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arXiv:cond-mat/0002061 · Physical review. B, Condensed matter

Magnetism and superconductivity in underscreened Kondo chains

Natan Andrei, E. Orignac

Published Jul 1, 2000• 4 citations
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Abstract

We present a one-dimensional model of electrons coupled to localized moments of spin $S>~1$ in which magnetism and superconductivity interplay in a nontrivial manner. This model has a non-Fermi-liquid ground state of the chiral spin liquid type. An unconventional odd-frequency pairing is shown to be the dominant instability of the system, together with antiferromagnetism of the local moments. We argue that this model captures the physics of the Kondo-Heisenberg spin $S=1$ chain, in the limit of strong Kondo coupling. Finally, we discuss briefly the effect of interchain coupling.

DOI
10.1103/physrevb.62.r763

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We present a one-dimensional model of electrons coupled to localized moments of spin S> 1S>~1S> 1 in which magnetism and superconductivity interplay in a nontrivial manner. This model has a non-Fermi-liquid ground state of the chiral spin liquid type. An unconventional odd-frequency pairing is shown to be the dominant instability of the system, together with antiferromagnetism of the local moments. We argue that this model captures the physics of the Kondo-Heisenberg spin S=1S=1S=1 chain, in the limit of strong Kondo coupling. Finally, we discuss briefly the effect of interchain coupling.
We use bosonization and renormalization group methods to determine the ground-state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-12\frac{1}{2}21​ Luttinger liquid coupled by a Kondo exchange interaction JK{J}_{K}JK​ to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling J1{J}_{1}J1​ and a next-nearest-neighbor (frustrating) exchange interaction J2{J}_{2}J2​. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling JK{J}_{K}JK​ with the Luttinger liquid. We discuss the structure of the phase diagram of this system as a function of the ratios JK/J1{J}_{K}/{J}_{1}JK​/J1​, J2/J1{J}_{2}/{J}_{1}J2​/J1​, and of the parameters of the Luttinger liquid. In particular, we discuss in detail the regimes in which a pair-density-wave state may be realized and its relation with the spin correlations in the frustrated antiferromagnetic chain.
Motivated by the recent discovery of an intermediate quantum critical phase between the antiferromagnetic order and the Fermi liquid in the frustrated Kondo lattice CePdAl, we study here a Kondo-Heisenberg chain with frustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ XXZ interactions among local spins using the density matrix renormalization group method. Our simulations reveal a global phase diagram with rich ground states including the antiferromagnetic order, the valence-bond-solid and bond-order-wave orders, the pair density wave state, the uniform superconducting state, and the Luttinger liquid state. We show that both the pair density wave and uniform superconductivity belong to the family of Luther-Emery liquids and may arise from pair instability of an intermediate quantum critical phase with medium Fermi volume in the presence of strong quantum fluctuations, while the Luttinger liquid has a large Fermi volume. Our work provides a comprehensive picture of the frustrated Kondo lattice physics at one dimension, and suggests a deep connection between the pair density wave, the unconventional superconductivity, and the non-Fermi liquid quantum critical phase.
We study a one-dimensional electron gas in a special antiferromagnetic environment made by two spin-1/2 Heisenberg chains and a one-dimensional two-channel Kondo-Heisenberg lattice away from half-filling. These models flow to an intermediate fixed point which belongs to the universality class of chirally stabilized liquids. Using a Toulouse point approach, the universal properties of the models are determined as well as the identification of the leading instabilities. It is shown that these models exhibit a non-Fermi-liquid behavior with strong enhanced composite pairing correlations.
Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model). We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U=0). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1/2 end states for chains with open boundary conditions. Our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.
We derive here a stability condition for a local moment in the presence of an interacting sea of conduction electrons. The conduction electrons are modeled as a Luttinger liquid in which chirality and spin are coupled. We show that an Anderson UUU defect in such an interacting system can be transformed onto a nearly Fermi-liquid problem. We find that correlations among the conduction electrons stabilize the local moment phase. A Schrieffer-Wolff transformation is then performed which results in an anisotropic exchange interaction indicative of the Kondo effect in a Luttinger liquid. The ground-state properties of this model are then equivalent to those of the Kondo model in a Luttinger liquid.
We consider a one-dimensional model for a ppp-wave magnet within the bosonization framework. The model consists of itinerant electrons described by an extended Hubbard model coupled to a chain of localized moments through the Kondo exchange. The classical ground state of the local-moment system captures the salient features of an odd-parity magnet. By bosonizing the coupled system, a description in terms of coupled Luttinger liquids follows, giving rise to a rich weak-coupling phase diagram. It is shown that the spin chain develops quasi long-range order consistent with the combined time-reversal and translation symmetry defining the ppp-wave magnet. We highlight the peculiar role played by this order in establishing a commensurability condition on the electronic filling under which additional interactions appear in the bosonic field theory. It is demonstrated that these interactions endow the electron spectral function with a pronounced ppp-wave character. Away from commensurate filling, these interactions are rendered irrelevant and the ensuing ppp-wave character is lost.