Crossband versus intraband pairing in superconductors: Signatures and consequences of the interplay

We analyze the paradigmatic competition between intraband and crossband Cooper-pair formation in two-band superconductors, neglected in most works to date. We derive the phase-sensitive gap equations and describe the crossover between the intraband-dominated and the crossband-dominated regimes, delimited by a ``gapless'' state. Experimental signatures of crosspairing comprise notable gap splitting in the excitation spectrum, non-BCS behavior of gaps versus temperature, as well as changes in the pairing symmetry as a function of temperature. The consequences of these findings are illustrated on the examples of ${\mathrm{MgB}}_{2}$ and ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$.