Pair-density-wave superconductor from doping Haldane chain and rung-singlet ladder

TL;DR

This paper numerically discovers a pair-density-wave superconductor emerging from doping spin-one Haldane chains or rung-singlet ladders, revealing a novel phase with potential experimental realizations in solid-state and cold atom systems.

Contribution

It introduces a generalized Kondo model showing PDW superconductivity from doping specific spin systems, with detailed analysis of phase transitions and a composite order parameter.

Findings

PDW phase emerges upon doping in the model.

Continuous transition between PDW and Luttinger liquid phases.

Identification of a composite Cooper pair order parameter.

Abstract

We report the numerical discovery of a pair-density-wave (PDW) superconductor from doping either (i) a spin-one Haldane chain or (ii) a two-leg ladder in the rung singlet phase in which the doped charges occupy a single leg. We model these systems using a generalized Kondo model. The itinerant electrons are correlated and described by the $t-J$ model, and are further coupled to a spin $1/2$ Heisenberg model through the Kondo coupling $J_K$. When the density of electrons $x$ is one, the Mott insulator is in a Haldane phase or in a rung singlet phase depending on whether $J_K$ is negative or positive. Upon doping, a pair-density-wave with $\mathbf Q=\pi$ can emerge for both signs of $J_K$. In the $J_K \rightarrow -\infty$ limit, the model reduces to the recently proposed type II t-J model and we observes a continuous transition between the PDW superconductor and an unconventional Luttinger liquid phase with doping. We also identify a composite order parameter for the superconductor, which can be understood as a Cooper pair formed by two nearby fermionic spin-polarons. Our model and the predicted PDW phase can be experimentally realized by doping S=1 chains formed by Ni$^{2+}$ in a solid state system or a two-leg ladder of fermionic cold atoms with a potential bias between legs, which preferentially dopes carriers into a single leg.