We investigate theoretically the properties of s-wave multiband
superconductors in the weak coupling (BCS) limit in the presence of
pair-breaking effects of magnetic field. It is shown that a qualitatively new
gapless superconducting state must appear in quasi-2D superconductors in
magnetic fields parallel to the plane, corresponding to a Sarma state induced
on one of the Fermi surfaces. The emergence of the new state in s-wave
multiband superconductors in the absence of anisotropy or spin-orbit
interaction is usually accompanied by a zero-temperature first-order
metamagnetic phase transition. For anisotropic or non s-wave multiband
superconductors the order of the zero-temperature metamagnetic transition
depends on model parameters, and it may take the form of a smooth crossover.
The details of the temperature-magnetic field phase diagram for multiband
superconductors are investigated analytically at zero temperature and
numerically at a finite temperature. It is shown the zero-temperatures
first-order phase transition gives rise to a critical region on the B-T phase
diagram. We suggest possible experiments to detect the new gapless state.Comment: 16 pages, 10 figure