Interest in modulated paired states, long sought since the first proposals by Fulde and Ferrell and by Larkin and Ovchinnikov, has grown recently in the context of strongly coupled superconductors under the name of pair density wave. However, there is little theoretical understanding of how such a state might arise out of strong coupling physics in simple models. Although density matrix renormalization group has been a powerful tool for exploring strong coupling modulation phenomena of spin and charge stripe in the Hubbard model and the t-J model, there has been no numerical evidence of PDW within these models using DMRG. Here we note that a system with inversion breaking, C3v point group symmetry may host a PDW-like state. Motivated by the fact that spin-valley locked band structure of hole-doped group VI transition metal dichalcogenides materializes such a setting, we use DMRG to study the superconducting tendencies in spin-valley locked systems with strong short-ranged repulsion. Remarkably we find robust evidence for a PDW and the first of such evidence within DMRG studies of a simple fermionic model.
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