian, respectively. These two parameters can be employed as a guide to engineer normal state Hamiltonians in order to favour or suppress superconducting order parameters with different symmetries and topological properties. To illustrate the applicability and power of this concept we study three cases: the non-centrosymmetric heavy fermion $\text{CePt}_3\text{Si}$, the hole doped iron pnictide $\text{KFe}_2\text{As}_2$ and the doped topological insulator $\text{Cu}_x\text{Bi}_2\text{Se}_3$.