Breakdown of phase-locked states and limit of the upper critical field controlled by interband scattering in two-gap superconductors.

The effect of weak interband scattering on the maximum upper critical field $H_{c2}$, which can be achieved in a two-band superconductor by increasing intraband impurity scattering is considered. Using the two-gap Usadel equations, we show how weak interband scattering provides the crossover from the orbitally limited to the paramagnetically limited $H_{c2}$, both in bulk samples and thin films. The results are applied to describe high $H_{c2}$ values in carbon-doped MgB$_2$ films. It is shown that interband scattering produces mixed gradient terms $\propto Re(\Pi^{*}\Psi_\sigma^{*}\Pi\Psi_\pi)$ in the free energy, where $\Pi = \nabla +2\pi A/\phi_0$, and $\Psi_\sigma=\Delta_\sigma\exp(i\theta_\sigma)$ and $\Psi_\pi = \Delta_\pi\exp(i\theta_\pi)$ are intraband order parameters. The mixed gradient coupling can provide parametric excitation of the plasmon Legget mode or large-amplitude interband phase textures by ac currents.