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 antiferromagnetic quantum critical point (QCP) located at slightly negative pressure in CeCoIn$_5$ and provide additional evidence for significant similarities between the heavy electron materials and the high $T_c$ cuprates.
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.
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 $m^*/m_0 \sim 16$.
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.
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…
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.
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 …
We develop a general Bethe Ansatz formalism for diagonalizing an integrable model of a magnetic impurity of arbitrary spin coupled ferro- or antiferromagnetically to a chain of interacting electrons. The method is applied to an open chain, with the exact solution revealing a ``hidden'' Kondo effect driven by forward electron scattering off the impurity. We argue that the so-called ``operator reflection matrices'' proposed in recent Bethe Ansatz studies of related models emulate only forward electron-impurity scattering which may explain the absence of complete Kondo screening for certain value…
Using a large-N approach, we demonstrate that the differential conductance and quasi-particle interference pattern measured in recent scanning tunneling spectroscopy experiments (A.R. Schmidt et al. Nature 465, 570 (2010); P. Aynajian et al., PNAS 107, 10383 (2010)) in URu2Si2 are consistent with the emergence of a coherent Kondo lattice below its hidden order transition (HOT). Its formation is driven by a significant increase in the quasi-particle lifetime, which could arise from the emergence of a yet unknown order parameter at the HOT.
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…
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 reveal the significance of kinetic-driven multiple-spin interactions hidden in geometrically-frustrated Kondo lattice models. Carefully examining the perturbation in terms of the spin-charge coupling up to the fourth order, we find that a positive biquadratic interaction is critically enhanced and plays a crucial role on stabilizing a spin scalar chiral order near 1/4 filling in a triangular lattice case. This is a generalized Kohn anomaly, appearing only when the second-order perturbation is inefficient because of the degeneracy under frustration. The mechanism is potentially common to fru…
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+…
We study, using high-resolution angle-resolved photoemission spectroscopy, the evolution of the electronic structure in URu2Si2 at the Gamma, Z and X high-symmetry points from the high-temperature Kondo-screened regime to the low-temperature `hidden-order' (HO) state. At all temperatures and symmetry points, we find structures resulting from the interaction between heavy and light bands, related to the Kondo lattice formation. At the X point, we directly measure a hybridization gap of 11 meV already open at temperatures above the ordered phase. Strikingly, we find that while the HO induces pro…
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 …
We measured the polarized optical conductivity of URu$_2$Si$_2$ from room temperature down to 5 K, covering the Kondo state, the coherent Kondo liquid regime, and the hidden-order phase. The normal state is characterized by an anisotropic behavior between the ab plane and c axis responses. The ab plane optical conductivity is strongly influenced by the formation of the coherent Kondo liquid: a sharp Drude peak develops and a hybridization gap at 12 meV leads to a spectral weight transfer to mid-infrared energies. The c axis conductivity has a different behavior: the Drude peak already exists a…
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…
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.
Motivated by the unconventional superconductivity observed in heavy-fermion metals, we investigate pairing susceptibilities near a continuous quantum phase transition of the Kondo-destruction type. We solve two-impurity Bose-Fermi Anderson models with Ising and Heisenberg forms of the interimpurity exchange interaction using continuous-time quantum Monte-Carlo and numerical renormalization-group methods. Each model exhibits a Kondo-destruction quantum critical point separating Kondo-screened and local-moment phases. For antiferromagnetic interimpurity exchange interactions, singlet pairing is …
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 study a spin-1/2 Kondo impurity coupled to an unconventional host in which the density of band states vanishes either precisely at (``gapless'' systems) or on some interval around the Fermi level (``gapped''systems). Despite an essentially nonlinear band dispersion, the system is proven to exhibit hidden integrability and is diagonalized exactly by the Bethe ansatz.
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 heavy fermion material CeB6 shows hidden magnetic ordered phases. Besides well-known Ferromagnetic(FM) and Antiferromagnetic(AFM) phases, CeB6 is speculated to form a unique antiferroquadrupolar (AFQ) phase that is orbital in nature. Hidden from many characterization methods that cannot assess orbital ordering, debate continue on the origins. From electronic-structure calculations, we find that these three phases are energetically almost degenerate, suggesting that magnetic domain walls form, possibly with defect boundaries. Only calculations with spin-orbit coupling reproduce most band st…
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 study the phase diagram of the Kondo-lattice model with nearest-neighbor hopping in the square lattice by means of the variational Monte Carlo technique. Specifically, we analyze a wide class of variational wave functions that allow magnetic and superconducting order parameters, so to assess the possibility that superconductivity might emerge close to the magnetic instability, as often observed in heavy fermion systems. Indeed, we do find evidence of d-wave superconductivity in the paramagnetic sector, i.e., when magnetic order is not allowed in the variational wave function. However, when …
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…
Kondo hybridization in partially filled f-electron systems conveys significant amount of electronic states sharply near the Fermi energy leading to various instabilities from superconductivity to exotic electronic orders. UGe2 is a 5f heavy fermion system, where the Kondo hybridization is interrupted by the formation of two ferromagnetic phases below a 2nd order transition Tc ~ 52 K and a crossover transition Tx ~ 32 K. These two ferromagnetic phases are concomitantly related to a spin-triplet superconductivity that only emerges and persists inside the magnetically ordered phase at high pressu…
Considerable efforts have been made in recent years to theoretically understand quantum phase transitions in Kondo lattice systems. A particular focus is on Kondo destruction, which leads to quantum criticality that goes beyond the Landau framework of order-parameter fluctuations. This unconventional quantum criticality has provided an understanding of the unusual dynamical scaling observed experimentally. It has also predicted a sudden jump of the Fermi surface and an extra (Kondo destruction) energy scale, both of which have been verified by systematic experiments. Considerations of Kondo de…
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…
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…
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）
Complex electronic matter exhibit subtle forms of self organization which are almost invisible to the available experimental tools, but which have dramatic physical consequences. One prominent example is provided by the actinide based heavy fermion material URu_2Si_2. At high temperature, the U-5f electrons in URu_2Si_2 carry a very large entropy. This entropy is released at 17.5K via a second order phase transition to a state which remains shrouded in mystery, and which was termed a "hidden order" state. Here we develop a first principles theoretical method to analyze the electronic spectrum …
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…
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 have measured the crystalline electric field (CEF) excitations of the CeMIn5 (M = Co, Rh, Ir) series of heavy fermion superconductors by means of inelastic neutron scattering. Fits to a CEF model reproduce the inelastic neutron scattering spectra and the high temperature magnetic susceptibility. The CEF parameters, energy level splittings, and wavefunctions are tabulated for each member of the CeMIn5 series and compared to each other as well as to the results of previous measurements. Our results indicate that the CEF level splitting in all three materials is similar, and can be thought of …
Building on the results of Ref. \cite{faye2018phase}, which identified an antiferromagnetic and Kondo singlet phases on the Kondo-Hubbard square lattice, we use the variational cluster approximation (VCA) to investigate the competition between these phases on a two-dimensional triangular lattice with $120^{o}$ spin orientation. In addition to the antiferromagnetic exchange interaction $J_{\perp}$ between the localized (impurity) and conduction (itinerant) electrons, our model includes the local repulsion $U$ of the conduction electrons and the Heisenberg interaction $J_H$ between the impuritie…
Heavy electronic states originating from the f atomic orbitals underlie a rich variety of quantum phases of matter. We use atomic scale imaging and spectroscopy with the scanning tunneling microscope (STM) to examine the novel electronic states that emerge from the uranium f states in URu2Si2. We find that as the temperature is lowered, partial screening of the f electrons' spins gives rise to a spatially modulated Kondo-Fano resonance that is maximal between the surface U atoms. At T=17.5 K, URu2Si2 is known to undergo a 2nd order phase transition from the Kondo lattice state into a phase wit…
The nature of the second order phase transition that occurs in URu2Si2 at 17.5 K remains puzzling despite intensive research over the past two and half decades. A key question emerging in the field is whether a hybridization gap between the renormalized bands can be identified as the long-sought 'hidden' order parameter. We report on the measurement of a hybridization gap in URu2Si2 employing a spectroscopic technique based on quasiparticle scattering across a ballistic metallic junction. The differential conductance exhibits an asymmetric double-peak structure, a clear signature for a Fano re…
We show that the Bose-Fermi Kondo model (BFKM), which may find applicability both to certain dissipative mesoscopic qubit devices and to heavy fermion systems described by the Kondo lattice model, can be mapped exactly onto the Caldeira-Leggett model. This mapping requires an ohmic bosonic bath and an Ising-type coupling between the latter and the impurity spin. This allows us to conclude unambiguously that there is an emergent Kosterlitz-Thouless quantum phase transition in the BFKM with an ohmic bosonic bath. By applying a bosonic numerical renormalization group approach, we thoroughly probe…
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…
