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+SC) phase may contain also a non-trivial spin-triplet gap component within the essentially spin-singlet pairing mechanism
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 theoretically study physical properties of the low-energy quasiparticle excitations at the vortex core in the full-gap superconducting state of the Kondo lattice coupled to compensated metals. Based on the mean-field description of the superconducting state, we numerically solve the Bogoliubov-de Gennes (BdG) equations for the tight-binding Hamiltonian. The isolated vortex is characterized by a length scale independent of the magnitude of the interaction and the energy level of the core bound state is the same order as the bulk gap. These properties are in strong contrast to the conventiona…
Orbital degrees of freedom of a Cooper pair play an important role in the unconventional superconductivity. To elucidate the orbital effect in the Kondo problem, we investigated a single magnetic impurity coupled to Cooper pairs with a $p_x +i p_y$ ($d_{x^2-y^2}+id_{xy}$) symmetry using the numerical renormalization group method. It is found that the ground state is always a spin doublet. The analytical solution for the strong coupling limit explicitly shows that the orbital dynamics of the Cooper pair generates the spin 1/2 of the ground state.
A new type of Kondo effect peculiar to unconventional superconductors is studied theoretically by using the Wilson's numerical renormalization group method. In this case, an angular momentum of a Cooper pair plays an important role in the Kondo effect. It produces multichannel exchange couplings with a local spin. Here we focus on a $p_x +i p_y$-wave state which is a full gap system. The calculated impurity susceptibility shows that the local spin is almost quenched by the Kondo effect in the strong coupling region ($T_{\rm K}/Δ\to \infty$), while the ground state is always a spin doublet over…
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…
The Kondo effect in superconductors is frequently investigated using the local quasiparticle density of states as sole bath characteristics, i.e., the presence of anomalous propagators is ignored. Here we point out that this treatment is exact for a number of situations, including point-like impurities in d-wave superconductors. We comment on recent investigations [M. Matsumoto and M. Koga, J. Phys. Soc. Jpn. 70, 2860 (2001), cond-mat/0011256, and Phys. Rev. B 65, 024508 (2002), cond-mat/0103053] which reached different conclusions: while their numerical results are likely correct, their inter…
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…
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…
A review is given of the experimental situation and theoretical predictions concerning unconventional magnetic ordering in dense Kondo 4f- and 5f-systems, including recently investigated on cerium, ytterbium, and actinide based ternary systems. This unconventional ordering is characterized by a small magnetic moment and exhibits features typical of both localized-spin and itinerant-electron magnets. Particular attention is paid to ferromagnetic systems and the competition among different types of magnetic ordering. The perturbation theory method, renormalization group approach, and auxiliary p…
The heavy quasiparticle bands in Kondo materials which originate in the hybridization of f- and conduction electrons exhibit numerous, sometimes coexisting, broken symmetry phases. Most notable are unconventional superconductivity, itinerant small moment antiferromagnetism and hidden order of higher order multipoles of f-electrons which all lead to a gapping of the heavy bands. In rare cases the chemical potential lies within the hybridization gap and the ground state is a Kondo semiconductor without ordering. The dynamical magnetic response of such gapped f-electron systems has been investiga…
We study the low-temperature properties of the generalized Anderson impurity model in which two localized configurations, one with two doublets and the other with a triplet, are mixed by two degenerate conduction channels. By using the numerical renormalization group and the non-crossing approximation, we analyze the impurity entropy, its spectral density, and the equilibrium conductance for several values of the model parameters. Marked differences with respect to the conventional one-channel spin $s=1/2$ Anderson model, that can be traced as hallmarks of an impurity spin $S=1$, are found in …
We study Kondo physics of a spin-$\frac{1}{2}$ impurity in electronic matter with strong spin-orbit interaction, which can be realized by depositing magnetic adatoms on the surface of a three-dimensional topological insulator. We show that magnetic properties of topological surface states and the very existence of Kondo screening strongly depend on details of the bulk material, and specifics of surface preparation encoded in time-reversal preserving boundary conditions for electronic wavefunctions. When this tunable Kondo effect occurs, the impurity spin is screened by purely orbital motion of…
We investigate the effect of unconventional density wave (UDW) condensate on an Anderson impurity using large-N technique at T=0. In accordance with previous treatments of a Kondo impurity in pseudogap phases, we find that Kondo effect occurs only in a certain range of parameters. The f-electron density of states reflects the influence of UDW at low energies and around the maximum of the density wave gap. The static spin susceptibility diverges at the critical coupling, indicating the transition from strong to weak coupling. In the dynamic spin susceptibility an additional peak appears showing…
Topology, symmetry, electron correlations, and the interplay between them have formed the cornerstone of our understanding of quantum materials in recent years and are used to identify new emerging phases. While the first two give a fair understanding of noninteracting and, in many cases, weakly interacting wave function of electron systems, the inclusion of strong correlations could change the picture substantially. The Kondo lattice model is a paradigmatic example of the interplay of electron correlations and conduction electrons of a metallic system, describing heavy fermion materials and a…
We show that the charge and thermal transport measurements on ultraclean crystals of URu2Si2 reveal a number of unprecedented superconducting properties. The uniqueness is best highlighted by the peculiar field dependence of thermal conductivity including the first order transition at Hc2 with a reduction of entropy flow. This is a consequence of multi-band superconductivity with compensated electronic structure in the hidden order state of this system. We provide strong evidence for a new type of unconventional superconductivity with two distinct gaps having different nodal topology.
In quantum materials, electrons that have strong correlations tend to localize, leading to quantum spins as the building blocks for low-energy physics. When strongly correlated electrons coexist with more weakly-correlated conduction electrons, multiple channels of effective interactions develop and compete with each other. The competition creates quantum fluctuations having a large spectral weight, with the associated entropies reaching significant fractions of $R\ln 2$ per electron. Advancing a framework to understand how the fluctuating local moments influence unconventional superconductivi…
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 …
Unconventional quantum criticality in heavy-fermion systems has been extensively analyzed in terms of a critical destruction of the Kondo effect. Motivated by a recent demonstration of quantum criticality in a mixed-valent heavy-fermion system, β-YbAlB4, we study a particle-hole-asymmetric Anderson impurity model with a pseudogapped density of states. We demonstrate Kondo destruction at a mixed-valent quantum critical point, where a collapsing Kondo energy scale is accompanied by a singular charge-fluctuation spectrum. Both spin and charge responses scale with energy over temperature (ω/T) and…
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…
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 …
To achieve room-temperature superconductivity, a mechanism is needed that provides heavy quasiparticles at room temperature. In heavy fermion systems such localization is prototypically present only at liquid helium temperatures. In these $f$-electron Kondo systems, conduction electrons magnetically couple to localized moments, enhancing their mass and scatting time. These quasiparticles may form Cooper pairs and cause unconventional superconductivity with a critical temperature $T_c$ of the order of the Fermi energy $\varepsilon_F$. In relative terms, this $T_c$ is much larger than in cuprate…
Electronic structure calculations combining the local-density approximation with an exact diagonalization of the Anderson impurity model show an intermediate 5f^5-5f^6-valence ground state and delocalization of the 5f^5 multiplet of the Pu atom 5f-shell in PuCoIn_5, PuCoGa_5, and δ-Pu. The 5f-local magnetic moment is compensated by a moment formed in the surrounding cloud of conduction electrons. For PuCoGa_5 and δ-Pu the compensation is complete and the Anderson impurity ground state is a singlet. For PuCoIn_5 the compensation is partial and the Pu ground state is magnetic. We suggest that th…
We briefly overview the importance of Hubbard and Anderson-lattice models as applied to explanation of high-temperature and heavy-fermion superconductivity. Application of the models during the last two decades provided an explanation of the paired states in correlated fermion systems and thus extended essentially their earlier usage to the description of itinerant magnetism, fluctuating valence, and the metal-insulator transition. In second part, we also present some of the new results concerning the unconventional superconductivity and obtained very recently in our group. A comparison with e…
We present sensitive measurements of the Hall effect and magnetoresistance in CeIrIn${_5}$ down to temperatures of 50 mK and magnetic fields up to 15 T. The presence of a low temperature coherent Kondo state is established. Deviations from Kohler's rule and a quadratic temperature dependence of the cotangent of the Hall angle are reminiscent of properties observed in the high temperature superconducting cuprates. The most striking observation pertains to the presence of a \textit{precursor} state--characterized by a change in the Hall mobility--that appears to precede the superconductivity in …
Magnetic impurities in three-dimensional Dirac and Weyl systems are shown to exhibit a fascinatingly diverse range of Kondo physics, with distinctive experimental spectroscopic signatures. When the Fermi level is precisely at the Dirac point, Dirac semimetals are in fact unlikely candidates for a Kondo effect due to the pseudogapped density of states. However, the influence of a nearby quantum critical point leads to the unconventional evolution of Kondo physics for even tiny deviations in the chemical potential. Separating the degenerate Dirac nodes produces a Weyl phase: time-reversal symmet…
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 theoretical study based on the Anderson model of the transport properties of a Kondo impurity (atom or quantum dot) connected to ferromagnetic leads, which can sustain a non-equilibrium spin current. We analyze the case where the spin current is injected by an external source and when it is generated by the voltage bias. Due to the presence of ferromagnetic contacts, a static exchange field is produced that eventually destroys the Kondo correlations. We find that such a field can be compensated by an appropriated combination of the spin-dependent chemical potentials leading to the…
In correlated electronic systems, strong interactions and the interplay between different degrees of freedom may give rise to anomalous charge transport properties, which can be tuned by external parameters like temperature and magnetic field. Recently, magnetic quantum oscillations and metallic low-temperature thermal conductivity have been observed in the Kondo insulator YbB$_{12}$, whose resistivity is a few orders of magnitude higher than those of conventional metals. As yet, these unusual observations are not fully understood. Here we present a detailed investigation of the behavior of Yb…
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…
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 …
Giant perpendicular Edelstein polarization in 2D compensated magnets via bichromatic Floquet driving
Georgetown University（乔治城大学）；Uppsala University（乌普萨拉大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理学研究所）；Czech Academy of Sciences（捷克科学院）
The nature of superconductivity in heavy-fermion materials is a subject under intense debate, and controlling this many-body state is central for its eventual understanding. Here, we examine how proximity effects may change this phenomenon, by investigating the effects of an additional metallic layer on the top of a Kondo-lattice, and allowing for pairing in the former. We analyze a bilayer Kondo Lattice Model with an on-site Hubbard interaction, $-U$, on the additional layer, using a mean-field approach. For $U=0$, we notice a drastic change in the density-of-states due to multiple-orbital si…
In this review article we present a survey of unconventional superconductors and their coexistence behaviour with magnetism. We focus on Ce- and U-based heavy fermion superconductors, in addition we discuss the rare earth borocarbide and skutterudite superconductors. We show that heavy fermion behaviour in Ce- and U- compounds should be described differently. While the Kondo-lattice model with localised 4f-electrons is appropriate for Ce-compounds, dual models including localised and itinerant 5f-electrons are necessary for U-compounds. We demonostrate that this leads to consistent results for…
Superconductivity without phonons has been proposed for strongly correlated electron materials that are tuned close to a zero-temperature magnetic instability of itinerant charge carriers. Near this boundary, quantum fluctuations of magnetic degrees of freedom assume the role of phonons in conventional superconductors, creating an attractive interaction that glues electrons into superconducting pairs. Here we show that superconductivity can arise from a very different spectrum of fluctuations associated with a local or Kondo-breakdown quantum-critical point that is revealed in isotropic scatte…
Whether the newly discovered KxFe2-ySe2 systems are doped Mott or band insulators is key to how superconductivity emerges at lower temperature. With extant theoretical studies supporting conflicting scenarios, a more realistic approach is urgently called for. Here, we use LDA+DMFT to study this issue in KxFe2-ySe2. We find that the undoped KFe1.6Se2 system is a new kind of Mott-Kondo insulator (MKI). Electron doping this MKI drives a Mott transition to an orbital-selective non-Fermi liquid metal. Good agreement with spectral and transport responses supports our view, implying that superconduct…
We propose a mechanism of unconventional superconductivity in two-dimensional strongly-correlated electron systems. We consider a two-dimensional Kondo lattice system or double-exchange system with spin-orbit coupling arising from buckling of the plane. We show that a Chern-Simons term is induced for a gauge field describing the phase fluctuations of the localized spins. Through the induced Chern-Simons term, carriers behave like skyrmion excitations that lead to a destruction mechanism of magnetic long-range order by carrier doping. After magnetic long-range order is destroyed by carrier dopi…
Microscopic models for heavy-fermion materials often assume a local, i.e., momentum-independent, hybridization between the conduction band and the local-moment f electrons. Motivated by recent experiments, we consider situations where this neglect of momentum dependence is inappropriate, namely when the hybridization function has nodes in momentum space. We explore the thermodynamic and optical properties of the highly anisotropic heavy Fermi liquid, resulting from Kondo screening in a higher angular-momentum channel. The dichotomy in momentum space has interesting consequences: While e.g. the…
Nanoscale systems of metal atoms antiferromagnetically exchange coupled to several magnetic impurities are shown to exhibit an unconventional re-entrant competition between Kondo screening and indirect magnetic exchange interaction. Depending on the atomic positions of the magnetic moments, the total ground-state spin deviates from predictions of standard Ruderman-Kittel-Kasuya-Yosida perturbation theory. The effect shows up on an energy scale larger than the level width induced by the coupling to the environment and is experimentally verifiable by studying magnetic field dependencies.
We investigate the many-body effects of a magnetic adatom in ferromagnetic graphene by using the numerical renormalization group method. The nontrivial band dispersion of ferromagnetic graphene gives rise to interesting Kondo physics different from that in conventional ferromagnetic materials. For a half-filled impurity in undoped graphene, the presence of ferromagnetism can bring forth Kondo correlations, yielding two kink structures in the local spectral function near the Fermi energy. When the spin splitting of local occupations is compensated by an external magnetic field, the two Kondo ki…
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 dynamics in the new Kondo insulator compound CeRu2Al10 has been studied using unpolarized and polarized neutron scattering on single crystals. In the unconventional ordered phase forming below T0 = 27.3 K, two excitation branches are observed with significant intensities, the lower one of which has a gap of 4.8 +/- 0.3 meV and a pronounced dispersion up to about 8.5 meV. Comparison with RPA magnon calculations assuming crystal-field and anisotropic exchange couplings captures major aspects of the data, but leaves unexplained discrepancies, pointing to a key role of direction-specific hybr…
The Kondo effect strongly depends on spin and orbital degrees of freedom of unconventional superconductivity. We focus on the Kondo effect in the $p_x + i p_y$-wave and $d_{x^2 - y^2} + i d_{xy}$-wave superconductors to compare the magnetic properties of the spin-triplet and spin-singlet Cooper pairs. The difference appears when both of the paired electrons couple to a local spin directly. For the $p_x + i p_y$-wave, the ground state is always a spin doublet for a $S_{\rm imp} = 1/2$ local spin, and it is always a spin singlet for $S_{\rm imp} = 1$. The latter is due to uniaxial spin anisotrop…
We study electron transport through a serial double quantum dot with Rashba spin-orbit interaction (SOI) and Zeeman field of amplitude B in presence of local Coulomb repulsion. The linear conductance as a function of a gate voltage Vg equally shifting the levels on both dots shows two B=0 Kondo ridges which are robust against SOI as time-reversal symmetry is preserved. Resulting from the crossing of a spin-up and a spin-down level at vanishing SOI two additional Kondo plateaus appear at finite B. They are not protected by symmetry and rapidly vanish if the SOI is turned on. Left-right asymmetr…
The interplay of magnetic energies in a Kondo lattice is the underlying physics of a heavy fermion system. Creating an artificial Kondo lattice system by localizing the moments in an ordered metallic array provides a prototype system to tune and study the energetic interplay while avoiding the complications introduced by random alloying of the material. In this article, we create a Kondo lattice system by fabricating a hexagonally ordered nanostructured array using niobium as the host metal and cobalt as the magnetic constituent. Electrical transport measurements and magnetoresistivity measure…
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…
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…
Strongly correlated electron systems at the border of magnetism are of active current interest, particularly because the accompanying quantum criticality provides a route towards both strange-metal non-Fermi liquid behavior and unconventional superconductivity. Among the many important questions is whether the magnetism acts simply as a source of fluctuations in the textbook Landau framework, or instead serves as a proxy for some unexpected new physics. We put into this general context the recent developments on quantum phase transitions in antiferromagnetic heavy fermion metals. Among these a…
The orthorhombic uranium dichalcogenide UTe$_2$ displays superconductivity below 1.7 K, with the anomalous feature of retaining 50$\%$ of normal state (ungapped) carriers, according to heat capacity data from two groups. Incoherent transport that crosses over from above 50 K toward a low temperature, Kondo lattice Fermi liquid regime indicates strong magnetic fluctuations and the need to include correlation effects in theoretical modeling. We report density functional theory plus Hubbard U (DFT+U) results for UTe$_2$ to provide a platform for modeling its unusual behavior, focusing on ferromag…
