We study the Kondo lattice model with additional attractive interaction between the conduction electrons within the dynamical mean-field theory using the numerical renormalization group to solve the effective quantum impurity problem. In addition to normal-state and magnetic phases we also allow for the occurrence of a superconducting phase. In the normal phase we observe a very sensitive dependence of the low-energy scale on the conduction-electron interaction. We discuss the dependence of the superconducting transition on the interplay between attractive interaction and Kondo exchange.
We present a theory of superconductivity in charge Kondo systems, materials with resonant quantum valence fluctuations, in the regime where the transition temperature is comparable to the charge Kondo resonance. We find superconductivity induced by charge Kondo impurities, study how pairing of a superconducting host is enhanced due to charge Kondo centers and investigate the interplay between Kondo-scattering and inter-impurity Josephson coupling. We discuss the implications of our theory for Tl-doped PbTe, which has recently been identified as a candidate charge Kondo system.
Inspired by the recent experimental evidence of antiferromagnetism and superconductivity coexistence in heavy fermion CeRhIn$_5$, we propose a fully microscopic approach based on the idea of real space pairing within the Anderson-Kondo lattice model. We present an overall phase diagram incorporating the emergence of a quantum critical point, where Kondo insulating (KI), antiferromagnetic (AF) and superconducting (SC) phases meet. We also obtain the Kondo insulating state with totally compensated magnetic moments as the parental state for the emerging SC phases. Furthermore, the coexistent (AF+…
Emergence of odd-frequency s-wave superconductivity is demonstrated in the two-channel Kondo lattice by means of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. Around half filling of the conduction bands, divergence of an odd-frequency pairing susceptibility is found, which signals instability toward the superconductivity. The corresponding order parameter is equivalent to a staggered composite-pair amplitude with even frequencies, which involves both localized spins and conduction electrons. A model wave function is constructed for the composite …
The discovery of superconducting nickelates reignited hope for elucidating the high-$T_{\textrm{c}}$ superconductivity mechanism in the isostructural cuprates. While in the cuprates, the superconducting gap opens up on a single-band of the quasi-2D Fermi surface, the nickelates are known to have 3D nature of electronic structure with multi-band. This raises a serious question about the role of 2D nature for the high-$T_{\textrm{c}}$ superconductivity. Here, employing dynamical mean field theory combined with GW method, we found the Kondo effect driven by the strong correlation of Nd-4$f$ and N…
Kondo-lattice theory for the t-J model and a phenomenological theory based on it are developed to study superconductivity in the vicinity of the Mott metal-insulator transition. Since the quenching of magnetic moments by single-site quantum spin fluctuations or the Kondo effect is reduced by the opening of a superconducting gap, spin density wave (SDW) can appear in a superconducting state and the Knight shift can deviate from the Yosida function to be small. The electron-phonon interaction, which arises from the modulation of the superexchange interaction by phonons, is crucial in the coexist…
The explanation of heavy-fermion superconductivity is a long-standing challenge to theory. It is commonly thought to be connected to non-local fluctuations of either spin or charge degrees of freedom and therefore of unconventional type. Here we present results for the Kondo-lattice model, a paradigmatic model to describe heavy-fermion compounds, obtained from dynamical mean-field theory which captures local correlation effects only. Unexpectedly, we find robust s-wave superconductivity in the heavy-fermion state. We argue that this novel type of pairing is tightly connected to the formation o…
To study the nature of partially substituted Yb-ions in a Ce-based Kondo lattice, we fabricated high quality Ce_{1-x}Yb_xCoIn_5 epitaxial thin films using molecular beam epitaxy. We find that the Yb-substitution leads to a linear decrease of the unit cell volume, indicating that Yb-ions are divalent forming Kondo-holes in Ce_{1-x}Yb_xCoIn_5, and leads to a strong suppression of the superconductivity and Kondo coherence. These results, combined with the measurements of Hall effect, indicate that Yb-ions act as nonmagnetic impurity scatters in the coherent Kondo lattice without serious suppressi…
We propose that mass-imbalanced superconductivity is realized in an effective two-channel Kondo lattice, and its characteristic property appears in electromagnetic responses such as the Meissner effect. Starting from an effective two-channel Kondo lattice model as a low-energy effective theory, and approximating it with two mean-field order parameter components in a self-consistent fashion, it is shown that the balance of the two components is sensitively reflected in the magnitude of the Meissner kernel, while thermodynamic properties are little affected by the balance. This remarkable behavi…
The possible heavy fermion superconductivity is carefully reexamined in the two-dimensional Kondo lattice model with an antiferromagnetic Heisenberg superexchange between local magnetic moments. In order to establish an effective mean field theory in the limit of the paramagnetic heavy Fermi liquid and near the half-filling case, we find that the spinon singlet pairing from the local antiferromagnetic short-range correlations can reduce the ground state energy substantially. In the presence of the Kondo screening effect, the Cooper pairs between the conduction electrons is induced. Depending o…
Pressure-induced superconductivity beyond magnetic quantum criticality in a Kondo ferromagnet
New Cornerstone Science Laboratory, Center for Correlated Matter and School of Physics, Zhejiang University（浙江大学物理学院关联物质中心新基石科学实验室）；Hubei Key Laboratory of Photoelectric Materials and Devices, School of Materials Science and Engineering, Hubei Normal University（湖北师范大学材料科学与工程学院光电材料与器件湖北省重点实验室）
The nature of unconventional superconductivity is intimately linked to the microscopic nature of the pairing interactions. In this work, motivated by cubic heavy fermion compounds with embedded multipolar moments, we theoretically investigate superconducting instabilities instigated by multipolar Kondo interactions. Employing multipolar fluctuations (mediated by RKKY interaction) coupled to conduction electrons via two-channel Kondo and novel multipolar Kondo interactions, we uncover a variety of superconducting states characterized by higher-angular momentum Cooper pairs, $J=0,1,2,3$. We demo…
We outline key elements of a theory that accounts for anomalous properties of the PuCoGa$_5$ and PuRhGa$_5$ compounds as a consequence of a two-body interference between two Kondo screening channels. Virtual valence fluctuations of the magnetic Pu configurations create two conduction channels of different symmetry. Using the symplectic large-N approach, we are able to demonstrate our pairing mechanism in an exactly solvable large-N limit. The critical temperature reaches its maximum when the energy levels of excited valence configurations are almost degenerate. The symmetry of the order parame…
Fractionalized Fermi liquids (FL$^\ast$) have been introduced as non-Fermi-liquid metallic phases, characterized by coexisting electron-like charge carriers and local moments which itself form a fractionalized spin liquid. Here we investigate a Kondo lattice model on the honeycomb lattice with compass interactions among the local moments, a concrete model hosting FL$^\ast$ phases based on Kitaev's $\mathbb{Z}_2$ spin liquid. We characterize the FL$^\ast$ phases via perturbation theory, and we employ a Majorana-fermion mean-field theory to map out the full phase diagram. Most remarkably we find…
Kondo singlet from ferromagnetic coupling: an analog of Anderson-Morel superconductivity in the magnetic channel
University College London（伦敦大学学院）；King’s College London（伦敦国王学院）；Universität Bonn（波恩大学）；London Centre for Nanotechnology, University College London（伦敦纳米技术中心，伦敦大学学院）；ISIS Facility, Rutherford Appleton Laboratory（鲁瑟福·阿普尔顿实验室 ISIS 设施）；Coventry University（考文垂大学）；Institute of Molecular Physics, Polish Academy of Sciences（波兰科学院分子物理研究所）；Trinity College, Cambridge（剑桥大学三一学院）
We calculate the superconducting critical temperature T_c and the Kondo temperature T_K of the Kondo lattice, decoupling the Kondo exchange interaction in the unrestricted Hartree-Fock (HF) Bardeen-Cooper-Schrieffer (BCS) approximation. We obtain that both T_K and T_c have an exponential dependence in the Kondo coupling J_K. For optimum doping and realistic parameters, both temperatures fall in the experimentally observed range.
Unconventional superconductivity and magnetism are intertwined on a microscopic level in a wide class of materials, including high-$T_c$ cuprates, iron pnictides, and heavy-fermion compounds. A new approach to this most fundamental and hotly debated subject focuses on the role of interactions between superconducting electrons and bosonic fluctuations at the interface between adjacent layers in heterostructures. A recent state-of-the-art molecular-beam-epitaxy technique has enabled us to fabricate superlattices consisting of different heavy-fermion compounds with atomic thickness. These Kondo s…
Hydrogen in metals has attracted much attention for a long time from both basic scientific and technological points of view. Its electronic state has been investigated in terms of a proton embedded in the electron gas mostly by the local density approximation (LDA) to the density functional theory. At high electronic densities, it is well described by a bare proton H^+ screened by metallic electrons (charge resonance), while at low densities two electrons are localized at the proton site to form a closed-shell negative ion H^- protected from surrounding metallic electrons by the Pauli exclusio…
We consider competition of Kondo effect and s-wave superconductivity in heavy fermion and mixed valence superconductors, using the phenomenological approach for the periodic Anderson model. Similar to the well known results for single-impurity Kondo effect in superconductors, we have found principal possibility of a re-entrant regime of the superconducting transition temperature, $T_c$, in heavy fermion superconductors in a narrow range of model parameters and concentration of f-electrons. Suppression of $T_c$ in mixed valence superconductors is much weaker. Our theory has most validity in the…
We investigate possible topological superconductivity in the Kondo-Kitaev model on the honeycomb lattice, where the Kitaev spin liquid is coupled to conduction electrons via the Kondo coupling. We use the self-consistent Abrikosov-fermion mean-field theory to map out the phase diagram. Upon increasing the Kondo coupling, a first order transition occurs from the decoupled phase of spin liquid and conduction electrons to a ferromagnetic topological superconductor of Class D with a single chiral Majorana edge mode. This is followed by a second order transition into a paramagnetic topological supe…
The cubic compound PrTi$_2$Al$_{20}$ is a quadrupolar Kondo lattice system that exhibits quadrupolar ordering due to the non-Kramers $Γ_3$ ground doublet and has strong hybridization between $4f$ and conduction electrons. Our study using high-purity single crystal reveals that PrTi$_2$Al$_{20}$ exhibits type-II superconductivity at $T_{\rm c} = 200$ mK in the nonmagnetic ferroquadrupolar state. The superconducting critical temperature and field phase diagram suggests moderately enhanced effective mass of $m^*/m_0 \sim 16$.
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…
We present a one dimensional model of electrons coupled to localized moments of spin $S\ge 1$ 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. A non-conventional 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.
We study the Falikov-Kimball model with the pair hopping between the conduction and localized bands to discuss how the charge Kondo effect is realized. By combining dynamical mean-field theory with the continuous time quantum Monte Carlo method, we clarify that the charge Kondo state survives even at zero temperature and this competes with the charge ordered and s-wave superconducting states. The role of the interorbital repulsion for the superconducting state is also addressed.
The evolution of the electronic state through the reduction annealing has been investigated in electron-doped Pr_1.3-x_La_0.7_Ce_x_CuO_4+delta_ (x=0.10) single crystals with the so-called T' structure. From the ab plane and c axis electrical resistivity measurements in magnetic fields, it has been found that, through the reduction annealing, the strongly localized state of carriers accompanied by the antiferromagnetic (AF) pseudogap in the as-grown crystal changes to a metallic state bringing about the Kondo effect without AF pseudogap and to a superconducting state. These results are able to …
In the two-dimensional Kondo-Heisenberg lattice model away from half-filled, the local antiferromagnetic exchange coupling can provide the pairing mechanism of quasiparticles via the Kondo screening effect, leading to the heavy fermion superconductivity. We find that the pairing symmetry \textit{strongly} depends on the Fermi surface (FS) structure in the normal metallic state. When $J_{H}/J_{K}$ is very small, the FS is a small hole-like circle around the corner of the Brillouin zone, and the s-wave pairing symmetry has a lower ground state energy. For the intermediate coupling values of $J_{…
To study the electron-phonon mechanism of superconductivity in NaxCoO2, we perform semiquantitative analysis of the electron-phonon interaction (EPI) between relevant optical phonons (breathing and shear phonons) and t_{2g} electrons (a_{1g} and e_g' electrons) in the presence of trigonal distortion. We consider two kinds of contributions to the EPI; the EPI originating from the Coulomb potential of O ions and that originating from the d-p transfer integral between Co and O in CoO_6 octahedron. We find that the EPI for shear phonons, which induces the interorbital hopping of electrons, is larg…
A theory of Kondo lattices is developed for the t-J model on a square lattice. The spin susceptibility is described in a form consistent with a physical picture of Kondo lattices: Local spin fluctuations at different sites interact with each other by a bare intersite exchange interaction, which is mainly composed of two terms such as the superexchange interaction, which arises from the virtual exchange of spin-channel pair excitations of electrons across the Mott-Hubbard gap, and an exchange interaction arising from that of Gutzwiller's quasi-particles. The bare exchange interaction is enhance…
We propose an exactly solvable model for $j_{\text{eff}}=\frac32$ local moments on the honeycomb lattice. Our construction is guided by a symmetry analysis and by the requirement of an exact solution in terms of a Majorana fermion representation for multipole operators. The main interaction in the model can be interpreted as a bond-dependent quadrupole-quadrupole interaction. When time reversal symmetry is explicitly broken, we obtain a gapped spin liquid with a single chiral Majorana edge mode. We also investigate another solvable model in which the time-reversal-invariant spin liquid is coup…
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…
We find evidence that superconductivity intrudes into the paramagnetic-to-magnetic transition of the Kondo lattice model if magnetic frustration is added. Specifically, we study by variational method the model on a square lattice in the presence of both nearest- ($t$) and next-nearest-neighbor ($t^\prime$) hopping of the conduction electrons. We find that when $t^\prime/t$ is finite a $d$-wave superconducting dome emerges between the magnetic and paramagnetic metal phases and close to the compensated regime, i.e., the number of conduction electrons equal to the number of localized spin-1/2 mom…
Motivated by recent experiments on magnetically frustrated heavy fermion metals, we theoretically study the phase diagram of the Kondo lattice model with a nonmagnetic valence bond solid ground state on a ladder. A similar physical setting may be naturally occurring in YbAl$_3$C$_3$, CeAgBi$_2$, and TmB$_4$ compounds. In the insulating limit, the application of a magnetic field drives a quantum phase transition to an easy-plane antiferromagnet, which is described by a Bose-Einstein condensation of magnons. Using a combination of field theoretical techniques and density matrix renormalization g…
Spin-flip scattering from magnetic impurities has a strong pair-breaking effect in $s$-wave superconductors where increasing the concentration of impurities rapidly destroys superconductivity. For small Kondo temperature $T_K$ the destruction of superconductivity is preceded by the reentrant superconductivity at finite temperature range $T_{c2} < T < T_{c1}$, while the normal phase reappears at $T<T_{c2} \sim T_K$. Here we explore the superconducting phase in a periodic system modeled as the Anderson lattice with additional attractive on-site (Hubbard) interaction $g$ acting on the conduction …
We investigate in detail antiferromagnetic (AF) and superconducting (SC) phases as well as their coexistence in the two-dimensional Kondo lattice model on a square lattice, which is a paradigmatic model for heavy fermion materials. The results presented are mainly obtained using the variational cluster approximation (VCA) and are complemented by analytical findings for the equations of motion of pairing susceptibilities. A particularly interesting aspect is the possibility to have s-wave SC near half filling as reported by Bodensiek \textit{et al.} [Phys. Rev. Lett. \textbf{110}, 146406 (2013)…
We study the interplay between the Kondo effect and (color) superconductivity in doped Dirac metals with magnetic impurities and in quark matter with colorful impurities. We first point out that the overscreened Kondo effect arises in the normal state of these systems. Next the (color) superconducting gap is incorporated as a mean field and the phase diagram for a varying gap and temperature is constructed nonperturbatively. A rich phase structure emerges from a competition of effects unique to a multichannel system. The Kondo-screened phase is shown to disappear for a sufficiently large gap. …
We investigate the competition between superconductivity, charge-ordering, magnetic-ordering, and the Kondo effect in a heavy fermion $s$-wave superconductor described by a Kondo lattice model with an attractive on-site Hubbard interaction. The model is solved using the real-space dynamical mean field theory. For this purpose, we develop a numerical renormalization group (NRG) framework in Nambu space, which is used to solve the superconducting impurity problem. This extended NRG scheme also allows for SU(2) spin symmetry broken solutions, enabling us to examine the competition or cooperation …
Mapping reservoir-enhanced superconductivity to near-long-range magnetic order in the undoped 1D Anderson- and Kondo-lattices
Heriot-Watt University（赫瑞-瓦特大学）；University of Geneva（日内瓦大学）；Weizmann Institute of Science（魏茨曼科学研究所）；Max-Planck-Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）
The Kondo lattice model enlarged by an antiferromagnetic coupling $J_{\rm AF}$ between the localized spins is here investigated using computational techniques. Our results suggest the existence of a d-wave superconducting phase close to half-filling mediated by antiferromagnetic fluctuations. This establishes a closer connection between theory and heavy fermion experiments than currently provided by the standard Kondo lattice model with $J_{\rm AF}$=0.
We consider the competition between the Kondo screening effect and ferromagnetic long-range order (FLRO) within a mean-field theory of the Kondo lattice model for low conduction electron densities $n_{c}$. Depending on the parameter values, several types of FLRO ground states are found. When $n_{c}<0.16$, a polarized FLRO phase is dominant. For $0.16<n_{c}<0.82$, a non-polarized FLRO phase appears in the weak Kondo coupling region; while in the intermediate coupling region the ground state corresponds to the polarized and non-polarized FLRO phases, respectively, coexisting with the Kondo scree…
We report Knight shift experiments on the superconducting heavy electron material CeCoIn$_5$ that allow one to track with some precision the behavior of the heavy electron Kondo liquid in the superconducting state with results in agreement with BCS theory. An analysis of the $^{115}$In nuclear quadrupole resonance (NQR) spin-lattice relaxation rate $T_1^{-1}$ measurements under pressure reveals the presence of 2d magnetic quantum critical fluctuations in the heavy electron component that are a promising candidate for the pairing mechanism in this material. Our results are consistent with an an…
The La dilution of the Kondo lattice CeCoIn_5 is studied. The scaling laws found for the magnetic susceptibility and the specific heat reveal two well-separated energy scales, corresponding to the single impurity Kondo temperature T_K and an intersite spin-liquid temperature T^*. The Ce-dilute alloy has the expected Fermi liquid ground state, while the specific heat and resistivity in the dense Kondo regime exhibit non-Fermi-liquid behavior, which scales with T^*. These observations indicate that the screening of the magnetic moments in the lattice involves antiferromagnetic intersite correlat…
We study the two-dimensional Kondo lattice model with an additional Heisenberg exchange between localized spins. In a first step we use mean-field theory with two order parameters. The first order parameter is a complex pairing amplitude between conduction electrons and localized spins which describes condensation of Kondo (or Zhang-Rice) singlets. A nonvanishing value implies that the localized spins contribute to the Fermi surface volume. The second order parameter describes singlet-pairing between the localized spins and competes with the Kondo-pairing order parameter. Reduction of the carr…
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.
Superconductivity, Kondo physics and magnetic order: Tuning the groundstate in the La$_{1-x}$Ce$_x$FeSiH solid solution through the interplay between $3d$ and $4f$ correlated electrons
University of Bordeaux（波尔多大学）；CNRS（法国国家科学研究中心）；Helmholtz-Zentrum Dresden-Rossendorf（亥姆霍兹德累斯顿-罗斯多夫中心）
We extend recent results on domain wall description of superconductivity in an Abelian Higgs model by introducing a particular Lorentz-violating term. The temperature of the system is interpreted through the fact that the soliton following accelerating orbits is a Rindler observer experiencing a thermal bath. We show that this term can be associated with the {\sl Kondo effect}, that is, the Lorentz-violating parameter is closely related to the concentration of magnetic impurities living on a superconducting domain wall. We also found that the critical temperature decreasing with the impurity c…
We discuss the possibility of a co-operative Kondo effect driven by channel interference in a Kondo lattice where local moments are coupled to a single Fermi sea via two orthogonal scattering channels. In this situation, the channel quantum number is not conserved. We argue that the absence of channel conservation causes the Kondo effect in the two channels to constructively interfere, giving rise to a superconducting condensate of composite pairs, formed between the local moments and the conduction electrons. Our arguments are based on the observation that a heavy Fermi surface gives rise to …
