Kondo Singlet Research Articles

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.

Magnetic field effects on the Andreev transport through a quantum dot

We investigate magnetic field effects on the transport through a quantum dot coupled to normal and superconducting leads. Using the modified second-order perturbation theory, we calculate the linear conductance due to the Andreev reflection. It is shown that a maximum structure appearing in the conductance shifts its position with the increase of magnetic field. The detailed analysis of the local density of states and the renormalized parameters elucidates that the maximum of the conductance in magnetic fields clearly characterizes the crossover among the superconducting singlet, the Kondo singlet and the spin-polarized state.

Field-induced quantum phase transition in the anisotropic Kondo necklace model

The anisotropic Kondo necklace model in 2D and 3D is treated as a genuine model for magnetic to Kondo singlet quantum phase transitions in the heavy fermion (HF) compounds. The variation of the quantum critical point (QCP) with anisotropy parameters has been investigated previously in the zero field case [1]. Here we extend the treatment to finite fields using a generalised bond operator representation including all triplet states. The variation of critical tc with external field H and the associated phase diagram is derived. The influence of anisotropies and the different g-factors for localised and itinerant spins on tc(H) is also investigated. It is found that three different types of behaviour may appear: (i) Destruction of antiferromangetism and appearance of a singlet state above a critical field. (ii) The inverese behaviour, namely field induced antiferromagnetism out of the Kondo singlet phase. (iii) Reentrance behaviour of the Kondo singlet phase as function of field strength.

Entanglement, measurement, and conditional evolution of the Kondo singlet interacting with a mesoscopic detector

We investigate various aspects of the Kondo singlet in a quantum dot (QD) electrostatically coupled to a mesoscopic detector. The two subsystems are represented by an entangled state between the Kondo singlet and the charge-dependent detector state. We show that the phase-coherence of the Kondo singlet is destroyed in a way that is sensitive to the charge-state information restored both in the magnitude and in the phase of the scattering coefficients of the detector. We also introduce the notion of the ‘conditional evolution’ of the Kondo singlet under projective measurement on the detector. Our study reveals that the state of the composite system is disentangled upon this measurement. The Kondo singlet evolves into a particular state with a fixed number of electrons in the QD. Its relaxation time is shown to be sensitive only to the QD-charge dependence of the transmission probability in the detector, which implies that the phase information is erased in this conditional evolution process. We discuss implications of our observations in view of the possible experimental realization.

Higher angular momentum Kondo liquids

Conventional heavy Fermi liquid phases of Kondo lattices involve the formation of a "Kondo singlet" between the local moments and the conduction electrons. This Kondo singlet is usually taken to be in an internal s-wave angular momentum state. Here we explore the possibility of phases where the Kondo singlet has internal angular momentum that is d-wave. Such states are readily accessed in a slave boson mean field formulation, and are energetically favorable when the Kondo interaction is between a local moment and an electron at a nearest neighbor site. The properties of the d-wave Kondo liquid are studied. Effective mass and quasiparticle residue show large angle dependence on the Fermi surface. Remarkably in certain cases, the quasiparticle residue goes to zero at isolated points (in two dimensions) on the Fermi surface. The excitations at these points then include a free fractionalized spinon. We also point out the possibility of quantum Hall phenomena in two dimensional Kondo {\em insulators}, if the Kondo singlet has complex internal angular momentum. We suggest that such d-wave Kondo pairing may provide a useful route to thinking about correlated Fermi liquids with strong anisotropy along the Fermi surface.

Hanbury Brown–Twiss Correlations and Noise in the Charge Transfer Statistics through a Multiterminal Kondo Dot

We analyze the charge transfer statistics through a quantum dot in the Kondo regime, when coupled to an arbitrary number of terminals N. Special attention is paid to current cross correlations between concurring transport channels, which show distinct Hanbury Brown-Twiss antibunching for N>2 reflecting the fermionic nature of charge carriers. While this effect weakens as one moves away from the Kondo fixed point, a new type of correlations between nonconcurring channels emerges which are due entirely to the virtual polarization of the Kondo singlet. As these are not obscured by the background from fixed-point correlations they provide a promising means for extracting information on the parameters of the underlying Fermi-liquid model from the experimental data.

Antiferromagnetic metal to heavy-fermion metal quantum phase transition in the Kondo lattice model: A strong-coupling approach

We study the quantum phase transition from an antiferromagnetic metal to a heavy fermion metal in the Kondo lattice model. Based on the strong coupling approach we {\it first} diagonalize the Kondo coupling term. Since this strong coupling approach makes the resulting Kondo term {\it relevant}, the Kondo hybridization persists even in the antiferromagnetic metal, indicating that fluctuations of Kondo singlets are not critical in the phase transition. We find that the quantum transition in our strong coupling approach results from {\it softening of antiferromagnetic spin fluctuations of localized spins}, driven by the Kondo interaction. Thus, the volume change of Fermi surface becomes continuous across the transition. ......

Kondo screening of a high-spin Nagaoka state in a triangular quantum dot

We study transport through a triangle triple quantum dot connected to two noninteracting leads using the numerical renormalization group (NRG). The triangle has a high-spin ground state of S = 1 caused by a Nagaoka ferromagnetism, when it is isolated and has one extra electron introduced into a half-filling. The results show that the conduction electrons screen the local moment via two separate stages with different energy scales. The half of the S = 1 is screened first by one of the channel degrees, and then at very low temperature the remaining half is fully screened to form a Kondo singlet. The transport is determined by two phase shifts for quasi-particles with even and odd parities, and then a two-terminal conductance in the series configuration is suppressed g series ≃ 0 , while plateau of a four-terminal parallel conductance reaches a unitary limit value g parallel ≃ 4 e 2 / h of two conducting modes.

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 .

Theory of controlled dephasing of the Kondo singlet in a quantum dot

We present a theory of controlled dephasing for the Kondo singlet in a quantum dot (QD) via charge detection in a nearby quantum point contact (QPC) device. By employing the variational ansatz for the singlet ground state of the quantum dot combined with the density matrix formulation for the coupled system, we show that the coherent Kondo singlet is destroyed by the phase-sensitive as well as the magnitude-sensitive detection in the scattering coefficients at the quantum point contact. We argue that the phase-sensitive component of the decoherence rate can be much larger than the magnitude-sensitive term in generic situation, which may explain the anomalous features observed in a recent experiment by Avinun-Kalish et al. [Phys. Rev. Lett. 92 (2004) 156801]. We also discuss the correlations of the shot noise at the quantum point contact detector and the decoherence in the quantum dot.

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).

Decoherence of the Kondo Singlet via a Quantum Point Contact Detector

We investigate the effect of the charge state measurement of the Kondo singlet in a quantum dot transistor via a capacitively coupled quantum point contact detector. By employing the variational ansatz for the singlet ground state of the quantum dot combined with the density matrix formulation for the coupled system, we show that the coherent Kondo singlet is destroyed by the phase-sensitive as well as the current-sensitive detection in the transmission and reflection coefficients at the quantum point contact. We argue that the phase-sensitive component of the decoherence rate may explain the anomalous features observed in a recent experiment by Avinun-Kalish et al. [Phys. Rev. Lett. 92, 156801 (2004)]. We also discuss the correlations of the shot noise at the quantum point contact detector and the decoherence in the quantum dot.

Critical-field theory of the Kondo lattice model in two dimensions

In the context of the U(1) slave boson theory we derive a critical field theory near the quantum critical point of the Kondo lattice model in two spatial dimensions. First we argue that strong gauge fluctuations in the U(1) slave boson theory give rise to confinement between spinons and holons, thus causing "neutralized" spinons in association with the slave boson U(1) gauge field. Second we show that critical fluctuations of Kondo singlets near the quantum critical point result in a new U(1) gauge field. This emergent gauge field has nothing to do with the slave boson U(1) gauge field. Third we find that the slave boson U(1) gauge field can be exactly integrated out in the low energy limit. As a result we find a critical field theory in terms of renormalized conduction electrons and neutralized spinons interacting via the new emergent U(1) gauge field. Based on this critical field theory we obtain the temperature dependence of specific heat and the imaginary part of the self-energy of the renormalized electrons. These quantities display non-Fermi liquid behavior near the quantum critical point.

Phase diagram of the Kondo necklace model at finite temperatures

A simplified version of the Kondo lattice model, the Kondo necklace model, is studied at finite temperature using a representation for the localized and conduction electron spins in terms of local Kondo singlet and triplet operators. We calculate the double time Green's functions to get the dispersion relation of the excitations of the system. We show that in 3-d there is an antiferromagnetic ordered state at finite temperatures, but in 2-d long-range magnetic order occurs only at T = 0 .

Field-induced phase transition in the periodic Anderson model

We investigate the effect of magnetic fields on a Kondo insulator by using the periodic Anderson model. The analysis by dynamical mean field theory combined with quantum Monte Carlo simulations reveals that the magnetic field drives the Kondo insulator to a transverse antiferromagnetic insulator at low temperatures. We calculate the staggered spin susceptibility and find its divergence signaling the antiferromagnetic instability. Further investigation of the spin correlation functions and the magnetization process clarifies how the magnetic field suppresses the Kondo singlet formation and induces the transverse antiferromagnetic ordering.

Quantum replica approach to the underscreened Kondo model

We extend the Schwinger boson large N treatment of the underscreened Kondo model in a way that correctly captures the finite elastic phase shift in the singular Fermi liquid. The new feature of the approach, is the introduction of a flavor quantum number with K possible values, associated with the Schwinger boson representation. The large N limit is taken maintaining the ratio k=K/N fixed. This approach differs from previous approaches, in that we do not explicitly enforce a constraint on the spin representation of the Schwinger bosons. Instead, the energetics of the Kondo model cause the bosonic degrees of freedom to ``self assemble'' into a ground-state in which the spins of K bosons and N-K conduction electrons are antisymmetrically arranged into a Kondo singlet. With this device, the large N limit can be taken, in such a way that a fraction K/N of the Abrikosov Suhl resonance is immersed inside the Fermi sea. We show how this method can be used to model the full energy dependence of the singular Abrikosov Suhl resonance in the underscreened Kondo model and the field-dependent magnetization.

The one-dimensional Kondo lattice model at partial band filling

The Kondo lattice model introduced in 1977 describes a lattice of localized magnetic moments interacting with a sea of conduction electrons. It is one of the most important canonical models in the study of a class of rare earth compounds, called heavy fermion systems, and as such has been studied intensively by a wide variety of techniques for more than a quarter of a century. This review focuses on the one dimensional case at partial band filling, in which the number of conduction electrons is less than the number of localized moments. The theoretical understanding, based on the bosonized solution, of the conventional Kondo lattice model is presented in great detail. This review divides naturally into two parts, the first relating to the description of the formalism, and the second to its application. After an all-inclusive description of the bosonization technique, the bosonized form of the Kondo lattice hamiltonian is constructed in detail. Next the double-exchange ordering, Kondo singlet formation, the RKKY interaction and spin polaron formation are described comprehensively. An in-depth analysis of the phase diagram follows, with special emphasis on the destruction of the ferromagnetic phase by spin-flip disorder scattering, and of recent numerical results. The results are shown to hold for both antiferromagnetic and ferromagnetic Kondo lattice. The general exposition is pedagogic in tone.

Instability of the Fermi surface in the one-dimensional Kondo lattice

The key parameters that characterize the long wavelength behaviour of correlationfunctions, including the Fermi momenta and the correlation length, are calculated using thetransfer matrix renormalization group for the one-dimensional Kondo lattice model. TheFermi momentum varies slowly at high temperatures, but changes sharply at lowtemperatures in association with the formation of the Kondo singlets. By comparison withthe temperature dependence of the conduction electron density, we find that the longwavelength correlations of conduction electrons are strongly affected by the localized spinsat low temperatures. At high temperatures, the conduction electrons behave as for asystem with a small Fermi surface. However, at low temperatures, the Fermi momentumof the conduction electrons is altered by the coupling with the localized spins.

Josephson current in a quantum dot in the Kondo regime connected to two superconductors

We apply a Gutzwiller-like variational technique to study Josephson conduction across a quantum dot with an odd number of electrons connected to two superconducting leads. Our method projects out all states on the dot but the Kondo singlet and is valid when Kondo correlations are dominant and no Andreev bound states localized at the dot are available for Kondo screening. In these conditions superconducting pairing is a competing effect and the junction is π-like, to optimize antiferromagnetic correlations on the dot. As the superconducting gap increases, the Josephson current also increases, but its phase dependence becomes strongly non-sinusoidal.

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.