Interband pairing in two-band superconductors with spin-orbit and Zeeman couplings

Interband pairing in multiband superconductors is often neglected because of its higher energetic cost compared with intraband pairing. We show that, in multiband systems, a Zeeman magnetic field can stabilize interband pairing through the near degeneracy of spin-split branches from different bands, even within a minimal on-site attractive interaction. Using hexagonal tight-binding models with locally broken inversion symmetry, we find a Zeeman-driven transition between a conventional intraband s-wave state and an interband-dominated superconducting Mixing state. The resulting quasiparticle spectrum is intrinsically gapless, leading to anomalous thermodynamic behavior, including a T-linear specific heat at low temperatures, reflecting a finite zero-energy density of states.