Kondo Singlet State Research Articles

Critical behavior in a Kondo-screening partially-ordered antiferromagnet CePdAl

A rare-earth compound CePdAl is a good example of the Kondo-screening partially-ordered antiferromagnet below TN = 2.7 K. In this compound, the formation of the Kondo-singlet state is realized as a new route of the relief of the frustration. The spin dynamics of CePdAl are, however, still controversial. In order to further investigate the spin dynamics of CePdAl, we have performed 27Al-NMR and specific heat single crystal measurements and reanalysed published powder neutron diffraction data. NMR intensities decrease with decreasing temperature in the ordered state suggesting the slow spin fluctuations below TN = 2.7 K, while the intensity of magnetic Bragg peak measured by neutron diffraction increases monotonously in the same temperature range. The critical exponents derived from the neutron diffraction and the specific heat measurements are not coincident with those of known universality classes. An unconventional magnetic order parameter or a charge degree of freedom originated from the coexistence of frustration and the Kondo effect may influence the critical behavior.

Block entropy and quantum phase transition in the anisotropic Kondo necklace model

We study the von Neumann block entropy in the Kondo necklace model for different anisotropies $\ensuremath{\eta}$ in the $\mathit{XY}$ interaction between conduction spins using the density matrix renormalization group method. It was found that the block entropy presents a maximum for each $\ensuremath{\eta}$ considered, and, comparing it with the results of the quantum criticality of the model based on the behavior of the energy gap, we observe that the maximum block entropy occurs at the quantum critical point between an antiferromagnetic and a Kondo singlet state, so this measure of entanglement is useful for giving information about where a quantum phase transition occurs in this model. We observe that the block entropy also presents a maximum at the quantum critical points that are obtained when an anisotropy $\ensuremath{\Delta}$ is included in the Kondo exchange between localized and conduction spins; when $\ensuremath{\Delta}$ diminishes for a fixed value of $\ensuremath{\eta}$, the critical point increases, favoring the antiferromagnetic phase.

Effect of Pd doping on the Kondo insulating state in CeRh1−xPdxSb

AbstractIt follows from our analysis that the formation of the Kondo insulator (KI) state in CeRh1−xPdxSb is due to the formation of the collective Kondo singlet state. The semiconducting gap in CeRhSb is strongly reduced with Pd substitution, the activated behaviour in the resistivity is observed only for $x\; < \;0.08$. In this paper, we present a schematic phase diagram for CeRh1−xPdxSb on the temperature T−x plane, based on the magnetic susceptibility data and resistivity. For $x \leq 0.06$ the intra‐atomic hybridization energy V dominates the KI ground state. With increase in x the hybridization V is strongly reduced, which leads to metallic properties of CeRh1−xPdxSb.

Correlated electron transport through double quantum dots coupled to normal and superconducting leads

We study Andreev transport through double quantum dots connected in series normal and superconducting (SC) leads, using the numerical renormalization group. The ground state of this system shows a crossover between a local Cooper-pairing singlet state and a Kondo singlet state, which is caused by the competition between the Coulomb interaction and the SC proximity. We show that the ground-state properties reflect this crossover especially for small values of the inter-dot coupling $t$, while in the opposite case, for large $t$, another singlet with an inter-dot character becomes dominant. We find that the conductance for the local SC singlet state has a peak with the unitary-limit value $4e^2/h$. In contrast, the Andreev reflection is suppressed in the Kondo regime by the Coulomb interaction. Furthermore, the conductance has two successive peaks in the transient region of the crossover. It is further elucidated that the gate voltage gives a different variation into the crossover. Specifically, as the energy level of the dot that is coupled to the normal lead varies, the Kondo screening cloud is deformed to a long-range singlet bond.

Gap formation and phase transition of the anisotropic Kondo necklace model: Density matrix renormalization group analysis

We analyze the one-dimensional Kondo necklace model, at zero temperature, with an anisotropy parameter $\ensuremath{\eta}$ in the interaction of the conduction chain, by means of the density matrix renormalization group. We calculate the energy gap and estimate the quantum critical points that separate a Kondo singlet state from an antiferromagnetic state, assuming a Kosterlitz-Thouless tendency. We also observe the correlation functions and the structure factors that support our critical points. The resulting phase diagram is presented and compared to that reported previously using Lanczos calculations. It is shown that the quantum critical points vary very slowly with $\ensuremath{\eta}$, but when $\ensuremath{\eta}$ approaches zero, they drop abruptly.

Effect of spin polarization on the ground state of Kondo system

The effect of spin polarization on the ground state of Kondo type system is a fundamental issue in study of Anderson model. By using variational and diagonal methods we analysis the stability of Kondo singlet state in s-d model and Zhang-Rice singlet state in two-component model for high Tc superconductivity when Cu site spin polarization is considered.

Effect of In–Ga intermixing on the electronic states in self-assembled InAs quantum dots probed by nanogap electrodes

We have investigated the effect of In–Ga intermixing on the electronic states in single self-assembled InAs quantum dots (QDs) coupled to nanogap metallic electrodes. The orbital quantization energies of the QDs and the tunnel resistances exhibited a strong dependence on growth temperature, TG, due to In–Ga intermixing during QD formation. When the intermixing was suppressed by reducing TG to 470 °C, the electron wave functions in the QDs become more extended in space and QD-electrode coupling sufficiently strong to form the Kondo singlet states at 4.3 K was realized even in a small QD of ∼45 nm diameter.

Anomaly in the heat capacity of Kondo superconductors

Using numerical renormalization group, we study thermodynamic properties of a magnetic impurity described by the Anderson impurity model in a superconducting host material described by the BCS Hamiltonian. When the Kondo temperature in the normal state, ${T}_{K}$, is comparable to the critical temperature of the superconducting transition, ${T}_{c}$, the magnetic doublet state may become degenerate with the Kondo singlet state, leading to a $\text{ln}\text{ }3$ peak in the temperature dependence of the impurity contribution to the entropy. This entropy increase translates into an anomalous feature in the heat capacity which might have already been experimentally observed.

Instability to partial Kondo-singlet state in the Kondo necklace model on frustrated lattices

We present our theoretical results on the Kondo necklace model, which is known to give a good description of the half-filled state of the Kondo lattice model, on geometrically frustrated lattices. We employ the Lanczos exact diagonalization method as well as the bond-operator mean-field approximation to clarify the magnetic state at zero temperature. We examine a possibility of relieving severe frustration by making a spatially-periodic arrangement of magnetic ordered sites and nonmagnetic ones, i.e., the magnetic moments vanish periodically due to the Kondo singlet formation. We call the composite of magnetic and Kondo-singlet subsystems ‘partial Kondo-singlet state’, by analogy with the partial order in frustrated spin systems. We demonstrate that small clusters of 1D and 2D frustrated models show a tendency to exhibit the partial Kondo-singlet formation, and compare the results with those by the bond-operator mean-field approximation.

Green’s function approach to quantum criticality in the anisotropic Kondo necklace model

We have studied the quantum phase transition between the antiferromagnetic and spin liquid phase for the two dimensional anisotropic Kondo-necklace model. The bond operator formalism has been implemented to transform the spin Hamiltonian to a bosonic one. We have used the Green's function approach including a hard core repulsion to find the low energy excitation spectrum of the model. The bosonic excitations become gapless at the quantum critical point where the phase transition from the Kondo singlet state to long range antiferromagnetic order takes place. We have studied the effect of both inter-site (delta) and local (Delta) anisotropies on the critical point and on the critical exponent of the excitation gap in the paramagnetic phase. We have also compared our results with previous bond operator mean field calculations.

Andreev transport through double quantum dots: Numerical renormalization group approach

We study the transport through double quantum dots coupled to normal and superconducting leads. Using the numerical renormalization group method, we calculate the linear conductance due to the Andreev reflection. As the Coulomb interaction in the dots gets larger, we find that the peak of the conductance is suppressed, which clearly features the crossover between two distinct regions of spin-singlet ground state, i.e. the superconducting singlet state and the Kondo singlet state. It is further elucidated that this crossover becomes smeared with the increase in the interdot coupling, which causes the suppression of the peaks in the gate-voltage dependence of the conductance.

Numerical Renormalization Group Approach to a Quantum Dot Coupled to Normal and Superconducting Leads

We study transport through a quantum dot coupled to normal and superconducting leads using the numerical renormalization group method. We show that the low-energy properties of the system are described by the local Fermi liquid theory despite of the superconducting correlations penetrated into the dot due to a proximity effect. We calculate the linear conductance due to the Andreev reflection in the presence of the Coulomb interaction. It is demonstrated that the maximum structure appearing in the conductance clearly characterizes a crossover between two distinct spin-singlet ground states, i.e. the superconducting singlet state and the Kondo singlet state. It is further elucidated that the gate-voltage dependence of the conductance shows different behavior in the superconducting singlet region from that in the Kondo singlet region.

Effect of localized spins in coherent transport through quantum dots

The effect of localized spins on the quantum coherence in solids is discussed. A quantum dot with an odd number of electrons can be a model system for a localized spin. It is experimentally shown that a spin flip scattering by a quantum dot pulls the trigger of quantum decoherence. On the other hand, spin flip scattering is the basic process to construct the Kondo singlet state around a magnetic impurity. Through an interference effect of the Kondo state (the Fano–Kondo effect) in a side-coupled dot system, we show experimentally that the Kondo singlet state is quantum mechanically coherent. The analysis of the Fano–Kondo lineshape indicates the locking of the phase shift to π / 2 , which is in agreement with theoretical predictions. The Fano–Kondo effect is also observed in an Aharonov–Bohm ring, in which a quantum dot is embedded, and also indicates the phase shift locking to π / 2 .

Magnetic properties of almost localized fermions revisited: spin dependent masses and quantum critical behavior

AbstractThe Editor's Choice [1] of this issue of physica status solidi (b) discusses spectacular phenomena in correlated electron systems viewed as quantum materials. The cover figure is a schematic representation of the transformation from the Kondo insulator (KI) state to the non‐Fermi liquid (NFL) state with short‐range antiferromagnetic correlations at the critical concentration, when the Kondo singlet state is destroyed. AFI denotes the antiferromagnetic insulating state.The author Jozef Spałek heads the Condensed Matter Theory Division in the Institute of Physics of the Jagiellonian University Kraków. His scientific interests include the theory of Mott–Hubbard and heavy‐fermion systems, with a particular emphasis on quantum critical behavior close to the electron localization.This issue contains presentations from The European Conference Physics of Magnetism (PM'05) held in Poznań, Poland, 24–27 June 2005. Further articles from PM'05 can be found in phys. stat. sol. (c) 3, No. 1 (2006).

Nonequilibrium Kondo effect in a quantum dot

We present a unified theoretical approach, the finite-U slave-boson mean-field approach developed initially by Kotliar and Ruckenstein (1986 Phys. Rev. Lett. 57 1362), for the description of the linear and nonlinear Kondo-type transport through coupled double quantum dots (DQDs) connected in series to leads and through a multi-level lateral quantum dot. We find that, with increasing inter-dot hopping, the DQDs manifest three distinct physical scenarios: the Kondo singlet state of each dot with its adjacent lead, the spin singlet state consisting of local spins on each dot and the doubly occupied bonding orbital of the coupled dots. For a two-level quantum dot, our calculation demonstrates a substantial conductance enhancement near the degeneracy point of the spin singlet and triplet states, a non-monotonic temperature dependence of conductance and a sharp dip and non-zero bias maximum of the differential conductance. These agree well with recent experimental observations.

Kondo lattice model with a direct exchange interaction between localized moments

We study the Kondo lattice model with a direct antiferromagnetic exchange interaction between localized moments. Ferromagnetically long-range ordered state coexisting with the Kondo screening shows a continuous quantum phase transition to the Kondo singlet state. We obtain the value of the critical point where the magnetizations of the localized moments and the conduction electrons vanish. The magnetization curves yield a universal critical exponent independent of the filling factors and the strength of the interaction between localized moments. It is shown that the direct exchange interaction between localized moments introduces another phase transition from an antiferromagnetic ordering to a ferromagnetic ordering for small Kondo exchange interaction. We also explain the local minimum of the Kondo temperature in recent experiments.

Kondo Effect in the Long-Range Antiferromagnetic Ordered State –CexNd1-xB6–

We have studied the coexistence and the competition between the Kondo singlet state and the long-range antiferro(AF)magnetic ordering in the Ce x Nd 1- x B 6 system. At high temperatures, the single impurity Kondo effect is observed in all the samples as in the Ce x La 1- x B 6 system. In the AF magnetic state formed mainly by Nd ions, Ce ions contribute to the AF magnetic ordering but at the same time exhibit the Kondo singlet character with a small effect from the magnetic ordering. The ground state of Ce x Nd 1- x B 6 changes with x ; in a small x region, the Kondo singlet state is destroyed by the exchange field from surrounding Nd moments. Above x ∼0.3, the long-range magnetic order takes place because the Ce–Ce interaction overcomes the Kondo effect. In an intermediate x value between the above two regions, the Kondo singlet state may continue to exist down to a very low temperature.

Kondo effect and antiferromagnetic correlation in transport through tunneling-coupled double quantum dots

We propose to study the transport through tunneling-coupled double quantum dots (DQDs) connected in series to leads, using the finite-$U$ slave-boson mean field approach developed initially by Kotliar and Ruckenstein [Phys. Rev. Lett. {\bf 57}, 1362 (1986)]. This approach treats the dot-lead coupling and the inter-dot tunnelling $t$ nonperturbatively at arbitrary Coulomb correlation $U$, thus allows the anti-ferromagnetic exchange coupling parameter $J=4t^2/U$ to appear naturally. We find that, with increasing the inter-dot hopping, the DQDs manifest three distinct physical scenarios: the Kondo singlet state of each dot with its adjacent lead, the spin singlet state consisting of local spins on each dot and the doubly occupied bonding orbital of the coupled dots. The three states exhibit remarkably distinct behavior in transmission spectrum, linear and differential conductance and their magnetic-field dependence. Theoretical predictions agree with numerical renormalization group and Lanczos calculations, and some of them have been observed in recent experiments.

Two-impurity Kondo effect in double-quantum-dot systems: Effect of interdot kinetic exchange coupling

Tunneling conductance through two quantum dots, which are connected in series to left and right leads, is calculated by using the numerical renormalization group method. As the hopping between the dots increases from a very small value, the following states continuously appear: (i) Kondo singlet state of each dot with its adjacent-site lead, (ii) singlet state between the local spins on the dots, and (iii) double occupancy in the bonding orbital of the two dots. The conductance shows peaks at the crossover regions between these states. The peak at the boundary between (i) and (ii) especially has the unitarity limit value of ${2e}^{2}/h$ because of coherent connection through the lead-dot-dot-lead. For the strongly correlated cases, the characteristic energy scale of the coherent peak shows anomalous decrease relating to the quantum critical transition known for the two-impurity Kondo effect. The two dot systems give a new realization of the two-impurity Kondo problem.

Atomic short-range order and magnetism inPt1−xCrxalloys

Atomic short-range order and magnetism in ${\mathrm{Pt}}_{1\ensuremath{-}x}{\mathrm{Cr}}_{x}$ alloys with $x=0.07,$ 0.10, 0.13, and 0.16 were studied by means of neutron scattering and susceptibility measurements. The latter showed a spin-glass-type anomaly at low temperature for $x=0.13$ and 0.16, but a monotonic increase towards the lowest temperature for $x=0.07$ and 0.10. In neutron scattering, broad satellite peaks with asymmetric intensities were observed for all specimens along the [1 0 0] direction, even at room temperature. These peaks are well explained as a concentration wave of constituent atoms accompanied with a periodic lattice deformation. Magnetic diffuse scattering was observed for the specimens with $x=0.13$ and 0.16. The origin of the spin-glass-like behavior in these alloys is ascribed to the dynamics and freezing of spin-density-wave cluster fluctuations, similar to the case of CuMn spin-glass alloys. A breakdown of the Kondo singlet state was studied for an $x=0.10$ nonmagnetic alloy using neutron scattering under a magnetic field of 6 T.