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

TL;DR

This paper introduces a generalized superconducting fitness concept using symmetry principles, providing a tool to analyze and engineer the stability of superconducting states in complex materials with multiple degrees of freedom.

Contribution

It develops a generalized framework for superconducting fitness applicable to complex materials, enabling targeted manipulation of superconducting properties based on symmetry considerations.

Findings

Applied to CePt₃Si, KFe₂As₂, and CuₓBi₂Se₃, demonstrating the framework's versatility.

Provided guidelines for engineering Hamiltonians to favor or suppress specific superconducting states.

Showed how superconducting fitness parameters relate to stability and topological features of superconductors.

Abstract

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 $\text{Cu}_x\text{Bi}_2\text{Se}_3$.