In-plane magnetic field-induced orbital FFLO superconductivity in twisted WSe$_2$ homobilayers

We theoretically predict the in-plane magnetic field-induced orbital Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting states in twisted WSe$_2$ homobilayers (tWSe$_2$), focusing on its dependence on layer polarization and Fermi surface geometry. For unpolarized layers, finite-momentum pairing emerges only at low temperatures and above a critical field $B_{c1,\parallel}$. When layer symmetry is broken, finite-momentum pairing is stabilized at any nonzero field, with a critical temperature higher than that of the zero-momentum state. Notably, we identify a phase transition, which separates two distinct FFLO phases, when there are two separate Fermi pockets residing in the two moiré mini-valleys associated with opposite layers. We further discuss the effects of twist angles and applied field directions. Our findings establish tWSe$_2$ as a promising platform for realizing and manipulating FFLO states via twist angle, displacement field, and filling factor.