Electron Spin Resonance (ESR) can microscopically probe both conduction electrons (ce) and local moment (LM) spin systems in different materials. A ce spin resonance (CESR) is observed in metallic systems based on light elements or with enhanced Pauli susceptibility. LM ESR is frequently seen in compounds with paramagnetic ions and localized d or f electrons. Here we report a remarkable and unprecedented ESR signal in the heavy fermion (HF) superconductor beta-YbAlB4[1] which behaves as a CESR at high temperatures and acquires characteristics of the Yb3+ LM ESR at low temperature. This dual behavior in same ESR spectra strikes as an in situ unique observation of the Kondo quasiparticles giving rise to a new ESR response called Kondo coupled resonant mode (KCRM). The proximity to a quantum critical point (QCP) may favor the observation of a KCRM and its dual character in beta-YbAlB4 may unveil the 4f-electrons nature at the QCP.
We report the effect of hydrostatic pressure on the resistivity of the heavy fermion Kondo lattice compound Yb$_2$Fe$_3$Si$_5$ in the temperature range 2-300 K and in pressures upto 10 Kbar. At ambient pressure the resistivity shows a prominent Kondo effect. The Kondo minimum shifts from 22.5 K at ambient pressure to 19.2 K at a pressure of 10 Kbar. The depth of the Kondo minimum also progressively decreases with pressure. These results suggest a possible weakening of the Kondo effect with the application of pressure.
The mechanism of strange metal (SM) with unconventional charge transport near magnetic phase transitions has become an outstanding open problem in correlated electron systems. Recently, an exotic quantum critical SM phase was observed in paramagnetic frustrated heavy-fermion materials near Kondo breakdown. We establish a controlled theoretical framework to this issue via a dynamical large-N fermionic multichannel approach to the two-dimensional Kondo-Heisenberg lattice model, where KB transition separates a heavy-Fermi liquid from fermionic spin-liquid state. With Kondo fluctuations being full…
We study the quantum phase transition from an antiferromagnetic metal to a heavy fermion metal in the Kondo lattice model. Based on the strong coupling approach we {\it first} diagonalize the Kondo coupling term. Since this strong coupling approach makes the resulting Kondo term {\it relevant}, the Kondo hybridization persists even in the antiferromagnetic metal, indicating that fluctuations of Kondo singlets are not critical in the phase transition. We find that the quantum transition in our strong coupling approach results from {\it softening of antiferromagnetic spin fluctuations of localiz…
Quantum criticality in certain heavy-fermion metals is believed to go beyond the Landau framework of order-parameter fluctuations. In particular, there is considerable evidence for Kondo destruction: a disappearance of the static Kondo singlet amplitude that results in a sudden reconstruction of Fermi surface across the quantum critical point and an extra critical energy scale. This effect can be analyzed in terms of a dynamical interplay between the Kondo and RKKY interactions. In the Kondo-destroyed phase, a well-defined Kondo resonance is lost, but Kondo singlet correlations remain at nonze…
We study the Kondo lattice model on the geometrically frustrated Shastry-Sutherland lattice focusing on the quantum phase transition between the valence bond solid and the heavy fermion liquid phase. By explicitly including spinon pairing of local moments at the mean-field level, we establish the emergence of a unique heavy fermion superconducting phase induced by dimer ordering of the local moments coexisting with Kondo hybridization. Furthermore, we demonstrate that for suitable choices of parameters, a partial Kondo-screening phase, where some of the valence bonds are broken, precedes the a…
Ground state properties of a Kondo lattice model with random configuration of $f$ electrons are investigated with a variational Monte Carlo method. We show that the crossover from a dilute-Kondo system to a heavy-fermion system occurs when the density of $c$ and $f$ electrons ($n_c$, $n_f$) become comparable, $n_f\lesssim n_c$. In the heavy-fermion region, the correlation between $f$ electrons is strong and the $f$ electrons themselves greatly contribute to the screening of other $f$-electron moments. We propose that the character of Kondo screening changes from "individual" to "collective" ac…
The unconventional critical behavior near magnetic quantum phase transitions in various heavy-fermion metals, apparently inconsistent with the standard spin-density-wave scenario, has triggered proposals on the breakdown of the Kondo effect at the critical point. Here we investigate, within one specific scenario, the fate of such a zero-temperature transition upon coupling of the electronic to lattice degrees of freedom. We study a Kondo-Heisenberg model with volume-dependent Kondo coupling -- this model displays both Kondo volume collapse and Kondo-breakdown transitions, as well as Lifshitz t…
Starting from the two-orbital Kondo-lattice model with classical t_2g spins, an effective spinless fermion model is derived for strong Hund coupling J_H with a projection technique. The model is studied by Monte Carlo simulations and analytically using a uniform hopping approximation. The results for the spinless fermion model are in remarkable agreement with those of the original Kondo-lattice model, independent of the carrier concentration, and even for moderate Hund coupling J_H. Phase separation, the phase diagram in uniform hopping approximation, as well as spectral properties including t…
Replacing a magnetic atom by a spinless atom in a heavy fermion compound generates a quantum state often referred to as a 'Kondo-hole'. No experimental imaging has been achieved of the atomic-scale electronic structure of a Kondo-hole, or of their destructive impact (Lawrence JM, et al. (1996) Kondo hole behavior in Ce0. 97La0. 03Pd3. Phys Rev B 53:12559-12562; Bauer ED, et al. (2011) Electronic inhomogeneity in a Kondo lattice. Proc Natl Acad Sci. 108:6857-6861) on the hybridization process between conduction and localized electrons which generates the heavy fermion state. Here we report visu…
We study the Kondo lattice model using a class of canonical transformations that allow us to faithfully represent the model entirely in terms of fermions without constraints. The transformations generate interacting theories that we study using mean field theory. Of particular interest is a new manifestly O(3)-symmetric representation in terms of Majorana fermions at half-filling on bipartite lattices. This representation suggests a natural O(3)-symmetric trial state that is investigated and characterized as a gapped spin liquid.
One of the challenges in strongly correlated electron systems, is to understand the anomalous electronic behavior that develops at an antiferromagnetic quantum critical point (QCP), a phenomenon that has been extensively studied in heavy fermion materials. Current theories have focused on the critical spin fluctuations and associated break-down of the Kondo effect. Here we argue that the abrupt change in Fermi surface volume that accompanies heavy fermion criticality leads to critical charge fluctuations. Using a model one dimensional Kondo lattice in which each moment is connected to a separa…
We present a study of the resonant inelastic scattering response of \ybin\ excited at the tender Yb $M_5$ X-ray edge. In the high-temperature, paramagnetic phase, we observe a multiplet structure which can be understood at an ionic level. Upon cooling through the valence transition at $T_v\sim$ 40$K$, we observe a strong renormalization of the low-energy spectra, indicating a sensitivity to the formation of an intermediate valence phase at low temperatures. Similar spectrum renormalization has been observed in the optical conductivity, which suggests that the low-energy electronic structure po…
We report experimental observation of Kondo-Fano resonant tunneling in Si-doped GaAs/AlAs multiple quantum wells. The spectrum of differential tunneling conductance at low bias shows a strong temperature dependent resonance, whose peak is split in the presence of a magnetic field, characteristic of a Kondo resonance. The data is well explained as a resonant tunneling of conduction electrons at the Fermi level through the doped silicon impurity states inside the wells by using an impurity Anderson model. The Coulomb blockade resonance of the impurity states induces a Fano dip above the Kondo re…
In this study, we investigate the Kondo effect induced by the s-d interaction where the conduction bands are occupied by Dirac fermions. The Dirac fermion has the linear dispersion and is described typically by the Hamiltonian such as $H_k= v{\bf k}\cdot σ+m σ_0$ for the wave number ${\bf k}$ where $σ_j$ are Pauli matrices and $σ_0$ is the unit matrix. We derived the formula of the Kondo temperature $T_K$ by means of the Green's function theory for Green's functions including Dirac fermions and the localized spin. The $T_K$ was determined from a singularity of Green's functions in the form $T_…
The conformal field theory (CFT) approach to Kondo problems, originally developed by Affleck and Ludwig (AL), has greatly advanced the fundamental knowledge of Kondo physics. The CFT approach to Kondo impurities is based on a necessary approximation, i.e., the linearization of the low-lying excitations in a narrow energy window about the Fermi surface. This treatment works well in normal metal baths, but encounters fundamental difficulties in systems with Fermi points and high-order dispersion relations. Prominent examples of such systems are the recently-proposed topological semimetals with e…
In this work we combine the well established Kondo problem with the more speculative field of a discrete space time. We show that a discrete energy space induces a flow towards a new fixed point by breaking the conservation of charge and spin and lifting the fermion parity. This parity lifting fixed point appears on a scale set by the discretization of energy space. In contrast to the Planck scale the associated energy scale is at very low energy scales, possibly given by the inverse size of the universe.
Kondo Echo Dynamics of Terahertz-Pumped Heavy Fermions
Physikalisches Institut and Bethe Center for Theoretical Physics, Universität Bonn（波恩大学物理研究所与贝特理论物理中心）；Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum Jülich（于利希研究中心量子计算分析研究所（PGI-12））；School of Physics and Astronomy, University of St. Andrews（圣安德鲁斯大学物理与天文学学院）
Kondo insulators are primary candidates in the search for strongly correlated topological quantum phases, which may host topological order, fractionalization, and non-Abelian statistics. Within some Kondo insulators, the hybridization gap is predicted to protect a nontrivial topological invariant and to harbor emergent heavy Dirac fermion surface modes. We use high-energy-resolution spectroscopic imaging in real and momentum space on the Kondo insulator, SmB$_6$. On cooling through $T^*_Δ\approx$ 35 K we observe the opening of an insulating gap that expands to $Δ\approx$ 10 meV at 2 K. Within …
Quantum criticality beyond the Landau paradigm represents a fundamental problem in condensed matter and statistical physics. Heavy fermion systems with multipolar degrees of freedom can play an important role in the search for its universal description. We consider a Kondo lattice model with both spin and quadrupole degrees of freedom, which we show to exhibit an antiferroquadrupolar phase. Using a field theoretical representation of the model, we find that Kondo couplings are exactly marginal in the renormalization group sense in this phase. This contrasts with the relevant nature of the Kond…
Resolving the heavy fermion band in the conduction electron momentum resolved spectral function of the Kondo lattice model is challenging since, in the weak coupling limit, its spectral weight is exponentially small. In this article we consider a composite fermion operator, consisting of a conduction electron dressed by spin fluctuations that shares the same quantum numbers as the electron operator. Using approximation free auxiliary field quantum Monte Carlo simulations we show that for the SU(2) spin-symmetric model on the square lattice at half filling, the composite fermion acts as a magni…
A spin-$\frac{1}{2}$ Kitaev sublattice interacting with a subsystem of spinless fermions is studied on a honeycomb lattice when the fermion band is half filled. The model Hamiltonian describes a topological Kondo lattice with the Kitaev interaction, it is solved exactly by reduction to free Majorana fermions in a static $\mathbb{Z}_2$ gauge field. An yet unsolved problem of a hybridization of fermions and local moments in the Kondo lattice at low temperatures is solved in the framework of the model proposed. The Kondo hybridization gap is opened and the system is fixed in insulator and spin in…
Dynamical tunneling systems have been proposed earlier to display a two-channel Kondo effect, the orbital index of the particle playing the role of a pseudospin in the equivalent Kondo problem, and the spin being a silent channel index. However, as shown recently by Aleiner et al. [Phys. Rev. Lett. 86, 2629 (2001)], the predicted two-channel Kondo behavior can never be observed in the weak coupling regime, where the tunneling induced splitting of the levels of the tunneling system always dominates the physics. Here we show that the above scenario changes completely if the conduction electrons …
The underlying Dirac point is central to the profound physics manifested in a wide class of materials. However, it is often difficult to drive a system with Dirac points across the massless fermionic critical point. Here by exploiting screening of local moments under spin-orbit interactions in a Kondo lattice, we show that below the Kondo temperature, the Kondo lattice undergoes a topological transition from a strong topological insulator to a weak topological insulator at a finite temperature $T_D$. At $T_D$, massless Dirac points emerge and the Kondo lattice becomes a Dirac semimetal. Our an…
The microscopic theory of interaction between the heavy fermions and the crystal field excitations in Kondo lattices is presented. It is shown that the heavy-fermion spectrum scaled by the Kondo temperature $T_K$ can be modified by the crystal field excitations with the energy $Δ_{CF}$ provided the inequality $Δ_{CF}<T_K$ is realized. On the base of general description of excitation spectrum the detailed qualitative and quantitative explanation of anisotropic inelastic neutron scattering spectra and low-temperature specific heat of orthorhombic CeNiSn is given. The theory resolves the apparent…
Heavy fermion metals typically exhibit unconventional quantum critical point or quantum critical phase at zero temperature due to competition of Kondo effect and magnetism. Previous theories were often based on certain local type of assumptions and a fully consistent explanation of experiments has not been achieved. Here we develop an efficient algorithm for the Schwinger boson approach to explore the effect of spatial correlations on the Kondo lattice and introduce the concept of nonlocal Kondo effect in the quantum critical region with deconfined spinons. We predict a global phase diagram co…
We address the phenomenon of critical Kondo destruction in pseudogap Bose-Fermi Anderson and Kondo quantum impurity models. These models describe a localized level coupled both to a fermionic bath having a density of states that vanishes like |ε|^r at the Fermi energy (ε=0) and, via one component of the impurity spin, to a bosonic bath having a sub-Ohmic spectral density proportional to |ω|^s. Each bath is capable by itself of suppressing the Kondo effect at a continuous quantum phase transition. We study the interplay between these two mechanisms for Kondo destruction using continuous-time qu…
We develop a theoretical basis for understanding the spin relaxation processes in Kondo lattice systems with heavy fermions as experimentally observed by electron spin resonance (ESR). The Kondo effect leads to a common energy scale that regulates a logarithmic divergence of different spin kinetic coefficients and supports a collective spin motion of the Kondo ions with conduction electrons. We find that the relaxation rate of a collective spin mode is greatly reduced due to a mutual cancelation of all the divergent contributions even in the case of the strongly anisotropic Kondo interaction. …
The breakdown of the lattice Kondo effect in local-moment metals can lead to non-trivial forms of quantum criticality and a variety of non-Fermi-liquid phases. Given indications that Kondo-breakdown transitions involve criticality not only in the spin but also in the charge sector, we investigate the interplay of Kondo breakdown and strong valence fluctuations in generalized Anderson lattice models. We employ a parton mean-field theory to describe the transitions between deconfined fractionalized Fermi liquids and various confined phases. We find that rapid valence changes near Kondo breakdown…
Heavy fermion metals hosting multipolar local moments set a new stage for exploring exotic spin-orbital entangled quantum phases. In such systems, the quadrupolar Kondo effect serves as the key ingredient in the orbital-driven non-Fermi liquid (NFL) behavior and quantum critical phenomena. The cubic heavy fermion superconductor Pr$Tr_2$Al$_{20}$ ($Tr$: Ti, V) is a prime candidate for realizing the quadrupolar Kondo lattice. Here, we present a systematic study of the NFL phenomena in PrV$_2$Al$_{20}$ based on magnetoresistance (MR), magnetic susceptibility and specific heat measurements. Upon e…
We investigate f-electron charge susceptibility in a two-impurity Anderson model on the basis of Wilson's numerical renormalization group method. The f-electron charge susceptibility diverges logarithmically at the critical point of this model when conduction-electron bands exhibit particle-hole symmetry. Although the critical point disappears without the particle-hole symmetry, the f-electron charge fluctuation is much more enhanced near the crossover regime between the Kondo-Yosida singlet and intersite spin-singlet states than that in the single-impurity case. This result shows that charge …
We show that a Majorana fermion description of the two channel Kondo model can emerge quite naturally as a representation of the algebra associated with the spin currents in the two channels. Using this representation we derive an exact equivalent Hamiltonian for the two channel model expressed entirely in terms of Majorana fermions. The part of the Hamiltonian that is coupled to the impurity spin corresponds to the vector part of the $σ$-$τ$ model (compactified two channel model). Consequently all the thermodynamic properties associated with the impurity spin can be calculated from the $σ$-$τ…
We study the competition between the Kondo effect and frustrating exchange interactions in a Kondo-lattice model within a large-${\cal N}$ dynamical mean-field theory. We find a T=0 phase transition between a heavy Fermi-liquid and a spin-liquid for a critical value of the exchange $J_c = T_{K}^0$, the single-impurity Kondo temperature. Close to the critical point, the Fermi liquid coherence scale $T^\star$ is strongly reduced and the effective mass strongly enhanced. The regime $T>T^\star$ is characterized by spin-liquid magnetic correlations and non-Fermi-liquid properties. It is suggested t…
Considerable recent theoretical and experimental efforts have been devoted to the study of quantum criticality and novel phases of antiferromagnetic heavy-fermion metals. In particular, quantum phase transitions have been discovered in the compound Yb$_2$Pt$_2$Pb. These developments have motivated us to study the competition between the RKKY and Kondo interactions on the Shastry-Sutherland lattice. We determine the zero-temperature phase diagram as a function of magnetic frustration and Kondo coupling within a slave-fermion approach. Pertinent phases include the Shastry-Sutherland valence bond…
The enhanced spin Hall effect in Au metal due to the resonant skew scattering is studied with first-principles band structure calculations. Especially the gigantic spin Hall angle $γ_S \cong 0.1$ observed recently (T.Seki et al., Nature Materials {\bf 7}, 125 (2008)) is attributed to the orbital-dependent Kondo effect of Fe in the Au host metal, where the $t_{2g}$-orbitals are in the mixed-valence region while $e_g$-orbitals are in the Kondo limit. The enhanced spin-orbit interaction by the electron correlation in the $t_{2g}$-orbitals leads to the gigantic spin Hall effect. Impurities with 5d…
We analyze a microscopic origin of the Kondo effect-assisted orbital order in heavy-fermion materials. By studying the periodic two-orbital Anderson model with two local electrons, we show that frustration of Hund's rule coupling due to the Kondo effect leads to an incommensurate spiral orbital and magnetic order, which exists only inside the Kondo screened (heavy-electron) phase. This spiral state can be observed in neutron and resonant X-ray scattering measurements in ${\rm U}$- and ${\rm Pr}$-based heavy-fermion compounds, and realized in cold atomic gases, e.g. fermionic ${}^{173}{\rm Yb}$…
We report that nonmagnetic heavy-fermion (HF) iron oxypnictide CeFePO with two-dimensional XY-type anisotropy shows a metamagnetic behavior at the metamagnetic field H_M \simeq 4 T perpendicular to the c-axis and that a critical behavior is observed around H_M. Although the magnetic character is entirely different from that in other Ce-based HF metamagnets, H_M in these metamagnets is linearly proportional to the inverse of the effective mass, or to the temperature where the susceptibility shows a peak. This finding suggests that H_M is a magnetic field breaking the local Kondo singlet, and th…
All models of interacting electrons and spins can be reformulated as theories of interacting Majorana fermions. We consider the Kondo lattice model that admits a symmetric representation in terms of Majorana fermions. In the first part of this work we study two variational states, which are natural in the Majorana formulation. At weak coupling a state in which three Majorana fermions tend to propagate together as bound objects is favored, while for strong coupling a better description is obtained by having deconfined Majorana fermions. This way of looking at the Kondo lattice offers an alterna…
Strongly correlated materials are characterized by the presence of electron-electron interactions in their electronic structure. They often have remarkable properties and transitions between competing phases of very different electronic and magnetic order. This thesis focuses on strongly correlated $f$-electron compounds containing Ce, Sm, and U. These materials exhibit a so-called heavy-fermion or Kondo-lattice behavior. They can become insulating due to hybridization effects (Kondo-insulator) or develop multipolar (hidden) order. Kondo insulators have recently been discussed in the context o…
It is becoming widely recognized that, contrary to earlier expectations, the usual one-band Hubbard model does not give an explanation for itinerant ferromagnetism. After reviewing the status of magnetic ordering in the one-band model, we discuss the possibility of ferromagnetism in some recently introduced two-band Hubbard models, and in generalized Anderson lattices. It is argued that these two classes of models are closely related and that it is their common feature that the ferromagnetic phase has to compete with a collective Kondo state.
We propose a new framework for first-principle calculations of heavy-fermion materials. These are described in terms of the Kondo lattice Hamiltonian with the parameters extracted from a realistic density functional based calculation which is then solved using continuous-time quantum Monte Carlo method and dynamical mean field theory. As an example, we show our results for the Neel temperatures of Cerium-122 compounds (CeX2Si2 with X=Ru, Rh, Pd, Cu, Ag, and Au) where the general trend around the magnetic quantum critical point is successfully reproduced. Our results are organized on a universa…
We investigate the impurity resonant state induced by non-magnetic impurities in d-wave cuprate superconductors in two different impurity models: (i) in a pure potential scattering model within the T-matrix approach and (ii) in a Bose-Fermi Kondo model within the large-N formalism. We modify the superconducting host to resemble the nanoscale electronic inhomogeneities seen in the scanning tunneling microscopy (STM) spectra (i.e., the small- and large-gap domains) and study how this influences the impurity resonance. In the pure potential scattering model the resonant state is found to be a rat…
Geometrically frustrated quantum impurities coupled to metallic leads have been shown to exhibit rich behavior with a quantum phase transition separating Kondo screened and local moment phases. Frustration in the quantum impurity can alternatively be introduced via Kitaev-couplings between different spins of the impurity cluster. We use the Numerical Renormalization Group (NRG) to study a range of systems where the quantum impurity comprising a Kitaev cluster is coupled to a bath of non-interacting fermions. The models exhibits a competition between Kitaev and Kondo dominated physics depending…
Recent studies of heavy-fermion systems with tunable quantum fluctuations have focused on a variety of zero-temperature phase transitions that involve not only the onset of magnetic order but also the destruction of Kondo entanglement. Motivated by these developments, we investigate the effect of enhanced quantum fluctuations induced by a transverse magnetic field in an Ising-anisotropic Kondo lattice model, solved within an extended dynamical mean field theory using the numerical renormalization group. A line of locally critical points describes a direct transition from a Kondo-screened param…
We report the thermodynamic, magnetic, and electronic transport properties of the new ternary intermetallic system (Ce,La)3Pt4In13. Ce3Pt4In13 orders antiferromagnetically at 0.95 K while the non-magnetic compound La3Pt4In13 is a conventional 3.3 K superconductor. Kondo lattice effects appear to limit the entropy associated with the Neel transition to (1/4)Rln2 as an electronic contribution to the specific heat of gamma = 1 J/mole-Ce K2 is observed at TN; roughly 35% of this gamma survives the ordering transition. Hall effect, thermoelectric power, and ambient-pressure resistivity measurements…
A purely fermionic representation is introduced for the ferromagnetic Kondo lattice model which allows conventional diagrammatic tools to be employed to study correlation effects. Quantum 1/S corrections to magnon excitations are investigated using a systematic inverse-degeneracy expansion scheme which incorporates correlation effects in the form of self-energy and vertex corrections, while explicitly preserving the continuous spin-rotation symmetry. Magnon self-energy is studied in the full range of interaction strength, and shown to result in strong magnon damping and anomalous softening for…
It has been a great challenge to explore many-body effects in heavy fermion systems with $ab$-$initio$ approaches. We computed the electronic structure of UTe$_{2}$ without purposive judgements, such as intentional selection of on-site Coulomb interaction and disregarding spin-orbit coupling. We show that U-5$f$ electrons are highly localized in the paramagnetic normal state, giving rise to the Kondo effect. It is also found that the hybridization between U-5$f$ and U-6$d$ predominantly in the orthorhombic $ab$-plane is responsible for the high-temperature Kondo effect. In contrast, the hybrid…
Abnormal electronic properties of complex systems require new ideas concerning explanation of their behavior and possibility of realization. In this acticle we show that a colossal magnetoresistance is realized in the state of the topological Kondo insulator, that is similar to the Kondo insulator state in the Kondo lattice. The mechanism of the phenomenon is the following: in the spin gapless phase an external magnetic field induces the gap in the spectrum of spin excitations, the gap in the spectrum of fermions is opened due to a hybridization between spin and fermion subsystems at half fill…
Non-abelian anyons are highly desired for topological quantum computation purposes, with Majorana fermions providing a promising route, particularly zero modes with non-trivial mutual statistics. Yet realizing Majorana zero modes in matter is a challenge, with various proposals in chiral superconductors, nanowires, and spin liquids, but no clear experimental examples. Heavy fermion materials have long been known to host Majorana fermions at two-channel Kondo impurity sites, however, these impurities cannot be moved adiabatically and generically occur in metals, where the absence of a gap remov…
Effective models focused on pertinent low-energy degrees of freedom have substantially contributed to our qualitative understanding of quantum materials. An iconic example, the Kondo model, was key to demonstrating that the rich phase diagrams of correlated metals originate from the interplay of localized and itinerant electrons. Modern electronic structure calculations suggest that to achieve quantitative material-specific models, accurate consideration of the crystal field and spin-orbit interactions is imperative. This poses the question of how local high-energy degrees of freedom become in…
Recent inelastic neutron scattering experiments in CeIn3 and CePd2Si2 single crystals, measured spin wave excitations at low temperatures. These two heavy fermion compounds exhibit antiferromagnetic long-range order, but a strong competition between the Ruderman-Kittel-Kasuya-Yosida(RKKY) interaction and Kondo effect is evidenced by their nearly equal Neel and Kondo temperatures. Our aim is to show how magnons such as measured in the antiferromagnetic phase of these Ce compounds, can be described with a microscopic Heisenberg-Kondo model as introduced by J.R.Iglesias, C.Lacroix and B.Coqblin, …
Using a canonical transformation it is possible to faithfully represent the Kondo lattice model in terms of Majorana fermions. Studying this representation we discovered an exact mapping between the Kondo lattice Hamiltonian and a Hamiltonian describing three spinless fermions interacting on a lattice. We investigate the effectiveness of this three fermion representation by performing a zero temperature mean-field study of the phase diagram at different couplings and fillings for the one-dimensional case, focusing on the appearance of ferromagnetism. The solutions agree in many respects with t…
These lecture notes give a brief introduction to heavy fermion physics, emphasizing aspects of particular modern interest. Following an introduction to the Kondo effect and the phenomenology of heavy fermions, the article introduces Kondo insulators, the simplest heavy fermions; the large N expansion for the Kondo lattice; heavy fermion superconductivity including the symplectic N approach; topological Kondo insulators and finally a discussion of the challenge of understanding the co-existence of magnetism and the Kondo effect.
We propose a microscopic physical mechanism that stabilizes coexistence of the Kondo effect and antiferromagnetism in heavy-fermion systems. We consider a two-dimensional quantum Kondo-Heisenberg lattice model and show that long-range electron hopping leads to a robust antiferromagnetic Kondo state. By using a modified slave-boson mean-field approach we analyze the stability of the heavy antiferromagnetic phase across a range or parameters, and discuss transitions between different phases. We also address connection to experiments on heavy fermion compounds.
Within a mean-field approximation, the ground state and finite temperature phase diagrams of the two-dimensional Kondo lattice model have been carefully studied as functions of the Kondo coupling $J$ and the conduction electron concentration $n_{c}$. In addition to the conventional hybridization between local moments and itinerant electrons, a staggered hybridization is proposed to characterize the interplay between the antiferromagnetism and the Kondo screening effect. As a result, a heavy fermion antiferromagnetic phase is obtained and separated from the pure antiferromagnetic ordered phase …
We report measurements of inelastic neutron scattering, magnetic susceptibility, magnetization, and the magnetic field dependence of the specific heat for the heavy Fermion compounds Ce$_3$In and Ce$_3$Sn. The neutron scattering results show that the excited crystal field levels have energies $E_1$ = 13.2 meV, $E_2$ = 44.8 meV for Ce$_3$In and $E_1$ = 18.5 meV, $E_2$ = 36.1 meV for Ce$_3$Sn. The Kondo temperature deduced from the quasielastic linewidth is 17 K for Ce$_3$In and 40 K for Ce$_3$Sn. The low temperature behavior of the specific heat, magnetization, and susceptibility can not be wel…
Recent inelastic neutron scattering experiments in CeIn$_{3}$ and CePd$_{2}$Si$_{2}$ single crystals measured spin wave excitations at low temperatures. These two heavy fermion compounds exhibit antiferromagnetic long-range order, but a strong competition between the Ruderman-Kittel-Kasuya-Yosida(RKKY) interaction and Kondo effect is evidenced by their nearly equal Néel and Kondo temperatures. Our aim is to show how magnons such as measured in the antiferromagnetic phase of these Ce compounds, can be described with a microscopic Heisenberg-Kondo model introduced by J.R.Iglesias, C.Lacroix and …
Kondo systems ranging from the single Kondo impurity to heavy fermion materials present us with a plethora of unconventional properties whose theoretical understanding is still one of the major open problems in condensed matter physics. Over the last few years, groundbreaking scanning tunneling spectroscopy (STS) experiments have provided unprecedented new insight into the electronic structure of Kondo systems. Interpreting the results of these experiments -- the differential conductance and the quasi-particle interference spectrum -- however, has been complicated by the fact that electrons tu…
