Kondo Singlet Research Articles

Local Kondo entanglement and symmetry protected local criticality in the two-impurity Kondo problem

The local Kondo entanglement is defined as the concurrence of a short-ranged Kondo singlet state consisting of a localized magnetic moment and a nearby conduction electron. We derive the entanglement phase diagram of the Rasul-Schlottmann model, the effective spin-only Hamiltonian for the two-impurity Kondo model in the numerical renormalization group approach. We show that the local Kondo entanglement vanishes exactly at the two-impurity Kondo critical point, associated concomitantly with a jump in the inter-impurity entanglement. We discuss how to generalize this result to a Kondo lattice model preserving the same enhanced spin symmetry.

Kondo effect in double quantum dots with ferromagnetic RKKY interaction

We study Kondo effect in parallel-coupled double quantum dots with ferromagnetic Ruderman–Kittel–Kasuya–Yoshida (RKKY) interaction, by using the exact and nonperturbative hierarchical equations of motion approach. We construct the phase diagram in the parameter plane of the inter-dot coupling t and the ferromagnetic exchange interaction J (J − 4t2/U plane). Three different ground states, the Kondo singlet, spin singlet and S = 1 Kondo, are determined in the diagram. We find the ferromagnetic coupling will raise the Kondo peak in the area of finite hopping t which is called ‘J-enhanced Kondo effect’. Another enhancement of the Kondo effect by t (‘t-enhanced Kondo effect’) at J = 0 is also presented. By checking the electron–electron interaction self-energy and magnetic susceptibility, we verify the ground state at large J is an under-screening Kondo state composed of a Fermi liquid with a residual spin 1/2, which is consistent with the ‘singular Fermi liquid state’ in the literature.

Direct evidence for suppression of the Kondo effect due to pure spin current

We study the effect of a pure spin current on the Kondo singlet in a diluted magnetic alloy using non-local lateral spin valve structures with highly spin polarized Co2FeSi electrodes. Temperature dependence of the non-local spin signals shows a sharp reduction with decreasing temperature, followed by a plateau corresponding to the low temperature Fermi liquid regime below the Kondo temperature (TK). The spin diffusion length of the Kondo alloy is found to increase with the evolution of spin accumulation. The results are in agreement with the intuitive description that the Kondo singlet cannot survive any more in sufficiently large spin accumulation even below TK.

Low-temperature behavior of transmission phase shift across a Kondo correlated quantum dot

We study the transmission phase shift across a Kondo correlated quantum dot in a GaAs heterostructure at temperatures below the Kondo temperature ($T < T_{\rm K}$), where the phase shift is expected to show a plateau at $\pi/2$ for an ideal Kondo singlet ground state. Our device is tuned such that the ratio $\Gamma/U$ of level width $\Gamma$ to charging energy $U$ is quite large ($\lesssim 0.5$ rather than $\ll 1$). This situation is commonly used in GaAs quantum dots to ensure Kondo temperatures large enough ($\simeq 100$ mK here) to be experimentally accessible; however it also implies that charge fluctuations are more pronounced than typically assumed in theoretical studies focusing on the regime $\Gamma/U \ll 1$ needed to ensure a well-defined local moment. Our measured phase evolves monotonically by $\pi$ across the two Coulomb peaks, but without being locked at $\pi/2$ in the Kondo valley for $T \ll T_{\rm K}$, due to a significant influence of large $\Gamma/U$. Only when $\Gamma/U$ is reduced sufficiently does the phase start to be locked around $\pi/2$ and develops into a plateau at $\pi/2$. Our observations are consistent with numerical renormalization group calculations, and can be understood as a direct consequence of the Friedel sum rule that relates the transmission phase shift to the local occupancy of the dot, and thermal average of a transmission coefficient through a resonance level near the Fermi energy.

Field-Enhanced Kondo Correlations in a Half-Filling Nanotube Dot: Evolution of an SU(N) Fermi-Liquid Fixed Point

We theoretically study an emergent SU(2) symmetry which is suggested by recent magneto-transport measurements, carried out near two electrons filling of a carbon nanotube quantum dot. It emerges in the case where the spin and orbital Zeeman splittings cancel each other out for two of the one-particle dot levels among four. Using the Wilson numerical renormalization group, we show that a crossover from the SU(4) to SU(2) Fermi-liquid behavior occurs at two impurity-electrons filling as magnetic field increases. We also find that the quasiparticles are significantly renormalized as the remaining two one-particle levels move away from the Fermi level and are frozen at high magnetic fields. In order to clarify how the ground state evolves during such a crossover, we also reexamine the SU(N) Kondo singlet state for M impurity-electrons filling in the limit of strong exchange interactions. We show that the nondegenerate Fermi-liquid fixed point of Nozi\`{e}es and Blandin can be described as a bosonic Perron-Frobenius vector for M hard-core bosons, each of which consists of one impurity-electron and one conduction hole. This interpretation can also be applied to the Fermi-liquid fixed-point without the SU(N) symmetry.

Feasibility of a metamagnetic transition in correlated systems

The long-standing issue of the competition between the magnetic field and the Kondo effect, favoring, respectively, triplet and singlet ground states, is addressed using a cluster slave-rotor mean-field theory for the Hubbard model and its spin-correlated, spin-frustrated extensions in two dimensions. The metamagnetic jump is established and compared with earlier results of dynamical mean-field theory. This approach also reproduces the emergent super-exchange energy scale in the insulating side. A scaling is found for the critical Zeeman field in terms of the intrinsic coherence scale just below the metal–insulator transition, where the critical spin fluctuations are soft. The conditions required for metamagnetism to appear at a reasonable field are also underlined. Gutzwiller analysis on the two-dimensional Hubbard model and a quantum Monte Carlo calculation on the Heisenberg spin system are performed to check the limiting cases of the cluster slave-rotor results for the Hubbard model. Low-field scaling features for magnetization are discussed.

Reappearance of the Kondo effect in serially coupled symmetric triple quantum dots

We investigate the spectral properties of a serially coupled triple quantum dot (STQD) system by means of the hierarchical equations of motion (HEOM) approach. We find that with the increase of the interdot coupling t, the first Kondo screening is followed by another Kondo effect reappearing due to the transition from the respective Kondo singlet state of individual QD to the coherence bonding state generated among the three QDs. The reappearance of the Kondo effect results in the three-peak structure of the spectral functions of peripheral QD-1(3). By investigating the susceptibility χ, we find that the local susceptibility of intermediate QD-2 is a positive value at weak interdot coupling, while it changes into a negative value at strong interdot coupling, at which the STQD system gives rise to the reappearance of the Kondo effect. We also find that the slopes of will deviate from a straight line behaviour at low temperature in the reappearing Kondo regime. In addition, the influence of temperature and dot-lead coupling strength on the reappearing Kondo effect as well as the Kondo-correlated transport properties are afterwards exploited in detail.

Magnetic anisotropy in Shiba bound states across a quantum phase transition.

The exchange coupling between magnetic adsorbates and a superconducting substrate leads to Shiba states inside the superconducting energy gap and a Kondo resonance outside the gap. The exchange coupling strength determines whether the quantum many-body ground state is a Kondo singlet or a singlet of the paired superconducting quasiparticles. Here we use scanning tunnelling spectroscopy to identify the different quantum ground states of manganese phthalocyanine on Pb(111). We observe Shiba states, which are split into triplets by magnetocrystalline anisotropy. Their characteristic spectral weight yields an unambiguous proof of the nature of the quantum ground state. Our results provide experimental insights into the phase diagram of a magnetic impurity on a superconducting host and shine light on the effects induced by magnetic anisotropy on many-body interactions.

Steady-State Dynamics and Effective Temperature for a Model of Quantum Criticality in an Open System.

We study the thermal and nonthermal steady-state scaling functions and the steady-state dynamics of a model of local quantum criticality. The model we consider, i.e., the pseudogap Kondo model, allows us to study the concept of effective temperatures near fully interacting as well as weak-coupling fixed points. In the vicinity of each fixed point we establish the existence of an effective temperature-different at each fixed point-such that the equilibrium fluctuation-dissipation theorem is recovered. Most notably, steady-state scaling functions in terms of the effective temperatures coincide with the equilibrium scaling functions. This result extends to higher correlation functions as is explicitly demonstrated for the Kondo singlet strength. The nonlinear charge transport is also studied and analyzed in terms of the effective temperature.

Emergence of a Kondo singlet state with Kondo temperature well beyond 1000 K in a proton-embedded electron gas

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 exclusion principle. However, no details are known about the transition from H^+ to H^- in the intermediate-density region. Here, by accurately determining the ground-state electron distribution n(r) by the combination of LDA and diffusion Monte Carlo simulations with the total electron number up to 170, we obtain a complete picture of the transition, in particular, a sharp transition from short-range H^+ screening charge resonance to long-range Kondo-like spin-singlet resonance, the emergence of which is confirmed by the presence of an anomalous Friedel oscillation characteristic to the Kondo singlet state with the Kondo temperature T_K well beyond 1,000K. This study not only reveals interesting competition between charge and spin resonances, enriching the century-old paradigm of metallic screening to a point charge, but also discovers a long-sought novel high-T_K system, opening an unexpected route to room-temperature superconductivity in a Kondo lattice made of protons.

Lateral manipulation and interplay of local Kondo resonances in a two-impurity Kondo system

The atomic-scale spatial relationship of a two-impurity Kondo system has been determined at varying lateral distance by scanning tunneling microscopy (STM) and spectroscopy. The localized spins of two cobalt magnetic adatoms that are placed on different electrodes of an STM form two individual Kondo singlet states, each showing quite different Kondo coupling, i.e., the tip-Kondo with low Kondo temperature and the sample-Kondo with high Kondo temperature. The differential conductance dI/dV spectra show the continuous changes of the resonance peak feature when approaching the Kondo tip laterally to the local sample-Kondo impurity on the surface. The result indicates a notable interplay between these two Kondo systems. We propose a convolution model based on the q factor of the sample-Kondo (qs) and tip-Kondo (qt) to interpret the change of various tunneling channels and the evolution of the experimental spectra.

Antiferromagnetism and Kondo screening on a honeycomb lattice**Project supported by the National Key Basic Research Special Foundation of China (Grants Nos. 2011CB921502 and 2012CB821305), the National Natural Science Foundation of China (Grants Nos. 61227902, 61378017, and 11434015), the State Key Laboratory for Quantum Optics and Quantum Optical Devices, China (Grant No. KF201403).

Magnetic adatoms in the honeycomb lattice have received tremendous attention due to the interplay between Ruderman–Kittel–Kasuya–Yosida interaction and Kondo coupling leading to very rich physics. Here we study the competition between the antiferromagnetism and Kondo screening of local moments by the conduction electrons on the honeycomb lattice using the determinant quantum Monte Carlo method. While changing the interband hybridization V, we systematically investigate the antiferromagnetic-order state and the Kondo singlet state transition, which is characterized by the behavior of the local moment, antiferromagnetic structure factor, and the short range spin-spin correlation. The evolution of the single particle spectrum are also calculated as a function of hybridization V, we find that the system presents a small gap in the antiferromagnetic-order region and a large gap in the Kondo singlet region in the Fermi level. We also find that the localized and itinerant electrons coupling leads to the midgap states in the conduction band in the Fermi level at very small V. Moreover, the formation of antiferromagnetic order and Kondo singlet are studied as on-site interaction U or temperature T increasing, we have derived the phase diagrams at on-site interaction U (or temperature T) and hybridization V plane.

Strong-coupling limit of depleted Kondo- and Anderson-lattice models

Fourth-order strong-coupling degenerate perturbation theory is used to derive an effective low-energy Hamiltonian for the Kondo-lattice model with a depleted system of localized spins. In the strong-J limit, completely local Kondo singlets are formed at the spinful sites which bind a fraction of conduction electrons. The low-energy theory describes the scattering of the excess conduction electrons at the Kondo singlets as well as their effective interactions generated by virtual excitations of the singlets. Besides the Hubbard term, already discussed by Nozieres, we find a ferromagnetic Heisenberg interaction, an antiferromagnetic isospin interaction, a correlated hopping and, in more than one dimensions, three- and four-site interactions. The interaction term can be cast into highly symmetric and formally simple spin-only form using the spin of the bonding orbital symmetrically centered around the Kondo singlet. This spin is non-local. We show that, depending on the geometry of the depleted lattice, spatial overlap of the non-local spins around different Kondo singlets may cause ferromagnetic order. This is sustained by a rigorous argument, applicable to the half-filled model, by a variational analysis of the stability of the fully polarized Fermi sea of excess conduction electrons as well as by exact diagonalization of the effective model. A similar fourth-order perturbative analysis is performed for the depleted Anderson lattice in the limit of strong hybridization. Even in a parameter regime where the Schrieffer-Wolff transformation does not apply, this yields the same effective theory albeit with a different coupling constant.

Cyclotron dynamics of a Kondo singlet in a spin-orbit-coupled alkaline-earth-metal atomic gas

We propose a scheme to investigate the interplay between Kondo-exchange interaction and quantum spin Hall effect with ultracold fermionic alkaline-earth atoms trapped in two-dimensional optical lattices using ultracold collision and laser-assisted tunneling. In the strong Kondo-coupling regime, though the loop trajectory of the mobile atom disappears, collective dynamics of an atom pair in two clock states can exhibit an unexpected spin-dependent cyclotron orbit in a plaquette, realizing the quantum spin Hall effect of the Kondo singlet. We demonstrate that the collective cyclotron dynamics of the spin-zero Kondo singlet is governed by an effective Harper-Hofstadter model in addition to second-order diagonal tunneling.

Dynamic response of a spin-12Kondo singlet

We present a study of spin 1/2 Kondo singlets in single electron transistors under a microwave frequency bias excitation. We compare time-averaged conductance $G$ to predicted universal response with respect to microwave frequency, oscillation amplitude and the Kondo temperature and find a non-adiabatic response when the microwave photon energy $hf$ is comparable to the Kondo temperature $k_B T_K$. We show that our measurements are qualitatively consistent with the predictions for the radiation-induced decoherence rate of the Kondo spin.

Cooperation of different exchange mechanisms in confined magnetic systems

The diluted Kondo lattice model is investigated at strong antiferromagnetic local exchange couplings J, where almost local Kondo clouds drastically restrict the motion of conduction electrons, giving rise to the possibility of quantum localization of conduction electrons for certain geometries of impurity spins. This localization may lead to the formation of local magnetic moments in the conduction-electron system, and the inverse indirect magnetic exchange (IIME), provided by virtual excitations of the Kondo singlets, couples those local moments to the remaining electrons. Exemplarily, we study the one-dimensional two-impurity Kondo model with impurity spins near the chain ends, which supports the formation of conduction-electron magnetic moments at the edges of the chain for sufficiently strong J. Employing degenerate perturbation theory as well as analyzing spin gaps numerically by means of the density-matrix renormalization group, it is shown that the low-energy physics of the model can be well captured within an effective antiferromagnetic RKKY-like two-spin model ("RKKY from IIME") or within an effective central-spin model, depending on edge-spin distance and system size.

Pseudogap and singlet formation in organic and cuprate superconductors

The pseudogap phase occurring in cuprate and organic superconductors is analyzed based on the dynamical cluster approximation approach to the Hubbard model. In this method a cluster embedded in a self-consistent bath is studied. With increasing Coulomb repulsion, $U$, the antinodal point [$\mathbf{k}=(\ensuremath{\pi},0)$] displays a gradual suppression of spectral density of states around the Fermi energy which is not observed at the nodal point [$\mathbf{k}=(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$]. The opening of the antinodal pseudogap is found to be related to the internal structure of the cluster and the much weaker bath-cluster couplings at the antinodal than nodal point. The role played by internal cluster correlations is elucidated from a simple four-level model. For small $U$, the cluster levels form Kondo singlets with their baths leading to a peak in the spectral density. As $U$ is increased a localized state is formed localizing the electrons in the cluster. If this cluster localized state is nondegenerate, the Kondo effect is destroyed and a pseudogap opens up in the spectra at the antinodal point. The pseudogap can be understood in terms of destructive interference between different paths for electrons hopping between the cluster and the bath. However, electrons at the nodal points remain in Kondo states up to larger $U$ since they are more strongly coupled to the bath. The strong correlation between the $(\ensuremath{\pi},0)$ and the $(0,\ensuremath{\pi})$ cluster levels in the localized state leads to a large correlation energy gain, which is important for localizing electrons and opening up a pseudogap at the antinodal point. Such a scenario is in contrast with two independent Mott transitions found in two-band systems with different bandwidths in which the localized cluster electron does not correlate strongly with any other cluster electron for intermediate $U$. The important intracluster sector correlations are associated with the resonating valence bond character of the cluster ground state containing $d$-wave singlet pairs. The low-energy excitations determining the pseudogap have suppressed $d$-wave pairing, indicating that the pseudogap can be related to breaking very short-range $d$-wave pairs. Geometrical frustration on the anisotropic triangular lattice relevant to $\ensuremath{\kappa}$-(BEDT-TTF)${}_{2}X$ leads to a switch in the character of the ground state of the cluster at intermediate hopping ratios ${t}^{\ensuremath{'}}/t\ensuremath{\sim}0.7$. Electron doping of the frustrated square lattice destroys the pseudogap, in agreement with photoemission experiments on cuprates, due to a larger Schrieffer-Wolff exchange coupling, ${J}_{K}$, and a stronger cluster-bath coupling for the antinodal point.

Composite Orders and Lifshitz Transition of Heavy Electrons

Magnetic and other unconventional electronic orders are discussed for heavy electrons. In addition to the ordinary Kondo lattice, we consider non-Kramers systems taking the two-channel Kondo lattice, and another lattice that consists of a singlet–triplet f2 configuration. The latter gives a scalar order with staggered sublattices of crystalline-electric-field (CEF) and Kondo singlets, which accounts for the observed order in PrFe4P12. In the two-channel Kondo lattice, an odd-frequency pairing is realized that becomes degenerate at half-filling with a diagonal composite order involving both localized and conduction electrons. The degeneracy is interpreted in terms of a hidden SO(5) symmetry. For the ordinary Kondo lattice with exchange interaction J, we take insulating ground states as reference. The metallic states are approached by infinitesimal doping of carriers either from the Kondo insulator or from the antiferromagnetic insulator. By adding intersite exchange we find that location of the band extremum of the heavy band depends on the value of J. The change of J gives topological change of the Fermi surface, which corresponds to a generalized version of the Lifshitz transition, and occurs separately from the quantum critical point of the antiferromagnetic order.

Evidence of a Kondo Destroying Quantum Critical Point in YbRh2Si2

The heavy-fermion metal YbRh$_{2}$Si$_{2}$ is a weak antiferromagnet below $T_{N} = 0.07$ K. Application of a low magnetic field $B_{c} = 0.06$ T ($\perp c$) is sufficient to continuously suppress the antiferromagnetic (AF) order. Below $T \approx 10$ K, the Sommerfeld coefficient of the electronic specific heat $\gamma(T)$ exhibits a logarithmic divergence. At $T < 0.3$ K, $\gamma(T) \sim T^{-\epsilon}$ ($\epsilon: 0.3 - 0.4$), while the electrical resistivity $\rho(T) = \rho_{0} + aT$ ($\rho_{0}$: residual resistivity). Upon extrapolating finite-$T$ data of transport and thermodynamic quantities to $T = 0$, one observes (i) a vanishing of the "Fermi surface crossover" scale $T^{*}(B)$, (ii) an abrupt jump of the initial Hall coefficient $R_{H}(B)$ and (iii) a violation of the Wiedemann Franz law at $B = B_{c}$, the field-induced quantum critical point (QCP). These observations are interpreted as evidence of a critical destruction of the heavy quasiparticles, i.e., propagating Kondo singlets, at the QCP of this material.

Entanglement switching via the Kondo effect in triple quantum dots

We consider a triple quantum dot system in a triangular geometry with one of the dots connected to metallic leads. Using Wilson's numerical renormalization group method, we investigate quantum entanglement and its relation to the thermodynamic and transport properties, in the regime where each of the dots is singly occupied on average, but with non-negligible charge fluctuations. It is shown that even in the regime of significant charge fluctuations the formation of the Kondo singlets induces switching between separable and perfectly entangled states. The quantum phase transition between unentangled and entangled states is analyzed quantitatively and the corresponding phase diagram is explained by exactly solvable spin model.