Orbital FFLO in two-dimensional superconductors

Since its first proposal, FFLO superconducting states have been pursued in systems where the electron cyclotron motion (i.e. vortices) under an external magnetic field is suppressed, such that the critical field is restricted by the Chandrasekhar-Clogston Pauli paramagnetic limit. This makes the observation of FFLO superconductivity challenging because the orbital response under a magnetic field, especially in three-dimensional superconductors, is usually unavoidable. However, in two-dimensional superconductors, the in-plane upper critical field at low temperatures can be significantly enhanced, depending on the interlayer coupling strength. This study examines FFLO states emerge purely from the orbital effect in two-dimensional superconductor, such as twisted transition metal dichalcogenides and multilayer graphene systems, where an in-plane magnetic field deforms and shifts the Fermi surfaces and the perfect Fermi surface nesting is destroyed by broken time reversal symmetry. By exploring the impact of Fermi surface geometry on the in-plane upper critical field, we show that spatially modulated orbital FFLO states is general in two-dimensional superconductors when the Zeeman effect can be ignored.