Pair-density-wave in the strong coupling limit of the Holstein-Hubbard model

A pair-density-wave (PDW) is a superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a density-matrix renormalization-group (DMRG) study of an effective t-J-V model, which is equivalent to the Holstein-Hubbard model in a strong-coupling limit, on long two-, four-, and six-leg triangular cylinders. While a state with long-range PDW order is precluded in one dimension, we find strong quasi-long-range PDW order with a divergent PDW susceptibility as well as the spontaneous breaking of time-reversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around the K and K' points in the Brillouin zone can be identified. We conclude that the state is valley-polarized and that the PDW arises from intra-pocket pairing with an incommensurate center of mass momentum. In the two-leg case, the exponential decay of spin correlations and the measured central charge c approximate to 1 are consistent with an unusual realization of a Luther-Emery liquid.

Automated summary

In this study, a density-matrix renormalization-group study was conducted on PDW superconducting states on long triangular cylinders, revealing strong quasi-long-range PDW order, divergent PDW susceptibility, and the spontaneous breaking of time-reversal and inversion symmetries. The state was identified as valley-polarized and the PDW was found to arise from intra-pocket pairing with an incommensurate center of mass momentum. This study also observed an unusual realization of a Luther-Emery liquid in the two-leg case.