Kondo Lattice Research Articles

Order fractionalization in a Kitaev-Kondo model

We describe a mechanism for order fractionalization in a two-dimensional Kondo lattice model, in which electrons interact with a gapless spin liquid of Majorana fermions described by the Yao-Lee (YL) model. When the Kondo coupling to the conduction electrons exceeds a critical value, the model develops a superconducting instability into a state where the spinor order parameter carries charge $e$ and spin $S=1/2$. The broken symmetry state develops a gapless Majorana Dirac cone in the bulk. By including an appropriate gauge string, we can show that the charge $e$, spinorial order develops off-diagonal long range order that allows electrons to coherently tunnel arbitrarily long distances through the spin liquid.

Z2 metallic spin liquid on a frustrated Kondo lattice

Metallic spin liquid has been reported in several correlated metals, but a satisfactory theoretical description is not yet available. Here we propose a potential route to realize the metallic spin liquid and construct an effective $\mathbb{Z}_2$ gauge theory with charged fractionalized excitations on the triangular Kondo lattice. This leads to a $\mathbb{Z}_2$ metallic spin liquid featured with long-lived, heavy holon excitations of spin 0 and charge $+e$ and a partially enlarged electron Fermi surface. It differs from the weak-coupling FL$^*$ state proposed earlier and may be viewed as a fractionalized heavy fermion liquid. Our theory provides a general framework to describe the metallic spin liquid in frustrated Kondo lattice systems.

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.

Quantum critical spin-liquid-like behavior in the S=12 quasikagome-lattice compound CeRh1−xPdxSn investigated using muon spin relaxation and neutron scattering

We present the results of muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) and neutron scattering on the Ce-based quasikagome lattice ${\mathrm{CeRh}}_{1\ensuremath{-}x}{\mathrm{Pd}}_{x}\mathrm{Sn}$ ($x=0.1$ to 0.75). Our zero-field (ZF) $\ensuremath{\mu}\mathrm{SR}$ results reveal the absence of both static long-range magnetic order and spin freezing down to 0.05 K in the single-crystal sample of $x=0.1$. The weak temperature-dependent plateaus of the dynamic spin fluctuations below 0.2 K in ZF-$\ensuremath{\mu}\mathrm{SR}$ together with its longitudinal-field (LF) dependence between 0 and 3 kG indicate the presence of dynamic spin fluctuations persisting even at $T=0.05\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ without static magnetic order. On the other hand, the magnetic specific heat divided by temperature ${C}_{\text{4f}}/T$ increases as $\ensuremath{-}\text{log}T$ on cooling below 0.9 K, passes through a broad maximum at 0.13 K, and slightly decreases on further cooling. The ac susceptibility also exhibits a frequency-independent broad peak at 0.16 K, which is prominent with an applied field $H$ along the $c$ direction. We, therefore, argue that such a behavior for $x=0.1$ [namely, a plateau in spin relaxation rate ($\ensuremath{\lambda}$) below 0.2 K and a linear $T$ dependence in ${C}_{\text{4f}}$ below 0.13 K] can be attributed to a metallic spin-liquid-like ground state near the quantum critical point in the frustrated Kondo lattice. The LF-$\ensuremath{\mu}\mathrm{SR}$ study suggests that the out of kagome plane spin fluctuations are responsible for the spin-liquid (SL) behavior. Low-energy inelastic neutron scattering (INS) of $x=0.1$ reveals gapless magnetic excitations, which are also supported by the behavior of ${C}_{\text{4f}}$ proportional to ${T}^{1.1}$ down to 0.06 K. Our high-energy INS study shows very weak and broad scattering in $x=0$ and 0.1, which transforms into well-localized crystal-field excitations with increasing $x$. The ZF-$\ensuremath{\mu}\mathrm{SR}$ results for the $x=0.2$ polycrystalline sample exhibit similar behavior to that of $x=0.1$. A saturation of $\ensuremath{\lambda}$ below 0.2 K suggests a spin-fluctuating SL ground state down to 0.05 K. The ZF-$\ensuremath{\mu}\mathrm{SR}$ results for the $x=0.5$ sample are interpreted as a long-range antiferromagnetic (AFM) ground state below ${T}_{\text{N}}=0.8\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, in which the AFM interaction of the enlarged moments probably overcomes the frustration effect. The long-range AFM ordering is also supported by the evolution of magnetic Bragg peaks in $x=0.75$ sample observed below 5 K in the neutron diffraction data.

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 ${\mathrm{UGe}}_{2}$.

Semimetallic Kondo lattice behavior in YbPdAs with a distorted kagome structure

We have synthesized YbPdAs with the hexagonal ZrNiAl-type structure, in which the Yb-atoms form a distorted kagome sublattice in the hexagonal basal plane. Magnetic, transport, and thermodynamic measurements indicate that YbPdAs is a low-carrier Kondo lattice compound with an antiferromagnetic transition at $T_\mathrm{N}$ = 6.6 K, which is slightly suppressed in applied magnetic fields up to 9 T. The magnetic entropy at $T_\mathrm{N}$ recovers only 33\% of $R\ln{2}$, the full entropy of the ground state doublet of the Yb-ions. The resistivity displays a $-\ln T$ dependence between 30 and 15 K, followed by a broad maximum at $T\rm_{coh}$ = 12 K upon cooling. Below $T\rm_{coh}$, the magnetoresistance changes from negative to positive, suggesting a crossover from single-ion Kondo scattering processes at intermediate temperatures to coherent Kondo lattice behaviors at low temperatures. Both the Hall resistivity measurements and band structure calculations indicate a relatively low carrier concentration in YbPdAs. Our results suggest that YbPdAs could provide an opportunity for examining the interplay of Kondo physics and magnetic frustration in low carrier systems.

Spin-polarized supercurrent through the van der Waals Kondo-lattice ferromagnet Fe3GeTe2

In the new van der Waals Kondo-lattice Fe$_3$GeTe$_2$, itinerant ferromagnetism and heavy fermionic behaviour coexist. Both the key properties of such a system namely a spin-polarized Fermi surface and a low Fermi momentum are expected to significantly alter Andreev reflection dominated transport at a contact with a superconducting electrode, and display unconventional proximity-induced superconductivity. We observed interplay between Andreev reflection and Kondo resonance at mesoscopic interfaces between superconducting Nb and Fe$_3$GeTe$_2$. Above the critical temperature ($T_c$) of Nb, the recorded differential conductance ($dI/dV$) spectra display a robust zero-bias anomaly which is described well by a characteristic Fano line shape arising from Kondo resonance. Below $T_c$, the Fano line mixes with Andreev reflection dominated $dI/dV$ leading to a dramatic, unconventional suppression of conductance at zero bias. As a consequence, an analysis of the Andreev reflection spectra within a spin-polarized model yields an anomalously large spin-polarization which is not explained by the density of states of the spin-split bands at the Fermi surface alone. The results open up the possibilities of fascinating interplay between various quantum phenomena that may potentially emerge at the mesoscopic superconducting interfaces involving Kondo lattice systems hosting spin-polarized conduction electrons.

Emergent Spinon Dispersion and Symmetry Breaking in Two-Channel Kondo Lattices.

Two-channel Kondo lattice serves as a model for a growing family of heavy-fermion compounds. We employ a dynamical large-N technique and go beyond the independent bath approximation to study this model both numerically and analytically using renormalization group ideas. We show that the Kondo effect induces dynamic magnetic correlations that lead to an emergent spinon dispersion. Furthermore, we develop a quantitative framework that interpolates between infinite dimension where the channel-symmetry broken results of mean-field theory are confirmed, and one-dimension where the channel symmetry is restored and a critical fractionalized mode is found.

Continuous ferromagnetic quantum phase transition on an anisotropic Kondo lattice

Motivated by the recent discovery of ferromagnetic quantum criticality in the heavy fermion compound ${\mathrm{CeRh}}_{6}{\mathrm{Ge}}_{4}$, we develop a numerical algorithm of infinite projected entangled pair states for the anisotropic ferromagnetic Kondo-Heisenberg model in two dimensions and study the ferromagnetic quantum phase transitions with varying magnetic and hopping anisotropy. Our calculations reveal a continuous ferromagnetic quantum phase transition in the large anisotropic region and first-order quantum phase transitions for smaller anisotropy. Our results highlight the importance of magnetic anisotropy on ferromagnetic quantum criticality in Kondo lattice systems and provide a possible explanation for the experimental observation in ${\mathrm{CeRh}}_{6}{\mathrm{Ge}}_{4}$ with a quasi-one-dimensional magnetic structure. Our work opens the avenue for future studies of the rich Kondo lattice physics using state-of-the-art tensor network approaches.

Gate-tunable heavy fermion quantum criticality in a moiré Kondo lattice

The authors propose a transition metal dichalcogenide moir\'e heterostructure that realizes a Kondo lattice and is capable of tuning across a quantum phase transition corresponding to the breakdown of Kondo screening. For a dual-gated setup, they theoretically identify the requisite gating conditions and find a quantum critical scenario where the local moments in a chiral spin-liquid state dissolve in the conduction electron Fermi sea to form an anomalous Hall heavy-fermion liquid. They discuss how the proposed gate-tunable Kondo lattice simulator can experimentally distinguish between various competing scenarios for the quantum phase transition, and thereby enable progress in the understanding of heavy-fermion quantum criticality.

Kondo entanglement in the quasi-two-dimensional heavy fermion compound CeSb2

In the heavy fermion system, development of the Kondo coherence usually occurs as a crossover behavior. However, accurate definition of the onset temperature for complete formation of the heavy quasiparticles is to some extent controversial. Here, the electronic structure of the quasi-two-dimensional Kondo lattice ${\mathrm{CeSb}}_{2}$ has been studied by high resolution angle-resolved photoemission spectroscopy (ARPES) and dynamical mean-field theory approach combined with density functional theory. A heavy quasiparticle band, which originates from the hybridization between $f$ electrons and conduction electrons, has been observed directly. Moreover, temperature-dependent electronic structure study reveals a transition from high-temperature local spins to low-temperature itinerant electrons in ${\mathrm{CeSb}}_{2}$ and the onset temperature of the hybridized c-f spectral weight revealed by laser-ARPES is consistent with the crossover temperature from transport and magnetic measurements. Our findings are essential for a microscopic understanding of different energy scales in the heavy fermion system and demonstrate the probability of laser-ARPES in studying the bulk 4f-electron properties of Ce-based compounds.

Combining bond particles with the Gutzwiller approximation: A variational theory of the Kondo lattice

We investigate the two-dimensional Kondo lattice, the minimal model of a heavy fermion compound. Despite its apparent simplicity, its dynamics are both complex and controversial. In the moderate-to-strong coupling regime, the bond fermion theory provides an approximate mapping to an easily solvable fermionic system. This works surprisingly well from a qualitative standpoint, but there are some shortcomings as the method has no precise mathematical foundation. We here try to address this and improve on the method by making an explicit connection to wave function based variational methods and the Gutzwiller approximation. We apply the improved method to both the previously studied N\'eel magnetic phases, as well as incommensurately and ferromagnetically ordered phase.

Molecular Lego for Functional 2D Materials: Self-Assembly and Ordering of Bi-Molecular 2D Spinlattices of M(II,III) Phthalocyanines and of Highly Crystalline Free Standing Networks

Single layer low-dimensional materials are presently of emerging interest, also in the context of magnetism. We further developed on-surface supra-molecular architecturing to create two-dimensional spin arrays. By chemical programming of the modules, different checkerboards were produced containing metals of different oxidation and spin states, diamagnetic zinc, and a metal-free ‘spacer’. [1] In an in-depth, spectro-microscopy and theoretical account, we correlate the structure and the magnetic properties of these tunable systems and discuss the emergence of 2D Kondo magnetism [2] from the spin-bearing components and via the physico-chemical bonding to the underlying substrate. The contributions of the individual elements, as well as the role of the electronic surface state in the bottom substrate, are discussed. Also we show the the first free-standing single layer networks of calixarenes stabilized via functional groups enabling vdW, coordination and dipole-dipole, interaction. [3]Fig. 1) Graphical animation of the 2D spin arrays built by C--H - F--C bonding of two different magnetic atom bearing phthalocyanines that have been exploited to investigate the assembly and properties of Kondo lattices.[1] M. Baljozovic et al. Magnetochemistry 2021, 7, 119.[2] J. Girovsky et al. Nature Communications 2017 8:15388[3] M. Moradi, N. Opara, L.G. Tulli, C. Wäckerlin, S.J. Dalgarno, S.J. Teat, M. Baljozovic, O. Popova, E. van Genderen, A. Kleibert, H. Stahlberg, J.P. Abrahams, C. Padeste, T.A. Jung, P. Shahgaldian, Sci. Adv. 2019; 5: eaav4489 Figure 1

Intermediate valence state in YbB4 revealed by resonant x-ray emission spectroscopy

We report the temperature dependence of the Yb valence in the geometrically frustrated compound from 12 to 300 K using resonant x-ray emission spectroscopy at the Yb transition. We find that the Yb valence, v, is hybridized between the v = 2 and v = 3 valence states, increasing from at 12 K to at 300 K, confirming that is a Kondo system in the intermediate valence regime. This result indicates that the Kondo interaction in is substantial, and is likely to be the reason why does not order magnetically at low temperature, rather than this being an effect of geometric frustration. Furthermore, the zero-point valence of the system is extracted from our data and compared with other Kondo lattice systems. The zero-point valence seems to be weakly dependent on the Kondo temperature scale, but not on the valence change temperature scale T v .

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)

Coexistence of Quasi-two-dimensional Superconductivity and Tunable Kondo Lattice in a van der Waals Superconductor

Realization of Kondo lattice in superconducting van der Waals materials not only provides a unique opportunity for tuning the Kondo lattice behavior by electrical gating or intercalation, but also is helpful for further understanding the heavy fermion superconductivity. Here we report a low-temperature and vector-magnetic-field scanning tunneling microscopy and spectroscopy study on a superconducting compound (4Hb-TaS2) with alternate stacking of 1T-TaS2 and 1H-TaS2 layers. We observe the quasi-two-dimensional superconductivity in the 1H-TaS2 layer with anisotropic response to the in-plane and out-of-plane magnetic fields. In the 1T-TaS2 layer, we detect the Kondo resonance peak that results from the Kondo screening of the unpaired electrons in the Star-of-David clusters. We also find that the intensity of the Kondo resonance peak is sensitive to its relative position with the Fermi level, and it can be significantly enhanced when it is further shifted towards the Fermi level by evaporating Pb atoms onto the 1T-TaS2 surface. Our results not only are important for fully understanding the electronic properties of 4Hb-TaS2, but also pave the way for creating tunable Kondo lattice in the superconducting van der Waals materials.

Giant spectral renormalization and complex hybridization physics in the Kondo lattice system CeCuSb2

We investigate the electronic structure of a Kondo lattice system, CeCuSb2 exhibiting significant mass enhancement and Kondo-type behavior. We observe multiple features in the hard x-ray photoemission spectra of Ce core levels due to strong final-state effects. The depth-resolved data exhibit a significant change in relative intensity of the features with the surface sensitivity of the probe. The extracted surface and bulk spectral functions are different and exhibit a Kondo-like feature at higher binding energies in addition to the well and poorly screened features. The core-level spectra of Sb exhibit huge and complex changes as a function of the surface sensitivity of the technique. The analysis of the experimental data suggests that the two non-equivalent Sb sites possess different electronic structures and in each category, the Sb layers close to the surface are different from the bulk ones. An increase in temperature influences the Ce-Sb hybridization significantly. The plasmon-excitation-induced loss features are also observed in all core level spectra. All these results reveal the importance of Ce-Sb hybridizations and indicate that the complex renormalization of Ce-Sb hybridization may be the reason for the exotic electronic properties of this system.

Electron liquid state in the spin-[Formula: see text] anisotropic Kondo lattice.

In the framework of the mean field approach, we provide analytical and numerical solution of the spin-frac{1}{2} anisotropic Kondo lattice for arbitrary dimension at half filling. Nontrivial solution for the amplitude of the field opens a gap in the fermion spectrum of an electron liquid in which local moments on the lattice sites are realized. The ground state in the insulator state is determined by a static {mathbb {Z}}_2 field of local moments, which forms the lattice with a double cell, conduction electrons move in this field. Due to hybridization between electron states a large Fermi surface is formed in the Kondo lattice. A gap in the quasi-particle spectrum is calculated depending on the magnitudes of exchange integrals for the simple lattices with different dimension. The proposed approach is also valid for describing the Kondo lattice with weak anisotropy of the exchange interaction, which makes it possible to study the behavior of the spin-frac{1}{2} Kondo lattice with an isotropic exchange interaction.

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.

Spin-liquid signatures in the quantum critical regime of pressurized CePdAl

CePdAl is a prototypical frustrated Kondo lattice with partial long-range order (LRO) at ${T}_{\mathrm{N}}=2.7$ K. Previous bulk experiments under hydrostatic pressure found signatures for a quantum critical regime that extends from ${p}_{\mathrm{c}}\ensuremath{\approx}0.9$ GPa, where LRO disappears, up to $\ensuremath{\sim}1.7$ GPa. We employed extensive muon spin relaxation and rotation experiments under pressure. The continuous and complete suppression of LRO at ${p}_{\mathrm{c}}$ is confirmed. Above ${T}_{\mathrm{N}}(p)$ and beyond ${p}_{\mathrm{c}}$, an additional crossover scale ${T}^{*}(p)$ characterizes the change from pure to stretched exponential relaxation in zero field. Remarkably, ${T}^{*}(p)$ agrees with previously determined signatures of entropy accumulation above LRO. This coincidence microscopically evidences fluctuating frustrated spins at $T\ensuremath{\le}{T}^{*}$ with spin-liquid behavior. Power-law divergences of the temperature and longitudinal field dependences of the relaxation rate, with time-field scaling, at pressures between ${p}_{c}$ and 1.7 GPa characterize this regime as quantum critical.