Tailoring Tc 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 functions FA(k) and FC(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 functions can be employed as a guide to engineer normal state Hamiltonians in order to favor 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 noncentrosymmetric heavy fermion CePt₃Si, the hole-doped iron pnictide KFe₂As₂, and the doped topological insulator CuₓBi₂Se₃.