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arXiv:2202.01224 · Physical review. B./Physical review. B

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

Ya-Hui Zhang, Ashvin Vishwanath

Published Jul 5, 2022• 24 citations
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Abstract

We report the numerical discovery of a Luther-Emery liquid with pair-density-wave (PDW) correlations 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 $t\text{\ensuremath{-}}J$ 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 $\mathbf{Q}=\ensuremath{\pi}$ can emerge for both signs of ${J}_{K}$. In the ${J}_{K}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ limit, the model reduces to the recently proposed type II $t\ensuremath{-}J$ model. 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 ${\mathrm{Ni}}^{2+}$ 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. Long-range order of the PDW can be achieved in quasi-one-dimensional system with finite interwire coupling.

DOI
10.1103/physrevb.106.045103

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We report the numerical discovery of a Luther-Emery liquid with pair-density-wave (PDW) correlations 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\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model, and are further coupled to a spin-1/21/21/2 Heisenberg model through the Kondo coupling JK{J}_{K}JK​. When the density of electrons xxx is one, the Mott insulator is in a Haldane phase or in a rung-singlet phase depending on whether JK{J}_{K}JK​ is negative or positive. Upon doping, a pair-density-wave with Q=\ensuremathπ\mathbf{Q}=\ensuremath{\pi}Q=\ensuremathπ can emerge for both signs of JK{J}_{K}JK​. In the JK\ensuremath→\ensuremath−\ensuremath∞{J}_{K}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}JK​\ensuremath→\ensuremath−\ensuremath∞ limit, the model reduces to the recently proposed type II t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model. 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=1S=1S=1 chains formed by Ni2+{\mathrm{Ni}}^{2+}Ni2+ 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. Long-range order of the PDW can be achieved in quasi-one-dimensional system with finite interwire coupling.
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Incommensurate pair-density-wave correlations in two-leg ladder ttt--JJJ--J⊥J_\perpJ⊥​ model
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Abstract In this article, we review some recent theoretical developments on potential high-temperature superconductors and unconventional metallic states that can arise from doping a spin-one Mott insulator in the d 8 valence. These studies are particularly relevant—though not limited—to the recently discovered bilayer nickelate superconductor La 3 Ni 2 O 7 . We focus on a ferromagnetic Kondo lattice model with mobile electrons in the d x 2 − y 2 orbital coupled to the localized spin moments in d z 2 orbital through a large Hund’s coupling J H . In the large J H limit, the model reduces to the type II t − J model with a mixture of spin-half singlon states and spin-one doublon states. We summarize density matrix renormalization group results on the Luther-Emery liquid in one dimensional chain and two-leg ladder. Then we mainly focus on bilayer square lattice and show that a large inter-layer coupling J ⊥ of d z 2 orbital can induce strong inter-layer pairing of d x 2 − y 2 orbital. In the strong J ⊥ limit, a kinetic-energy driven high T c superconductivity is demonstrated in an ideal model with only a single hopping term. Furthermore, the model predicts a symmetric pseudogap metal—dubbed ‘second Fermi liquid (FL)’—in the underdoped regime, yielding a phase diagram analogous to that of hole-doped cuprates. The bilayer Kondo model therefore presents a promising platform for both realizing higher- T c superconductors and exploring non-FL physics. We also comment on the possible limitations of the current models for the bilayer nickelate material and point out some future directions.
The mechanism of superconductivity in a purely interacting electron system has been one of the most challenging issues in condensed matter physics. In the BCS theory, the Landau's Fermi liquid is the ground state of weakly interacting fermions dictated by the fermion sign structure, and the superconducting instability only occurs when an additional pairing force is added. By contrast, as shown by density matrix renormalization group calculation, a quasi-one-dimensional superconducting state (specifically a Luther-Emery state) is an intrinsic ground state of the $t\ensuremath{-}J$ two-leg ladder and four-leg cylinder at finite doping. Such a Luther-Emery state with pairing can be directly turned into a Fermi-gas-like normal state without pairing by merely switching off the phase-string signs hidden in the model via two schemes, which reduce the sign structure to the trivial fermion signs associated with doped holes. It thus demonstrates a new pairing paradigm in a model-doped Mott insulator as due to the generic phase-string sign structure. Finally, as an example, the latter is explicitly shown to lead to a ``stringlike'' pairing force after adiabatically connecting to a strong anisotropic limit of the model.
Correlated-electron theories of superconductivity in layered cuprates often start from the premise of a gapped spin-liquid phase proximate to the superconducting state. This assumption is justified based on analytical and numerical demonstrations of a superconducting Luther-Emery phase in the doped 2-leg one-band Hubbard ladder, and the perceived analogy between coupled ladders and the two-dimensional CuO2{\mathrm{CuO}}_{2}CuO2​ layer. We demonstrate from accurate density matrix renormalization group studies the absence of the superconducting Luther-Emery phase in the doped 2-leg three-band ladder consisting of both copper and oxygen, even as the spin gap is large in the undoped three-band ladder. For realistic oxygen-oxygen hopping and Hubbard repulsion on the oxygen atoms, density-density rather than pairing correlations are dominant at long range. This result is equally valid whether or not the oxygens outside the ladder proper, over and above the rung and leg oxygens, are included in the computation. These results demonstrate the critical importance of oxygen orbitals, and raise disturbing questions about the applicability of many of the existing correlated-electron theories of superconductivity.