Kondo Lattice Model Research Articles

Ferromagnetism in the SU( N ) Kondo lattice model: SU( N ) double exchange and supersymmetry

We study the ground-state properties of the SU(N)-generalization of the Kondo-lattice model in one dimension when the Kondo coupling J_K (both ferromagnetic and antiferromagnetic) is sufficiently strong. Both cases can be realized using alkaline-earth-like cold gases in optical lattices. Specifically, we first carry out the strong-coupling expansion and identify two insulating phases (one of which is the SU(N)-analogue of the well-known gapped Kondo singlet phase). We then rigorously establish that the ground state in the low-density (for J_K<0) or the high-density (for J_K>0) region is ferromagnetic. The results are accounted for by generalizing the double-exchange mechanism to SU(N) "spins". Possible realizations of Bose-Fermi supersymmetry SU(N|1) in the (generalized) SU(N) Kondo-lattice model are discussed as well.

Ferrochiral, antiferrochiral, and ferrichiral skyrmion crystals in an itinerant honeycomb magnet

Topological spin textures, such as a skyrmion crystal, are a source of unusual physical phenomena owing to the interplay between magnetism and topology. Since physical phenomena depend on the topological property and the symmetry of underlying spin structures, the search for new topological spin textures and emergent phenomena is one of the challenges in condensed matter physics. In this letter, we theoretically explore new topological spin textures arising from the synergy between spin, charge, and sublattice degrees of freedom in an itinerant magnet. By performing simulated annealing for an effective spin model of the honeycomb Kondo lattice model, we find a plethora of skyrmion crystal instabilities at low temperatures, whose topological spin textures are classified into three types: ferrochiral, antiferrochiral, and ferrichiral skyrmion crystals. We show that the obtained skyrmion crystals are the consequence of the spin-orbit-coupling-free honeycomb structure. Our results reveal the potential for itinerant honeycomb magnets to host a wide variety of SkXs and emergent phenomena.

Low-temperature theory of inversion and quantum oscillations in Kondo insulators

The half-filled Kondo lattice model is studied at low temperatures on a simple cubic lattice using the self-consistent theory developed by Ram and Kumar [Phys. Rev. B 96, 075115 (2017)]. It is found to have three distinct insulating phases in the temperature-hopping plane, namely, the strong-coupling Kondo singlet (KS) phase, the inverted Kondo singlet (iKS) phase distinguished from the KS by inversion, and the antiferromagnetic (AFM) phase. The quasiparticle density of states across the inversion transition is noted to exhibit a dimensional reduction, which can differentiate between the KS and iKS insulators in experiments. Magnetic quantum oscillations obtained in the iKS and AFM phases are found to show a Lifshitz-Kosevich-like behavior with temperature as well as quantum fluctuations induced by the Kondo interaction.

Rigorous analysis of the effects of electron–phonon interactions on magnetic properties in the one-electron Kondo lattice model

The Kondo lattice model (KLM) is a typical model describing heavy fermion systems. In this paper, we consider the interaction of phonons with the system described by the one-electron KLM. Magnetic properties of the ground state of this model are revealed in a rigorous form. Furthermore, we derive the effective Hamiltonian in the strong coupling limit (\(J\rightarrow \infty \)) for the strength of the spin-exchange interaction J; we examine the magnetic properties of the ground state of the effective Hamiltonian and prove that the Aizenman–Lieb theorem concerning the magnetization holds for the effective Hamiltonian at finite temperatures. Generalizing the obtained results, we clarify a mechanism for the stability of magnetic properties of the ground state in the one-electron KLM system.

Absolute Adsorption Calculation of Shale Gas Based on the Ono–Kondo Lattice Model

Absolute Adsorption Calculation of Shale Gas Based on the Ono–Kondo Lattice Model

Phase transition and fractionalization in the superconducting Kondo lattice model

Topology, symmetry, electron correlations, and the interplay between them have formed the cornerstone of our understanding of quantum materials in recent years and are used to identify new emerging phases. While the first two give a fair understanding of noninteracting and, in many cases, weakly interacting wave function of electron systems, the inclusion of strong correlations could change the picture substantially. The Kondo lattice model is a paradigmatic example of the interplay of electron correlations and conduction electrons of a metallic system, describing heavy fermion materials and also fractionalized Fermi liquid pertaining to an underlying gauge symmetry and topological orders. In this work, we study a superconducting Kondo lattice model, a network of 1D Kitaev superconductors Kondo coupled to a lattice of magnetic moments. Using slave-particle representation of spins and exact numerical calculations, we obtain the phase diagram of the model in terms of Kondo coupling $J_K$ and identify a topological order phase for $J_{K}<J_{K}^c$ and a Kondo compensated phase for $J_{K}>J_{K}^c$, where $J_{K}^c$ is the critical point. Setting the energy scales of electron hopping and pairing to unity, the mean-field theory calculations achives $J_{K}^c=2$ and in exact numerics we found $J_{K}^c\simeq 1.76$, both of which show that the topological order is a robust phase. We argue that in terms of slave particles, the compensated phase corresponds to an invertible phase, and a Mott insulating transition leads to a topological order phase. Furthermore, we show that in the regime $J_{K}<J_{K}^c$ in addition to the low-energy topological states, a branch of subgap states appears inside the superconducting gap.

Breakdown of heavy quasiparticles in a honeycomb Kondo lattice: A quantum Monte Carlo study

We show that for the half-filled Kondo lattice model on the honeycomb lattice a Kondo breakdown occurs at small Kondo couplings $J_k$ within the magnetically ordered phase. Our conclusions are based on auxiliary field quantum Monte Carlo simulations of the so-called composite fermion spectral function. Within a U(1) gauge theory formulation of the Kondo model, it becomes apparent that a Higgs mechanism dictates the weight of the resonance in the spectral function. For the honeycomb lattice we observe that for small $J_k$ the quasiparticle pole gives way to incoherent spectral weight but it remains well defined for the square lattice. Our result provides an explicit example where the magnetic transition and the breakdown of heavy quasiparticles are detached as observed in Yb(Rh$_{0.93}$Co$_{0.07}$)$_2$Si$_2$ [Friedemann et al., Nat. Phys. \textbf{5}, 465 (2009)].

Non-Fermi liquid behavior and quantum criticality in cubic heavy fermion systems with non-Kramers multipolar local moments

Notable non-Fermi liquid and quantum critical behaviors are observed in rare-earth metallic systems with non-Kramers local moments supporting a number of different multipolar moments. A prominent example is $\text{Pr(Ti,V)}_{2}\text{Al}_{20}$, where the non-Kramers doublet of the $\text{Pr}^{3+}$ ion allows quadrupolar and octupolar moments, but lacks a dipolar moment. Previous theoretical studies show that a single impurity Kondo problem with such an unusual local moment leads to novel non-Fermi liquid states. In this work, we investigate possible quantum critical behaviors arising from the competition between non-Fermi liquid states and multipolar-ordered phases induced by the RKKY interaction. We consider a local version of the corresponding Kondo lattice model, namely the Bose-Fermi Kondo model. Here, the multipolar local moments are coupled to fermionic and bosonic bath degrees of freedom representing the multipolar Kondo effect and RKKY interactions. Using a perturbative renormalization group (RG) study up to two loop order, we find critical points between non-Fermi liquid Kondo fixed points and a quadrupolar ordered fixed point. The critical points describe quantum critical behaviors at the corresponding phase transitions and can be distinguished by higher order corrections in the octupolar susceptibility that can be measured by ultrasound experiments. Our results imply the existence of a rich expansion of the phases and quantum critical behaviors in multipolar heavy fermion systems.

Solvable 3D Kondo Lattice Exhibiting Pair Density Wave, Odd-Frequency Pairing, and Order Fractionalization.

The Kondo lattice model plays a key role in our understanding of quantum materials, but a lack of small parameters has posed a long-standing problem. We present a three-dimensional S=1/2 Kondo lattice model describing a spin liquid within an electron sea. Strong correlations in the spin liquid are treated exactly, enabling a controlled analytical approach. Like a Peierls or BCS phase, a logarithmically divergent susceptibility leads to an instability into a new phase at arbitrarily small Kondo coupling. Our solution captures a plethora of emergent phenomena, including odd-frequency pairing, pair density wave formation and order fractionalization. The ground-state state is a pair density wave with a fractionalized charge e, S=1/2 order parameter, formed between electrons and Majorana fermions.

Topological semimetal driven by strong correlations and crystalline symmetry

Electron correlations amplify quantum fluctuations and, as such, they have been recognized as the origin of a rich landscape of quantum phases. Whether and how they lead to gapless topological states is an outstanding question, and a framework that allows for determining novel phases and identifying new materials is in pressing need. Here we advance a general approach, in which strong correlations cooperate with crystalline symmetry to drive gapless topological states. We test this materials design principle by exploring Kondo lattice models and materials whose space group symmetries may promote different kinds of electronic degeneracies, with a particular focus on square-net systems. Weyl-Kondo nodal-line semimetals -- with nodes pinned to the Fermi energy -- are identified. We describe how this approach can be applied to discover strongly correlated topological semimetals, identify three heavy fermion compounds as new candidates, provide first direct experimental evidence for our prediction in Ce$_2$Au$_3$In$_5$, and discuss how our approach may lead to many more. Our findings illustrate the potential of the proposed materials design principle to guide the search for new topological metals in a broad range of strongly correlated systems.

Metamagnetism and tricritical behavior in the Kondo lattice model

The phase diagram of the Kondo lattice model is explored around the ferromagnetic region, including an external magnetic field, and allowing the coexistence of ferromagnetism and Kondo effect ($\mathrm{FM}+\mathrm{K}$). Considering the combined effect of temperature and pressure, the evolution of the $\mathrm{FM}+\mathrm{K}$ phase yields a wing structure phase diagram with a tricritical point and a ferromagnetic quantum critical end point. The evolution of the spin-selective Kondo insulator phase, inside the coexistence region, introduces another critical end point. The results show a correspondence with the experimental phase diagram of heavy-fermion compounds, in particular, the ferromagnetic superconductor ${\mathrm{UGe}}_{2}$.

Electric and magnetic properties of higher-spin Kondo-Heisenberg models at strong coupling

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.

Low-Energy Excitations of Skyrmion Crystals in a Centrosymmetric Kondo-Lattice Magnet: Decoupled Spin-Charge Excitations and Nonreciprocity.

We theoretically study spin and charge excitations of skyrmion crystals stabilized by conduction-electron-mediated magnetic interactions via spin-charge coupling in a centrosymmetric Kondo-lattice model by large-scale spin-dynamics simulations combined with the kernel polynomial method. We reveal clear segregation of spin and charge excitation channels and nonreciprocal nature of the spin excitations governed by the Fermi-surface geometry, which are unique to the skyrmion crystals in centrosymmetric itinerant hosts and can be a source of novel physical phenomena.

Erratum: Channel-selective non-Fermi liquid behavior in the two-channel Kondo lattice model under a magnetic field [Phys. Rev. B 102 , 155126 (2020)

Erratum: Channel-selective non-Fermi liquid behavior in the two-channel Kondo lattice model under a magnetic field [Phys. Rev. B <b>102</b> , 155126 (2020)

Non-Abelian bosonization in a (3+1) -d Kondo semimetal via quantum anomalies

Kondo lattice models have established themselves as an ideal platform for studying the interplay between topology and strong correlations such as in topological Kondo insulators or Weyl-Kondo semimetals. The nature of these systems requires the use of nonperturbative techniques, which are few in number, especially in high dimensions. Motivated by this we study a model of Dirac fermions in $(3+1)$ dimensions coupled to an arbitrary array of spins via a generalization of functional non-Abelian bosonization. We show that there exists an exact transformation of the fermions, which allows us to write the system as decoupled free fermions and interacting spins. This decoupling transformation consists of a local chiral, Weyl, and Lorentz transformation parameterized by solutions to a set of nonlinear differential equations, which order by order takes the form of Maxwell's equations with the spins acting as sources. Owing to its chiral and Weyl components this transformation is anomalous and generates a contribution to the action. From this we obtain the effective action for the spins and expressions for the anomalous transport in the system. In the former we find that the coupling to the fermions generates kinetic terms for the spins, a long-ranged interaction, and a Wess-Zumino-like term. In the latter we find generalizations of the chiral magnetic and Hall effects.

Photoinduced 120-degree spin order in the Kondo-lattice model on a triangular lattice

We theoretically predict the emergence of 120-degree spin order as a nonequilibrium steady state in the photodriven Kondo-lattice model on a triangular lattice. In the system away from the half filling with ferromagnetic ground state, the photoexcitation of conduction electrons and the photoinduced renormalization of bandwidth cause reconstruction of the band structure and subsequent redistribution of the electrons through relaxations, which result in an electronic structure similar to that in the half-filled system at equilibrium, where the 120-degree spin order is stabilized. In this photoinduced 120-degree spin ordered phase, domains of different spin-ordered planes are formed, and vortices of spin chirality vectors called ${Z}_{2}$ vortices appear at points where multiple domains meet. We also discuss favorable conditions and experimental feasibility to observe the predicted photoinduced magnetic phase transition by investigating dependencies on the light parameters (amplitude, frequency, and polarization), the electron filling, the strength of Kondo coupling, and the effects of antiferromagnetic coupling among the localized spins. Photoinduced magnetic structures proposed so far have been limited to simple collinear (anti)ferromagnetic orders or local magnetic defects in magnets. The present work paves a way to the optical creation of complex noncollinear magnetisms as a global nonequilibrium steady phase in photodriven systems.

Emergence of electronic modes by doping Kondo insulators in the Kondo lattice and periodic Anderson models

Heavy-fermion or Kondo lattice materials are considered to be typical strongly correlated systems, for which mean-field approximations have shown that the Coulomb interaction increases the effective mass and narrows the band gap. In this paper, to clarify interaction effects on the electronic excitation, the spectral function of the Kondo lattice and periodic Anderson models is studied around Kondo insulators in the strong-coupling regime, by using the non-Abelian dynamical density-matrix renormalization group method and perturbation theory. Upon doping a Kondo insulator, an electronic mode emerges in the Kondo insulating gap, exhibiting the momentum-shifted magnetic dispersion relation. Although the ground-state properties are similar to those of a doped band insulator, the emergence of the electronic mode reflecting spin-charge separation of the Kondo insulator is a crucial interaction effect that allows us to regard the Kondo-insulator--metal transition as a type of Mott transition. In addition, electronic modes emerge even in the high-energy regime by doping in the periodic Anderson model. These strong-correlation effects have not been expected in conventional mean-field approximations and would bring a different perspective on heavy-fermion or Kondo lattice systems.

Channel order in the two-channel Kondo lattice

We discuss the two-channel Kondo lattice model where a single localized spin per unit cell is coupled to two different conduction electron orbitals per unit cell. The calculation is done using the bond fermion formalism. For a Hamiltonian which is symmetric under exchange of the conduction channels we find a spontaneous breaking of this symmetry, i.e., the Kondo singlets are formed almost exclusively between the localized spin and only one of the two conduction orbitals. In addition to this channel-ferromagnetic phase we also find a channel-antiferromagnetic phase where the preferred conduction electron orbital alternates between sublattices. The parameter which determines the transition between these phases is the interchannel hybridization.

Ferromagnetic-antiferromagnetic Competition in Diluted Magnetic Semiconductors

The signature of the magnetic competition in a nearly filled impurity band diluted magnetic semiconductors is addressed. In the formalism of the Kondo lattice model, self-consistent equations determining the Green function of the itinerant carrier in the system are evaluated by use of the dynamical mean-field theory. An analytical solution of the static spin susceptibility of the itinerant carrier to specify the magnetic instability is then established. Once the impurity band is nearly filled, one finds the antiferromagnetic instability against the ferromagnetic state. Phase diagrams of the magnetic structures in the diluted magnetic semiconductor were also discussed.&#x0D;

Phase shift, ellipticity, angle, and topological number in skyrmion lattices

We theoretically study skyrmion lattices realized in a Kondo lattice model on a triangular lattice, focusing on the phase, ellipticity, and angle of the constituent multiple-Q waves. Analyzing the numerical data obtained in the previous study [Ozawa R, Hayami S and Motome Y 2017 Phys. Rev. Lett. 118 147205], we extract these parameters for the two types of skyrmion lattices with the skyrmion number of 1 and 2. We show that the topological transition between the two skyrmion lattices driven by an external magnetic field is accompanied by significant modulations of all three parameters.