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The electron-phonon interaction can produce a retarded attraction. A carrier distorts the ionic lattice; a second carrier can lower its energy in that distortion. Integrating out a phonon gives a frequency-dependent interaction with an attractive low-frequency region. A schematic Matsubara-frequency contribution is $V_{\mathrm{ph}}(\mathbf{q},i{\omega }_n)\propto -|g_{\mathbf{q}}{|}^2{\omega }_{\mathbf{q}}/({\omega }_n^2+{\omega }_{\mathbf{q}}^2)$. It must be combined with the screened Coulomb repulsion, not treated as a statement that the bare electron-electron force is attractive.

Retardation separates the electronic and phonon energy scales and reduces the repulsive contribution in the pairing channel to a Coulomb pseudopotential. In the simplest weak-coupling approximation, a positive net dimensionless pairing strength givesThe formula assumes a phonon cutoff and simplified coupling; strong-coupling calculations need the spectral interaction rather than this one-number replacement. The phonon frequency's dependence on ionic mass motivates an isotope effect, whose actual exponent can be modified by other physics.

An interaction need not be attractive in every momentum channel to support pairing. Spin fluctuations or other electronic correlations can favor a sign-changing gap: in the gap equation, repulsive scattering between two regions can contribute constructively when their gap signs differ. Such mechanisms are candidates for unconventional superconductivity. Observing a d-wave gap identifies symmetry information but does not, by itself, establish a unique microscopic pairing mechanism in a cuprate.

An unconventional superconductor realizes unconventional superconductivity: its pairing cannot be described by the simple conventional isotropic spin-singlet model. The precise usage should be stated, since unconventional gap symmetry and an unconventional microscopic pairing mechanism are different claims.

A d-wave superconductor supplies a concrete example. Its superconducting gap function changes sign with momentum direction and can vanish at nodes, permitting low-energy Bogoliubov quasiparticles. Nodal quasiparticle power laws probe those excitations, while a phase-sensitive test of d-wave pairing probes the relative gap signs. An unusual superconducting transition temperature alone does not establish a particular pairing symmetry, and a real d-wave gap does not automatically imply broken time reversal.