= Solution
In weak-coupling conventional <superconductivity>, a useful guide is $k_BT_c\sim\hbar\omega_{\rm ph}\exp[-1/\lambda_{\rm eff}]$: an appreciable phonon scale and an effective attraction after Coulomb effects are favorable. A large <density of states> at the <Fermi level> can strengthen pairing, while light constituent masses can raise relevant phonon frequencies. Increasing <electron>–phonon coupling without limit is not a general strategy: lattice instabilities, competing order and changes to the phonon spectrum constrain it, and stronger coupling requires treatment beyond the simple exponential expression.
For unconventional high-temperature superconductivity, strong electronic interactions and magnetic fluctuations can support sign-changing pairing, as in <d-wave superconductivity>. Layered structures and proximity to magnetic order may enhance useful correlations, but can also promote competing insulating or density-wave states. Sufficient mobile-carrier <phase stiffness> is needed to turn pairing into coherent superconductivity; strong pairing alone does not guarantee a large transition <temperature>. Disorder that is relatively harmless to an isotropic conventional pair state can be pair-breaking for sign-changing gaps. There is no universal recipe established by these qualitative conditions: the pairing interaction, symmetry, carrier density, competing phases and phase coherence must all be considered.
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