Magnetic-field-induced gapless state in multiband superconductors

Abstract

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 gapless superconducting state must appear in quasi-two-dimensional superconductors in magnetic fields parallel to the plane, corresponding to a Sarma state induced on one of the Fermi surfaces. The emergence of the 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 $B\text{\ensuremath{-}}T$ phase diagram. We suggest possible experiments to detect the gapless state.