A robust theory of the mechanism of pair density wave (PDW) superconductivity (i.e., where Cooper pairs have nonzero center of mass momentum) remains elusive. Here we explore the triangular lattice $t\text{−}J\text{−}V$ model, a low-energy effective theory derived from the strong-coupling limit of the Holstein-Hubbard model, by large-scale variational Monte Carlo simulations. When the electron density is sufficiently low, the favored ground state is an s-wave PDW, consistent with results obtained from previous studies in this limit. Additionally, a PDW ground state with nematic d-wave pairing emerges in the intermediate range of electron densities and phonon frequencies. For these s-wave and d-wave PDWs arising in states with spontaneous breaking of time-reversal and inversion symmetries, PDW formation derives from valley-polarization and intrapocket pairing.

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• Charge density waves
• Magnetic order
• Pair density wave
• Pairing mechanisms
• Hubbard model
• Monte Carlo methods
• t-J model