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

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 $F_A(\mathbf{k})$ and $F_C(\mathbf{k})$ 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 ${\text{Cu}}_x{\text{Bi}}_2{\text{Se}}_3$.

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• Anapole superconductivity from $\mathcal{P}\mathcal{T}$-symmetric mixed-parity interband pairing
• Theory of optical responses in clean multi-band superconductors
• Superconductivity without inversion and time-reversal symmetries
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• Superconductivity in disordered locally noncentrosymmetric materials: an application to CeRh${}_2$As${}_2$
• Shadowed triplet pairings in Hund's metals with spin-orbit coupling
• Spin response and topology of a staggered Rashba superconductor
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• Quantum-geometry-induced anapole superconductivity
• Loop currents and anomalous Hall effect from time-reversal symmetry-breaking superconductivity on the honeycomb lattice
• Higher angular momentum pairings in interorbital shadowed-triplet superconductors: Application to Sr${}_2$RuO${}_4$
• Multiorbital singlet pairing and $d+d$ superconductivity
• Nonlinear optical responses in noncentrosymmetric superconductors
• Hund's coupling stabilized superconductivity in the presence of spin-orbit interactions
• Bulk odd-frequency pairing in the superconducting Su-Schrieffer-Heeger model
• Robustness of unconventional $s$-wave superconducting states against disorder
• Nonunitary Superconductivity in Complex Quantum Materials
• Origin of the anomalous Hall effect in two-band chiral superconductors
• Superconductivity of anomalous pseudospin
• General theory of robustness against disorder in multi-band superconductors
• Residual spin susceptibility in the spin-triplet, orbital-singlet model
• The effect of interorbital scattering on superconductivity in doped Dirac materials
• Using Disorder to Identify Bogoliubov Fermi-Surface States
• Quasiperiodic criticality and spin-triplet superconductivity in superconductor-antiferromagnet moire patterns
• Designing spin-textured flat bands in twisted graphene multilayers via helimagnet encapsulation
• Theory of the low- and high-field superconducting phases of UTe${}_2$
• Spontaneous magnetization in unitary superconductors with time reversal symmetry breaking
• Topological superconductivity on the honeycomb lattice: Effect of normal state topology
• Nodal gaps from local interactions in Sr${}_2$RuO${}_4$
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• Unconventional High Temperature Superconductivity in Cubic Zinc-blende Transition Metal Compounds
• Pair-breaking in superconductors with strong spin-orbit coupling
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• Monopole versus spherical harmonic superconductors: Topological repulsion, coexistence and stability
• Bardasis-Schrieffer-like phase mode in a superconducting bilayer
• Bound states around impurities in a superconducting bilayer
• Proximity-induced collective modes in an unconventional superconductor heterostructure
• Spin Susceptibility of a J=3/2 Superconductor
• Discontinuous Transition to Superconducting Phase
• Vertex correction for the linear and nonlinear optical responses in superconductors: multiband effect and topological superconductivity
• Fragile superconductivity in a Dirac metal
• Decoding the drive-bath interplay: A guideline to enhance superconductivity
• Superconducting magnetoelectric effects in mesoscopic hybrid structures
• Quantum geometric magnetic monopole and two-phase superconductivity in CeRh${}_2$As${}_2$
• Low-temperature anomaly and anisotropy of critical magnetic fields in transition-metal dichalcogenide superconductors
• Fibration, Nexus and Cosmological Composite Topological Defects in Uniaxially Disordered Superfluid ${}^3$He
• "Universal" ${\Delta }_{max}/T_c$ in Fe Based Superconductors
• Sensitivity of superconducting states to the impurity location in layered materials
• Odd-frequency superfluidity from a particle-number-conserving perspective