  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.
