Interband coupling and nonmagnetic interband scattering in±ssuperconductors

A two-band model with repulsive interband coupling and interband potential scattering is considered to elucidate their effects on material properties. In agreement with previous work, we find that the bands' order parameters ${\mathrm{\ensuremath{\Delta}}}_1,2$ differ, and the larger is at the band with a smaller normal density of states (DOS), ${N}_n2<{N}_n1$. However, the bands' energy gaps, as determined by the energy dependence of the DOS, are equal due to scattering. For each temperature, the gaps become zero at a certain critical interband scattering rate; i.e., for strong enough scattering the model material becomes gapless. In the gapless state, the DOS at band 2 is close to the normal state value, whereas at band 1 it has a V shape with nonzero minimum. When the normal bands DOS are mismatched, ${N}_n1\ensuremath{\ne}{N}_n2$, the critical temperature ${T}_c$ is suppressed even in the absence of interband scattering, ${T}_c({N}_n1)$ has a domelike shape. With increasing interband scattering, the London penetration depth at low temperatures evolves from being exponentially flat to a power law and even to near linear behavior in the gapless state, the latter being easily misinterpreted as caused by order parameter nodes.