Two-dimensional bulk Fulde–Ferrell state and gapless superconducting edge modes in the 1T'-WS₂/2H-WS₂ heterophase bilayer

We propose a material platform comprised of transition metal dichalcogenide (TMDC) heterostructures to realize the two-dimensional (2D) Fulde–Ferrell (FF) state and gapless superconducting edge modes. By van der Waals stacking a 2D superconductor (1T'-WS₂ with inversion symmetry) on top of a 2D topological insulator (2H-WS₂ with mirror symmetry), the resulting TMDC bilayer exhibits Rashba superconductivity with broken inversion symmetry. Under an external in-plane magnetic field, the system can host finite-momentum Cooper pairing, evidenced by the divergence in the particle-particle susceptibility calculated from a k · p Hamiltonian fitted to the ab initio theory band structure.  The resulting bulk FF state can induce superconductivity in the edge states with its spatially varying order parameter. By varying the strength of the in-plane magnetic field, we demonstrate that the edge state can undergo a phase transition to a one-dimensional gapless phase with narrow Fermi segments corresponding to zero-energy Bogoliubov quasi-particles. The controllable one-dimensional gapless phase serves as a clear experimental fingerprint of FF state and has potential applications on nonreciprocal superconducting transport and the engineering of Majorana-based quantum devices.