Kondo Phases Research Articles

Spin current Kondo effect in frustrated Kondo systems

Magnetic frustrations can enhance quantum zero-point motion in spin systems and lead to exotic topological insulating states. When coupled to mobile electrons, they may lead to unusual non-Fermi liquid or metallic spin liquid states whose nature has not been well explored. Here, we propose a spin current Kondo mechanism underlying a series of non-Fermi liquid phases on the border of Kondo and magnetic phases in a frustrated three-impurity Kondo model. This mechanism is confirmed by renormalization group analysis and describes movable Kondo singlets called "holons" induced by an effective coupling between the spin current of conduction electrons and the vector chirality of localized spins. Similar mechanism may widely exist in all frustrated Kondo systems and be detected through spin-current noise measurements.

Photo-emission signatures of coherence breakdown in Kondo alloys: dynamical mean-field theory approach

We study the Kondo alloy model on a square lattice using dynamical mean-field theory for Kondo substitution and disorder effects, together with static mean-field approximations. We computed and analyzed photoemission properties as a function of electronic filling n c , Kondo impurity concentration x, and strength of Kondo temperature T K. We provide a complete description of the angle resolved photoemission spectroscopy (ARPES) signals expected in the paramagnetic (PM) Kondo phases. By analyzing the Fermi surface (FS), we observe the Lifshitz-like transition predicted previously for strong T K at x = n c and we discuss the evolution of the dispersion from the dense coherent to the dilute Kondo regimes. At smaller T K, we find that this transition marking the breakdown of coherence at x = n c becomes a crossover. However, we identify another transition at a smaller concentration x ⋆ where the effective mass continuously vanishes. x ⋆ separates the one-branch and the two-branches ARPES dispersions characterizing respectively dilute and dense Kondo PM regimes. The x − T K phase diagrams are also described, suggesting that the transition at x ⋆ might be experimentally observable since magnetically ordered phases are stabilized at much lower T K. FS reconstructions in antiferromagnetic and ferromagnetic phases are also discussed.

Quantum Critical Point between Two-Channel Kondo and Fermi-Liquid Phases

We investigate the emergence of quantum critical points near a two-channel Kondo phase by evaluating an $f$-electron entropy of a seven-orbital impurity Anderson model hybridized with three ($\Gamma_7$ and $\Gamma_8$) conduction bands with the use of a numerical renormalization group method First we consider the case of Pr$^{3+}$ ion, in which quadrupole two-channel Kondo effect is known to occur for the local $\Gamma_3$ doublet state. When we control crystalline electric field (CEF) potentials so as to change the local CEF ground state from $\Gamma_3$ doublet to $\Gamma_1$ singlet or $\Gamma_5$ triplet, we commonly observe a residual entropy of $\log \phi$ with the golden ratio $\phi=(1+\sqrt{5})/2$, which is equal to that for three-channel Kondo effect. This peculiar residual entropy is also observed for the case of Nd$^{3+}$ ion, in which magnetic two-channel Kondo phase is found to occur for the local $\Gamma_6$ doublet state. We envisage a scenario that the quantum critical point characterized by $\log \phi$ generally appears between two-channel Kondo and Fermi-liquid phases.

Magnetic Kondo regimes in a frustrated half-filled trimer

We analyze theoretically the phase diagram of a triangular triple quantum dot with strong onsite repulsion coupled to ferromagnetic leads. This model includes the competition of magnetic ordering of local or itinerant magnetic moments, geometric frustration and Kondo screening. We identify all the phases resulting from this competition. We find that three Kondo phases -- the conventional one, the two-stage underscreened one, and the one resulting from the ferromagnetic Kondo effect -- can be realized at zero temperature, and all are very susceptible to the proximity of ferromagnetic leads. In particular, we find that the quantum dots are spin-polarized in each of these phases. Further, we discuss the fate of the phases at non-zero temperatures, where a plethora of competing energy scales gives rise to complex landscape of crossovers. Each Kondo regime splits into a pair of phases, one not magnetized and one comprising magnetically polarized quantum dots. We discuss our results in the context of heavy-fermion physics in frustrated Kondo lattices.

Magnetic effects on the Chern Kondo insulator

We examine the Chern Kondo insulator proposed in a square optical lattice with staggered flux induced by $s$-$p$ orbital hybridization by revisiting its realization and taking into account the magnetic effects for the Kondo phases. The Ruderman-Kittel-Kasuya-Yoshida interaction is analyzed at the weak $s$-$p$ hybridization regime, with the anisotropic magnetic effects being discussed. Furthermore, the paramagnetic and magnetic phases coexisting with Kondo couplings are systematically investigated through the slave-boson theory, for which the rich phases are obtained, including the antiferromagnetic, collinear antiferromagnetic Kondo insulator, and Kondo metal phases. The magnetic orders are shown to enhance the effective Kondo hybridization compared with the case without taking into account magnetic effects, and exhibit different influences on the bulk topology. In particular, the antiferromagnetic order always enhances the topological phase by increasing bulk gap of the Chern Kondo phases. The results show the rich topological and magnetic effects obtained in the present Chern Kondo lattice model. We also investigate how to identify the topology and strong correlation effects through measuring the Hall conductance and double occupancy, which are achievable in ultracold atom experiments.

Kondo-semimetal to Fermi-liquid phase crossover in black phosphorus to pressure-induced orbital-nematic gray phosphorus

We perform a comparative study of the electronic structures and electrical resistivity properties of black $(A17)$ and of pressurized gray $(A7)$ phosphorus, showing band-selective Kondoesque electronic reconstruction in these layered $p$-band phosphorus allotropes. Based on density functional dynamical mean-field theory calculations, we show that gray phosphorus can host a three-dimensional Kondo semimetal to a Fermi liquid phase crossover under anisotropic compression, which lifts in-layer orbital degeneracy. Therein, the $3p$ spectrum is almost unaffected both in the semiconducting and semimetallic Kondo phases, however in the Fermi liquid regime strong electronic reconstruction is predicted to exist in the orbital nematic phase of compressed gray phosphorus. These findings contribute to the microscopic understanding of the role played by dynamical multiorbital electronic interactions in the low energy spectrum of correlated semiconductors and topological semimetals.

Mott transitions in the periodic Anderson model

The periodic Anderson model (PAM) is studied within the framework of dynamical mean-field theory, with particular emphasis on the interaction-driven Mott transition it contains, and on resultant Mott insulators of both Mott–Hubbard and charge-transfer type. The form of the PAM phase diagram is first deduced on general grounds using two exact results, over the full range of model parameters and including metallic, Mott, Kondo and band insulator phases. The effective low-energy model which describes the PAM in the vicinity of a Mott transition is then shown to be a one-band Hubbard model, with effective hoppings that are not in general solely nearest neighbour, but decay exponentially with distance. This mapping is shown to have a range of implications for the physics of the problem, from phase boundaries to single-particle dynamics; all of which are confirmed and supplemented by NRG calculations. Finally we consider the locally degenerate, non-Fermi liquid Mott insulator, to describe which requires a two-self-energy description. This is shown to yield a number of exact results for the associated local moment, charge, and interaction-renormalised levels, together with a generalisation of Luttinger’s theorem to the Mott insulator.

Coexistence of magnetic order and Kondo effect in the Kondo-Heisenberg model

The Kondo lattice model is investigated through a fermionic mean-field approximation. The obtained phase diagram, including the pure ferromagnetic (FM), antiferromagnetic (AF), Kondo (K), and mixed phases, is in good agreement with previous studies. Calculations on the simple cubic and square lattices confirm a robust coexistence of ferromagnetism and Kondo effect (FM + K), sustained by a partial Kondo screening, which leads to the concept of a spin selective Kondo insulator. We have also obtained a coexistence of antiferromagnetism and Kondo effect (AF + K), which requires the intervenience of a next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ and a Heisenberg exchange ${J}_{ij}$. The effect of temperature and pressure is described by the behavior of the order parameters. The corresponding N\'eel temperature ${T}_{N}$ and Kondo temperature ${T}_{K}$ are plotted in the form of a Doniach diagram. The presence of the intermediate mixed phases is fundamental to determine the order of the magnetic phase transitions as one approaches the quantum critical point.

Two-channel Kondo phases and frustration-induced transitions in triple quantum dots

We consider a ring of three quantum dots mutually coupled by antiferromagnetic exchange interactions, and tunnel-coupled to two metallic leads: the simplest device in which the consequences of local frustration arising from internal degrees of freedom may be studied within a 2-channel environment. Two-channel Kondo (2CK) physics is found to predominate at low-energies in the mirror-symmetric systems considered, with a residual spin 1/2 overscreened by coupling to both leads. It is however shown that two distinct 2CK phases, with different ground state parities, arise on tuning the interdot exchange couplings. In consequence a frustration-induced quantum phase transition occurs, the 2CK phases being separated by a quantum critical point for which an effective low-energy model is derived. Precisely at the transition, parity mixing of the quasi-degenerate local trimer states acts to destabilise the 2CK fixed points; and the critical fixed point is shown to consist of a free pseudospin together with effective 1-channel spin quenching, itself reflecting underlying channel-anisotropy in the inherently 2-channel system. Numerical renormalization group techniques and physical arguments are used to obtain a detailed understanding of the problem, including study of both thermodynamic and dynamical properties of the system.

Entanglement and the Kondo effect in serially coupled double quantum dots

We investigate entanglement between electrons in serially coupled double quantum dots attached to non interacting leads. In addition to local repulsion we consider the influence of capacitive inter-dot interaction. We show how the competition between extended Kondo and local singlet phases determines the ground state and thereby the entanglement.

Diatomic molecule as a quantum entanglement switch

We investigate a pair entanglement of electrons in diatomic molecule, modeled as a correlated double quantum dot attached to the leads. The low-temperature properties are derived from the ground state obtained by utilizing the Rejec–Ramšak variational technique within the framework of EDABI method, which combines exact diagonalization with ab initio calculations. The results show, that single-particle basis renormalization modifies the entanglement-switch effectiveness significantly. We also found the entanglement signature of a competition between an extended Kondo and singlet phases.

Transmission in double quantum dots in the Kondo regime: Quantum-critical transitions and interference effects

We study the transmission through a double quantum-dot system in the Kondo regime. An exact expression for the transmission coefficient in terms of fully interacting many-body Green's functions is obtained. By mapping the system into an effective Anderson impurity model, one can determine the transmission using numerical renormalization group methods. The transmission exhibits signatures of the different Kondo regimes of the effective model, including an unusual Kondo phase with split peaks in the spectral function, as well as a pseudogapped regime exhibiting a quantum critical transition between Kondo and unscreened phases.

Zero-Field Kondo Splitting and Quantum-Critical Transition in Double Quantum Dots

Double quantum dots offer unique possibilities for the study of many-body correlations. A system containing one Kondo dot and one effectively noninteracting dot maps onto a single-impurity Anderson model with a structured (nonconstant) density of states. Numerical renormalization-group calculations show that, while band filtering through the resonant dot splits the Kondo resonance, the singlet ground state is robust. The system can also be continuously tuned to create a pseudogapped density of states and access a quantum-critical point separating Kondo and non-Kondo phases.

Kondo effect in double quantum dots with interdot repulsion

We investigate a symmetrical double quantum dot system serially attached to the leads. The emphasis is on the numerical analysis of finite inter-dot tunneling in the presence of inter-dot repulsive capacitive coupling. The results reveal the competition between extended Kondo phases and local singlet phases in spin and charge degrees of freedom. The corresponding phase diagram is determined quantitatively.

Kondo effect in triple quantum dots

Numerical analysis of the simplest odd-numbered system of coupled quantum dots reveals an interplay between magnetic ordering, charge fluctuations and the tendency of itinerant electrons in the leads to screen magnetic moments. The transition from local-moment to molecular-orbital behavior is visible in the evolution of correlation functions as the inter-dot coupling is increased. Resulting novel Kondo phases are presented in a phase diagram which can be sampled by measuring the zero-bias conductance. We discuss the origin of the even-odd effects by comparing with the double quantum dot.

Phase diagram of the Kondo necklace: a mean-field renormalization group approach

In this paper we investigate the magnetic properties of heavy fermions in the antiferromagnetic and dense Kondo phases in the framework of the Kondo necklace model. We use a mean field renormalization group approach to obtain a temperature versus Kondo coupling $(T-J)$ phase diagram for this model in qualitative agreement with Doniach's diagram, proposed on physical grounds. We further analyze the magnetically disordered phase using a two-sites approach. We calculate the correlation functions and the magnetic susceptibility that allow to identify the crossover between the spin-liquid and the local moment regimes, which occurs at a {\em coherence} temperature.

Spin-glass freezing in Kondo-lattice compounds

It is presented a theory that describes a spin glass phase at finite temperatures in Kondo lattice systems with an additional RKKY interaction represented by long range, random couplings among localized spins like in the Sherrington- Kirkpatrick (SK) spin glass model. The problem is studied within the functional integral formalism where the spin operators are represented by bilinear combinations of fermionic (anticommuting) Grassmann variables. The Kondo and spin glass transitions are both described with the mean field like static ansatz that reproduces good results in the two well known limits. At high temperatures and low values of the Kondo coupling there is a paramagnetic (disordered) phase with vanishing Kondo and spin glass order parameters. By lowering the temperature a second order transition line is found at Tsg to a spin glass phase. For larger values of the Kondo coupling there is a second order transition line at roughly Tk to a Kondo ordered state. For T<Tsg the transition between the Kondo and spin glass phases becomes first order.

On the competition between magnetic order and local Kondo effect in Kondo lattice

We investigate the competition between magnetic order and local Kondo effect in a Kondo lattice model (i.e. the Coqblin-Schrieffer Hamiltonian extended to a lattice) in a mean-field approximation, taking account of the spin-orbit degeneracy N s.o. of each localized f level. This leads to the definition of a N s.o. dependent Kondo temperature. We study the Kondo phase and compare its energy with the energies of magnetic phases, when the number of the conduction band electron per site is near one. We present a phase diagram which shows the occurrence of three phases: Kondo, antiferromagnetic and paramagnetic phases. Our model in the mean-field approximation also shows a somewhat flat Kondo temperature, for large values of N s.o., as a function of the exchange coupling J between conduction and localized f electrons. Finally we show some scaling effects between N s.o. and J and we define a corresponding Kondo temperature.