Kondo Coupling Research Articles

Uniaxial stress tuning of geometrical frustration in a Kondo lattice

Hexagonal CeRhSn with paramagnetic $4f$ moments on a distorted Kagome lattice displays zero-field quantum critical behavior related to geometrical frustration. We report high-resolution thermal expansion and magnetostriction measurements under multiextreme conditions such as uniaxial stress up to 200 MPa, temperatures down to 0.1 K and magnetic fields up to 10 T. Under uniaxial stress along the $a$-direction, quantum criticality disappears and a complex magnetic phase diagram arises with a sequence of phases below 1.2 K and fields between 0 and 3 T ($\parallel a$). Since the Kondo coupling increases with stress, which alone would stabilize paramagnetic behavior in CeRhSn, the observed order arises from the release of geometrical frustration by in-plane stress.

Enhancing Kondo coupling in alkaline-earth-metal atomic gases with confinement-induced resonances in mixed dimensions

The Kondo effect describes the spin-exchanging interaction between localized impurity and the itinerant fermions. The ultracold alkaline-earth atomic gas provides a natural platform for quantum simulation of the Kondo model, utilizing its long-lived clock state and the nuclear-spin exchanging interaction between the clock state and the ground state. One of the key issue now is whether the Kondo temperature can be high enough to be reached in current experiment, for which we have proposed using a transverse confinement to confine atoms into a one-dimensional tube and to utilize the confinement-induced resonance to enhance the Kondo coupling. In this work, we further consider the $1+0$ dimensional scattering problem when the clock state is further confined by an axial harmonic confinement. We show that this axial confinement for the clock state atoms not only plays a role for localizing them, but also can act as an additional control knob to reach the confinement-induced resonance. We show that by combining both the transverse and the axial confinements, the confinement-induced resonance can be reached in the practical conditions and the Kondo effect can be attainable in this system.

Topological bootstrap: Fractionalization from Kondo coupling.

Topologically ordered phases of matter can host fractionalized excitations known as "anyons," which obey neither Bose nor Fermi statistics. Despite forming the basis for topological quantum computation, experimental access to these exotic phases has been very limited. We present a new route toward realizing fractionalized topological phases by literally building on unfractionalized phases, which are much more easily realized experimentally. Our approach involves a Kondo lattice model in which a gapped electronic system of noninteracting fermions is coupled to local moments via the exchange interaction. Using general entanglement-based arguments and explicit lattice models, we show that gapped spin liquids can be induced in the spin system, and we demonstrate the power of this "topological bootstrap" by realizing chiral and Z2 spin liquids. This technique enables the realization of many long sought-after fractionalized phases of matter.

Hybridization oscillation in the one-dimensional Kondo-Heisenberg model with Kondo holes

We use the density matrix renormalization group method to study the properties of the one-dimensional Kondo-Heisenberg model doped with Kondo holes. We find that the perturbation of the Kondo holes to the local hybridization exhibits spatial oscillation pattern and its amplitude decays exponentially with distance away from the Kondo hole sites. The hybridization oscillation is correlated with both the charge density oscillation of the conduction electrons and the oscillation in the correlation function of the Heisenberg spins. In particular, we find that the oscillation wavelength for intermediate Kondo couplings is given by the Fermi wavevector of the large Fermi surface even before it is formed. This suggests that heavy electrons responsible for the oscillation are already present in this regime and start to accumulate around the to-be-formed large Fermi surface in the Brillouin zone.

Field-Induced Transitions in Anisotropic Kondo Lattice — Application to CeT2Al10 —

The magnetic properties of an anisotropic Kondo lattice are investigated under a magnetic field using dynamical mean field theory and the continuous-time quantum Monte Carlo method. The magnetic phase diagram is determined from the temperature dependence of both uniform and staggered magnetizations in magnetic fields. We find a spin-flop transition inside the antiferromagnetic (AF) phase, whose transition field increases with increasing Kondo coupling while the AF transition temperature decreases. These results cannot be described by a simple spin Hamiltonian and are consistent with the experimental results of the field-induced transition observed in CeT2Al10 (T = Ru, Os). The anisotropic susceptibilities of CeT2Al10 are reproduced in the whole temperature range by incorporating the effects of the crystalline electric field (CEF) in the anisotropic Kondo lattice. We also propose a possible explanation for the difference in anisotropies between the magnetic susceptibility and AF moments observed in experim...

Chiral helimagnetic state in a Kondo lattice model with the Dzyaloshinskii–Moriya interaction

Monoaxial chiral magnets can form a noncollinear twisted spin structure called the chiral helimagnetic state. We study magnetic properties of such a chiral helimagnetic state, with emphasis on the effect of itinerant electrons. Modeling a monoaxial chiral helimagnet by a one-dimensional Kondo lattice model with the Dzyaloshinskii–Moriya interaction, we perform a variational calculation to elucidate the stable spin configuration in the ground state. We obtain a chiral helimagnetic state as a candidate for the ground state, whose helical pitch is modulated by the model parameters: the Kondo coupling, the Dzyaloshinski–Moriya interaction, and electron filling.

Electronic orders and phase transitions in a honeycomb Kondo lattice system

We study the electronic orders in a honeycomb-Kondo lattice. For the ground state, we use variational quantum Monte Carlo to find the transition from antiferromagnetic insulator to Kondo insulator is continuous, in contrast to the discontinuous transition in mean-field theory. Moreover, the hybridization parameter between the conduction electron and the Kondo spin is nonzero even within the antiferromagnetic phase. At finite temperatures, we resort to dynamical mean-field theory, which not only captures local quantum fluctuations but also accesses the thermodynamic limit directly. There are three phases, namely, antiferromagnetic insulator, Kondo insulator, and paramagnetic phase. The transition from antiferromagnetic phase to paramagnetic phase is likely discontinuous, while that from antiferromagnetic phase to Kondo insulator phase remains to be continuous at finite temperatures. There is a crossover from the paramagnetic phase, where spin excitations are gapless, to the Kondo insulator phase, where spin excitations are gapped. Our results indicate a significant effect of fluctuations beyond mean-field theory in the honeycomb-Kondo lattice. Since the transition from the antiferromagnetic phase to the Kondo insulating phase occurs at a sizable Kondo coupling, where the Kondo lattice model is inequivalent to the Anderson lattice model, our results are complementary to that for a honeycomb-Anderson lattice.

Theory of quantum oscillations of magnetization in Kondo insulators

The Kondo lattice model of spin-1/2 local moments coupled to the conduction electrons at half-filling is studied for its orbital response to magnetic field on bipartite lattices. Through an effective charge dynamics, in a canonical representation of electrons that appropriately describes the Kondo insulating ground state, the magnetization is found to show de Haas-van Alphen oscillations from intermediate to weak Kondo coupling. These oscillations are ascribed to Lifshitz-like inversion of a dispersion of the gapped quasiparticles, whose chemical potential surface is measured by the oscillation frequency. Such oscillations are also predicted to occur in spin-density wave insulators.

Holographic Kondo and Fano resonances

We use holography to study a $(1+1)$-dimensional Conformal Field Theory (CFT) coupled to an impurity. The CFT is an $SU(N)$ gauge theory at large $N$, with strong gauge interactions. The impurity is an $SU(N)$ spin. We trigger an impurity Renormalization Group (RG) flow via a Kondo coupling. The Kondo effect occurs only below the critical temperature of a large-$N$ mean-field transition. We show that at all temperatures $T$, impurity spectral functions exhibit a Fano resonance, which in the low-$T$ phase is a large-$N$ manifestation of the Kondo resonance. We thus provide an example in which the Kondo resonance survives strong correlations, and uncover a novel mechanism for generating Fano resonances, via RG flows between $(0 + 1)$-dimensional fixed points

Single-molecule quantum dot as a Kondo simulator

Structural flexibility of molecule-based systems is key to realizing the novel functionalities. Tuning the structure in the atomic scale enables us to manipulate the quantum state in the molecule-based system. Here we present the reversible Hamiltonian manipulation in a single-molecule quantum dot consisting of an iron phthalocyanine molecule attached to an Au electrode and a scanning tunnelling microscope tip. We precisely controlled the position of Fe2+ ion in the molecular cage by using the tip, and tuned the Kondo coupling between the molecular spins and the Au electrode. Then, we realized the crossover between the strong-coupling Kondo regime and the weak-coupling regime governed by spin–orbit interaction in the molecule. The results open an avenue to simulate low-energy quantum many-body physics and quantum phase transition through the molecular flexibility.

Kondo Insulator to Semimetal Transformation Tuned by Spin-Orbit Coupling.

Recent theoretical studies of topologically nontrivial electronic states in Kondo insulators have pointed to the importance of spin-orbit coupling (SOC) for stabilizing these states. However, systematic experimental studies that tune the SOC parameter λ_{SOC} in Kondo insulators remain elusive. The main reason is that variations of (chemical) pressure or doping strongly influence the Kondo coupling J_{K} and the chemical potential μ-both essential parameters determining the ground state of the material-and thus possible λ_{SOC} tuning effects have remained unnoticed. Here, we present the successful growth of the substitution series Ce_{3}Bi_{4}(Pt_{1-x}Pd_{x})_{3} (0≤x≤1) of the archetypal (noncentrosymmetric) Kondo insulator Ce_{3}Bi_{4}Pt_{3}. The Pt-Pd substitution is isostructural, isoelectronic, and isosize, and it therefore is likely to leave J_{K} and μ essentially unchanged. By contrast, the large mass difference between the 5d element Pt and the 4d element Pd leads to a large difference in λ_{SOC}, which thus is the dominating tuning parameter in the series. Surprisingly, with increasing x (decreasing λ_{SOC}), we observe a Kondo insulator to semimetal transition, demonstrating an unprecedented drastic influence of the SOC. The fully substituted end compound Ce_{3}Bi_{4}Pd_{3} shows thermodynamic signatures of a recently predicted Weyl-Kondo semimetal.

Nonlinear entangled quantum dynamics in many-body systems with strong electron correlation

A quantum impurity system out of equilibrium comprises two metallic reservoirs with different chemical potentials and one mediating spin impurity between them. We study the highly nonlinear tunneling conductance of this system, and clarify that three coherent peaks, one zero-bias peak and two side peaks, naturally appear in the tunneling conductance. We use the Liouvillian approach, in which a complete set of basis operators is available, and construct a Liouville matrix to obtain Green’s function at the mediating site. We show that the two coherent side peaks are the outcome of steady-state nonequilibrium combined with strong electron correlation at the mediating site. Tunneling in the quantum impurity system out of equilibrium is performed by an entangled state which is a linear combination of two Kondo singlets formed by the spin at the mediating site and the coherent spins in each reservoir. The fluctuation by incoherent spins is also included. The spectral weights and positions of the three coherent peaks are analytically discussed via atomic limit analysis. Our theoretical results well fit experimental data obtained for quantum point contacts with symmetric and asymmetric Kondo couplings.

Quantum quenches in a holographic Kondo model

We study non-equilibrium dynamics and quantum quenches in a recent gauge/gravity duality model for a strongly coupled system interacting with a magnetic impurity with SU(N ) spin. At large N , it is convenient to write the impurity spin as a bilinear in Abrikosov fermions. The model describes an RG flow triggered by the marginally relevant Kondo operator. There is a phase transition at a critical temperature, below which an operator condenses which involves both an electron and an Abrikosov fermion field. This corresponds to a holographic superconductor in AdS2 and models the impurity screening. We quench the Kondo coupling either by a Gaussian pulse or by a hyperbolic tangent, the latter taking the system from the condensed to the uncondensed phase or vice-versa. We study the time dependence of the condensate induced by this quench. The timescale for equilibration is generically given by the leading quasinormal mode of the dual gravity model. This mode also governs the formation of the screening cloud, which is obtained as the decrease of impurity degrees of freedom with time. In the condensed phase, the leading quasinormal mode is imaginary and the relaxation of the condensate is over-damped. For quenches whose final state is close to the critical point of the large N phase transition, we study the critical slowing down and obtain the combination of critical exponents zν = 1. When the final state is exactly at the phase transition, we find that the exponential ringing of the quasinormal modes is replaced by a power-law behaviour of the form ∼ t−a sin(b log t). This indicates the emergence of a discrete scale invariance.

Switchable Multiple Spin States in the Kondo description of Doped Molecular Magnets

We show that introducing electrons in magnetic clusters and molecular magnets lead to rich phase diagrams with a variety of low-spin and high-spin states allowing for multiple switchability. The analysis is carried out for a quantum spin-fermion model using the exact diagonalization, and the cluster mean-field approach. The model is relevant for a number of molecular magnets with triangular motifs consisting of transition metal ions such as Cr, Cu and V. Re-entrant spin-state behavior and chirality on-off transitions exist over a wide parameter regime. A subtle competition among geometrical frustration effects, electron itinerancy, and Kondo coupling at the molecular level is highlighted. Our results demonstrate that electron doping provides a viable mean to tame the magnetic properties of molecular magnets towards potential technological applications.

Doping Effects on the Electronic Structure of an Anisotropic Kondo Semiconductor CeOs2Al10: An Optical Study with Re and Ir Substitution

An anisotropic Kondo semiconductor CeOs$_2$Al$_{10}$ exhibits an unusual antiferromagnetic order at rather high transition temperature $T_0$ of 28.5 K. Two possible origins of the magnetic order have been proposed so far, one is the Kondo coupling of the hybridization between the conduction ($c$) and the $4f$ states and the other is the charge-density wave/charge ordering along the orthorhombic $b$ axis. To clarify the origin of the magnetic order, we have investigated the electronic structure of hole- and electron-doped CeOs$_2$Al$_{10}$ [Ce(Os$_{1-y}$Re$_y$)$_2$Al$_{10}$ and Ce(Os$_{1-x}$Ir$_x$)$_2$Al$_{10}$, respectively] by using optical conductivity spectra along the $b$ axis. The intensity of the $c$-$f$ hybridization gap at $\hbar\omega\sim50$ meV continuously decreases from $y=0.10$ to $x=0.12$ via $x=y=0$. The intensity of the charge excitation observed at $\hbar\omega\sim20$ meV has the maximum at $x=y=0$ as similar with the doping dependence of $T_{\rm 0}$. The fact that the charge excitation is strongly related to the magnetic order strengthens the possibility of the charge density wave/charge ordering as the origin of the magnetic order.

Phase diagram of the Kondo-Heisenberg model on honeycomb lattice with geometrical frustration

We calculated the phase diagram of the Kondo-Heisenberg model on a two-dimensional honeycomb lattice with both nearest-neighbor and next-nearest-neighbor antiferromagnetic spin exchanges, to investigate the interplay between RKKY and Kondo interactions in the presence of magnetic frustration. Within a mean-field decoupling technology in slave-fermion representation, we derived the zero-temperature phase diagram as a function of Kondo coupling Jk and frustration strength Q. The geometrical frustration can destroy the magnetic order, driving the original antiferromagnetic (AF) phase to non-magnetic valence bond solids (VBS). In addition, we found two distinct VBS. As Jk is increased, a phase transition from AF to Kondo paramagnetic (KP) phase occurs, without the intermediate phase coexisting AF order with Kondo screening found in square lattice systems. In the KP phase, the enhancement of frustration weakens the Kondo screening effect, resulting in a phase transition from KP to VBS. We also found a process to recover the AF order from VBS by increasing Jk in a wide range of frustration strength. Our work may provide predictions for future experimental observation of new processes of quantum phase transitions in frustrated heavy-fermion compounds.

Order by disorder decision making via Berry flux

Order by disorder is a decision making process for frustrated systems but often leads to simple answers. We study order by disorder in the kagome Kondo model known for its complexity seeking rich decision making capabilities. At half filling and large Kondo coupling to hopping ratio $J_K/t$, the full manifold of 120$^o$ kagome ground states are degenerate at second order in $t/J_K$. We show this degeneracy lifts at sixth order when a fermion can hop around a hexagon and feel the Berry flux induced by a given spin texture. Using Monte-Carlo we then seek the ground state of this sixth order Hamiltonian and find in a 4x4 unit cell system that a co-planar 2x4 unit cell order is selected over the $\sqrt{3}\times\sqrt{3}$, $q=0$ and cuboc1 states, a result that survives even in the thermodynamic limit. This state is selected for its SU(2) flux properties induced by the spin texture and is analogous to the integer quantum Hall effect. Given the existence of numerous quantum Hall plateaus in other systems, the existence of this 2x4 unit cell state suggests that complex decision making is possible on the manifold of 120$^o$ states and achievable in different kagome-Kondo models.

Topological quantum phase transition in strongly correlated Kondo insulators in 1D

We investigate, by means of a field-theory analysis combined with the density-matrix renormalization group (DMRG) method, a theoretical model for a strongly correlated quantum system in one dimension realizing a topologically-ordered Haldane phase ground state. The model consists of a spin-1/2 Heisenberg chain coupled to a tight-binding chain via two competing Kondo exchange couplings of different type: a ``$s$-wave'' Kondo coupling ($J^s_{K}$), and a less common ``$p$-wave'' ($J^p_{K}$) Kondo coupling. While the first coupling is the standard Kondo interaction studied in many condensed-matter systems, the latter has been recently introduced by Alexandrov and Coleman [Phys. Rev. B 90, 115147 (2014)] as a possible mechanism leading to a topological Kondo-insulating ground state in one dimension. As a result of this competition, a topological quantum phase transition (TQPT) occurs in the system for a critical value of the ratio $J^s_{K}/J^p_{K}$, separating a (Haldane-type) topological phase from a topologically trivial ground state where the system can be essentially described as a product of local singlets. We study and characterize the TQPT by means of the magnetization profile, the entanglement entropy and the full entanglement spectrum of the ground state. Our results might be relevant to understand how topologically-ordered phases of fermions emerge in strongly interacting quantum systems. Received: 1 July 2016, Accepted: 30 August 2016; Edited by: K. Hallberg; Reviewed by: D. C. Cabra, Instituto de Física La Plata, La Plata, Argentina; DOI: http://dx.doi.org/10.4279/PIP.080005Cite as: F T Lisandrini, A M Lobos, A O Dobry, C J Gazza, Papers in Physics 8, 080005 (2016)This paper, by F T Lisandrini, A M Lobos, A O Dobry, C J Gazza, is licensed under the Creative Commons Attribution License 3.0.

Kondo effect in a quantum wire with spin-orbit coupling

The influence of spin-orbit interactions on the Kondo effect has been under debate recently. Studies conducted recently on a system composed by an Anderson impurity on a 2DEG with Rashba spin-orbit have been shown that it can enhance or suppress the Kondo temperature ($T_{\rm K}$), depending on the relative energy level position of the impurity with respect to the particle-hole symmetric point. Here we investigate a system composed by a single Anderson impurity side-coupled to a quantum wire with spin-orbit coupling (SOC). We derive an effective Hamiltonian in which the Kondo coupling is modified by the SOC. In addition, the Hamiltonian contains two other scattering terms, the so called Dzaloshinskyi-Moriya interaction, know to appear in these systems, and a new one describing processes similar to the Elliott-Yafet scattering mechanisms. By performing a renormalization group analysis on the effective Hamiltonian, we find that the correction on the Kondo coupling due to the SOC favors and enhancement of the Kondo temperature even in the particle-hole symmetric point of the Anderson model, agreeing with the NRG results. Moreover, away from the particle-hole symmetric point, $T_{\rm K}$ always increases with the SOC, accordingly with the previous renormalization group analysis.

Signatures of Majorana Kramers pairs in superconductor-Luttinger liquid and superconductor-quantum dot-normal lead junctions

Time-reversal invariant topological superconductors are characterized by the presence of Majorana Kramers pairs localized at defects. One of the transport signatures of Majorana Kramers pairs is the quantized differential conductance of $4e^2/h$ when such a one-dimensional superconductor is coupled to a normal-metal lead. The resonant Andreev reflection, responsible for this phenomenon, can be understood as the boundary condition change for lead electrons at low energies. In this paper, we study the stability of the Andreev reflection fixed point with respect to electron-electron interactions in the Luttinger liquid. We first calculate the phase diagram for the Luttinger liquid-Majorana Kramers pair junction and show that its low-energy properties are determined by Andreev reflection scattering processes in the spin-triplet channel, i.e. the corresponding Andreev boundary conditions are similar to that in a spin-triplet superconductor - normal lead junction. We also study here a quantum dot coupled to a normal lead and a Majorana Kramers pair and investigate the effect of local repulsive interactions leading to an interplay between Kondo and Majorana correlations. Using a combination of renormalization group analysis and slave-boson mean-field theory, we show that the system flows to a new fixed point which is controlled by the Majorana interaction rather than the Kondo coupling. This Majorana fixed point is characterized by correlations between the localized spin and the fermion parity of each spin sector of the topological superconductor. We investigate the stability of the Majorana phase with respect to Gaussian fluctuations.