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arXiv:1910.06545 · Journal of the Physical Society of Japan

Superconducting Correlations in the One-Dimensional Kondo Lattice Models under Magnetic Fields

Kohei Suzuki, Kazumasa Hattori

Published Feb 13, 2020• 5 citations

Abstract

We analyze superconducting correlations in the one-dimensional Kondo lattice models with Ising anisotropy under transverse magnetic fields, using the density matrix renormalization group. For the spin-1/2 local spin model, the Ising anisotropy is introduced by the ferromagnetic Ising interaction between the local spins, while for the spin-1 model, it is taken by the single-ion anisotropy. The magnetic properties under the transverse fields for the spin-1/2 model are very similar to those for the spin-1 model [K. Suzuki and K. Hattori, J. Phys. Soc. Jpn. 88, 024707 (2019).]. For the superconducting correlations, we analyze various Cooper pairs within nearest-neighbor pairs including composite ones between the local spins and the electrons. We find that, for the spin-1/2 model, the superconducting correlations are highly enhanced in the Tomonaga-Luttinger liquid state near the Kondo-plateau phase, where the conduction electrons and the local spins are strongly coupled with a finite spin gap for the Ising axis. This is a clear contrast to the model under the longitudinal magnetic fields, where there are no noticeable superconducting correlations. Competitions between the transverse magnetic field and the Kondo singlet formation lead to this enhanced superconducting correlations. For the spin-1 model, the single-ion anisotropy suppresses the superconducting correlation and there is no noticeable enhancement. We also examine the large Kondo exchange coupling limit. For the moderate ferromagnetic Ising interaction between the local spins, we find that another type of superconducting correlation is enhanced inside the ferromagnetic phase. We discuss a possible relation between our results and reentrant superconductivity in U-based ferromagnetic superconductors under transverse magnetic fields.

DOI: 10.7566/jpsj.89.034703

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We study the effects of transverse magnetic fields on the

S=1

one-dimensional Kondo lattice model with a uniaxial anisotropy using the density matrix renormalization group. The model can be regarded as a simplified one for analyzing the Ising ferromagnetic superconductor URhGe. We find various phases such as ferromagnetic and antiferromagnetic phases, Kondo plateau (KP) phases, Tomonaga-Luttinger liquids, and fully polarized phases. In the KP phase, a pseudoplateau emerges in the magnetization due to strongly bound pairs between the local and the conduction electron spins. This is why we call this phase the Kondo plateau. At the critical field between the ferromagnetic and KP phases, we find metamagnetic behavior in the magnetization curve. We discuss various correlation functions and the Friedel oscillations in detail, and the experimental data under transverse magnetic fields in URhGe are discussed on the basis of the present results.

We investigate the magnetic order and related strongly correlated effects in a one-dimensional Ising-Kondo lattice with transverse field. This model is the anisotropic limit of the conventional isotropic Kondo lattice model, in the sense that the itinerant electrons interact with the localized magnetic moments via only longitudinal Kondo exchange. Adopting the numerical density-matrix renormalization group method, we map out the ground-state phase diagram in various parameter spaces. Depending on the Kondo coupling and filling number, three distinct phases, including a metallic paramagnetic, a metallic ferromagnetic, and a gapped spin-density wave phase, are obtained. The spin-density wave is characterized by an ordering wave vector, which coincides with the nesting wave vector of the Fermi surface. This makes the corresponding magnetic transition a spin analog of the Peierls transition occurring in the one-dimensional metal. Moreover, by analyzing the momentum distribution function and charge correlation function, the conduction electrons are shown to behave like free spinless fermions in the ferromagnetic phase. We finally discuss the effect of the repulsive Hubbard interaction between conduction electrons. Our paper enriches the Kondo physics and deepens the current understanding of the heavy fermion compounds.

Two aspects of strongly correlated electron systems are studied in this thesis. Hubbard-type models are thought to be at the basis of high-critical-temperature superconductivity. One interaction which has not had much study is the nearest-neighbour hopping of on-site singlet pairs. We refine earlier renormalization group arguments and, using the density-matrix renormalization group method, numerically confirm their prediction that a spin gap opens at infinitesimal pair-hopping amplitude V > 0 in the one-dimensional tight-binding model. We also find a phase separation transition at a finite V > 0 as well as a spin-gap transition at a finite V < 0. The exotic magnetic behaviour of heavy-fermion materials involves an interplay between the screening of local moments from each other and the formation of a magnetic state of long range order. While the single-impurity Kondo Hamiltonian is thought to model some aspects of this behaviour, the properties of the Kondo lattice model away from half-filling are largely unknown. We determine the presence of a spin-gap region in the phase diagram of the one-dimensional Heisenberg-Kondo lattice model and make predictions about certain concealed dimerization order parameters.

We study the effect of the nearest neighbor anisotropic exchange interaction on superconductivity in extended Hubbard model in a square lattice. This Hamiltonian is one of a base model to describe various effects on triplet superconductors, e.g. Sr 2 RuO 4 , because the ferromagnetic exchange is advantagous for triplet pairing. Within a one-band meanfield approximation, we calculate the critical temperatures of spin singlet and triplet superconductivity. We obtain a phase diagram in the longitudinal vs transverse exchange couplings and we show how the stable pairing state is controlled by the anisotropy of the exchange interaction.

We study higher-spin ($S\ensuremath{\ge}1$) generalization of the one-dimensional Kondo-Heisenberg model, in which the local spin-

S

moments of the Kondo-lattice model interact with each other via the antiferromagnetic Heisenberg interaction (

{J}_{\text{H}}

), by analytical and numerical methods. The strong-coupling (i.e., large Kondo coupling) expansion maps out an insulating phase at half-filling whose magnetic correlation depends on the parity of

2S

as well as a ferromagnetic metallic phase which dominates the strong-coupling region at generic fillings. Then, we carried out the density-matrix renormalization-group simulations for

S=1

to closely investigate the phase structure at large but finite Kondo coupling. At half-filling, the Kondo coupling and

{J}_{\text{H}}

do not compete and the insulating spin-gapless phase is stable, while the competition of the two leads to a stepwise collapse of the strong-coupling ferromagnetism via an intervening dimerized insulating phase with power-law spin correlation at quarter-filling.

Using a non-Abelian density matrix renormalization group method we determine the phase diagram of the Kondo lattice model in one dimension, by directly measuring the magnetization of the ground state. This allowed us to discover a second ferromagnetic phase missed in previous approaches. The phase transitions are found to be continuous. The spin-spin correlation function is studied in detail, and we determine in which regions the large and small Fermi surfaces dominate. The importance of double-exchange ordering and its competition with Kondo singlet formation is emphasized in understanding the complexity of the model.