Zeeman-induced gapless superconductivity with a partial Fermi surface

We show that an in-plane magnetic field can drive two-dimensional spin-orbit-coupled systems under the superconducting proximity effect into a gapless phase where parts of the normal state Fermi surface are gapped, and the ungapped parts are reconstructed into a small Fermi surface of Bogoliubov quasiparticles at zero energy. The charge distribution, spin texture, and density of states of such a ``partial Fermi surface'' are discussed. Material platforms for its physical realization are proposed.