Incommensurate pair-density-wave correlations in two-leg ladder $t$--$J$--$J_\perp$ model

TL;DR

This paper discovers a new incommensurate pair-density-wave phase in a two-leg ladder $t$-$J$-$J_ot$ model, characterized by oscillating pair correlations driven by layer polarization, with potential experimental relevance.

Contribution

It identifies a generalized Luther-Emery liquid phase with incommensurate PDW correlations in the ladder model, combining DMRG simulations and bosonization analysis.

Findings

Incommensurate pair-density-wave correlations are observed in the model.

The phase exhibits FFLO-like oscillations driven by layer polarization.

Finite interlayer hopping destabilizes the phase toward charge-4e correlations.

Abstract

We report the discovery of a generalized Luther-Emery liquid phase characterized by incommensurate pair-density-wave (iC-PDW) correlations in the two-leg $t$-$J$-$J_\perp$ ladder model. By tuning the potential difference between the legs, we explore the regime of intermediate layer polarization $P$. Combining density-matrix renormalization group (DMRG) simulations with bosonization analysis, we identify a spin-gapped phase at finite $P$, where the interlayer and intralayer pair correlations both oscillate, but with distinct periodicities. The interlayer correlations exhibit FFLO-like oscillations, driven by pairing between layers with mismatched Fermi momenta, with a period determined by their momentum difference. In contrast, the intralayer pair correlations arise from the coupling between charges on one layer and spin fluctuations on the opposite layer, with a momentum equal to twice the Fermi momentum of the opposite layer. The iC-PDW state is robust across a wide range of doping and polarization, although finite interlayer hopping eventually destabilizes it toward a state with charge-$4e$ correlations. We conclude by discussing the experimental realization of this model in optical lattice platforms and its relevance to the bilayer nickelate La$_3$Ni$_2$O$_7$.