Kondo Temperature Research Articles

A large-$N$ approach to magnetic impurities in superconductors

Quantum spin impurities coupled to superconductors are under intense investigation for their relevance to fundamental research as well as the prospects to engineer novel quantum phases of matter. Here we develop a large-NN mean-field theory of a strongly coupled spin-\tfrac{1}{2}12 quantum impurity in a conventional ss-wave superconductor. The approach is benchmarked against Wilson’s numerical renormalization group (NRG). While the large-NN method is not applicable in the weak-coupling regime where the Kondo temperature T_KTK is smaller than the superconducting gap \DeltaΔ, it performs very well in the strong coupling regime where T_K \gtrsim \DeltaTK≳Δ, thus allowing us to obtain a reasonably accurate description of experimentally relevant quantities. The latter include the energy of the Yu-Shiba-Rusinov subgap states, their spectral weight, as well as the local density of continuum states. The method provides a reliable analytical tool that complements other perturbative and non-perturbative methods, and can be extended to more complex impurity models for which NRG may not be easily applicable.

Exotic Kondo effect in two one-dimensional spin-1/2 chains coupled to two localized spin-1/2 magnets

We study an exotic Kondo effect in a system consisting of two one-dimensional XX Heisenberg ferromagnetic spin-1/2 chains (denoted by α=u,d for up and down chains) coupled to a quantum dot consisting of two localized spin-1/2 magnets. Using the Jordan–Wigner transformation on the Heisenberg Hamiltonian of the two chains, this system can be expressed in terms of non-interacting spinless fermionic quasiparticles. As a result, the Hamiltonian of the whole system is expressed as an Anderson model for spin-1/2 fermions interacting with a spin-1/2 impurity. Thus, we study the scattering of fermionic quasiparticles (propagating along spin chains) by a pair of localized magnetic impurities. At low temperature, the localized spin-1/2 magnets are shielded by the chain “spins” via the Kondo effect. We calculate the Kondo temperature TK and derive the temperature dependence of the entropy, the specific heat and the “magnetic susceptibility” of the dot for T≫TK. Our results can be generalized to the case of antiferromagnetic XX chains.

Signature of the Kondo effect in superparamagnetic GO incorporated Cobalt substituted Ni/NiO nanoparticles

The study reports on the magnetization, magnetoresistance, and transport properties of superparamagnetic 10% Co-doped Ni/NiO (C10-NN), Graphene Oxide (GO) incorporated 10% Co-doped Ni/NiO (C10-NNG), and 15% Co-doped Ni/NiO (C15-NN) nanoparticles synthesized via a microwave-assisted sol-gel auto-combustion method. All samples show hysteresis in negative Magnetoresistance (M-R) at different temperatures. Resistivity ρ(T) versus temperature plots of samples C10-NN and C15-NN show metallic behavior with applied fields of 0, 1, 5, 8 T, and at 0 T, 1 T respectively. However, the plot of R-T of the C15-NN sample shows a significant difference at 0 T and 1 T. At 0 T for this sample, the metallic behavior is observed for temperature T > TM, with the resistivity falling abruptly at and above TM = 246 K. The resistivity decreases with increasing temperature, exhibiting metallic behavior again above TMM < 276 K. This jump at 276 K, indicating a metal-to metal transition. The Kondo effect is observed for the first time in C10-NNG sample. The upturn of resistivity ρ(T) towards low temperature in the C10-NNG sample is well described by the power series equation and Kondo term. This sample exhibits the upturn resistivity along with a metal–insulator transition above and below the Kondo temperature TK≈ 93.51(2) K at the 0 T, 1 T, 5 T, and 8 T fields.

Artificial superconducting Kondo lattice in a van der Waals heterostructure

Engineering Kondo lattice with tailored functionality is desirable for elucidating the heavy fermion physics. We realize the construction of an artificial Kondo lattice/superconductor heterojunction by growing monolayer VSe2 on bulk 2H-NbSe2 with molecular beam epitaxy. Spectroscopic imaging scanning tunneling microscopy measurements show the emergence of a new charge density wave (CDW) phase with 3×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{3}\ imes$$\\end{document}3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{3}$$\\end{document} periodicity on the monolayer VSe2. Unexpectedly, a pronounced Kondo resonance appears around the Fermi level, and distributes uniformly over the entire film, evidencing the formation of Kondo lattice. Density functional theory calculations suggest the existence of magnetic interstitial V atoms in VSe2/NbSe2, which play a key role in forming the CDW phase along with the Kondo lattice observed in VSe2. The Kondo origin is verified from both the magnetic field and temperature dependences of the resonance peak, yielding a Kondo temperature of ~ 44 K. Moreover, a superconducting proximity gap opens on monolayer VSe2, whose shape deviates from the function of one-band BCS superconductor, but is reproduced by model calculations with heavy electrons participating the pairing condensate. Our work lays the experimental foundation for studying interactions between the heavy fermion liquids and the superconducting condensate.

Protracted Kondo coherence with dilute carrier density in cerium based nickel pnictides

Protracted Kondo coherence with dilute carrier density in cerium based nickel pnictides

Vacancy-Induced Tunable Kondo Effect in Twisted Bilayer Graphene.

In single sheets of graphene, vacancy-induced states have been shown to host an effective spin-1/2 hole that can be Kondo screened at low temperatures. Here, we show how these vacancy-induced impurity states survive in twisted bilayer graphene (TBG), which thus provides a tunable system to probe the critical destruction of the Kondo effect in pseudogap hosts. Abinitio calculations and atomic-scale modeling are used to determine the nature of the vacancy states in the vicinity of the magic angle in TBG, demonstrating that the vacancy can be treated as a quantum impurity. Utilizing this insight, we construct an Anderson impurity model with a TBG host that we solve using the numerical renormalization group combined with the kernel polynomial method. We determine the phase diagram of the model and show how there is a strict dichotomy between vacancies in the AA/BB versus AB/BA tunneling regions. In AB/BA vacancies, the Kondo temperature at the magic angle develops a broad distribution with a tail to vanishing temperatures due to multifractal wave functions at the magic angle. We argue that scanning tunneling microscopy in the vicinity of the vacancy can act as a probe of both the critical single-particle states and the underlying many-body ground state in magic-angle TBG.

Molecule-Supported Magnetic-Atom Dimers on Au(111): Multiple Structures and Kondo Resonances

Molecule-Supported Magnetic-Atom Dimers on Au(111): Multiple Structures and Kondo Resonances

A mesoscopic device for a realization of the topological Kondo effect

Abstract The search for anyons is a field of immense interest owing to its potential application in the field of quantum information. Quantum critical Kondo impurities constitute one possible platform for their realization and topological Kondo effect (TKE) by virtue of remaining critical in the presence of perturbations, seems to be especially promising in this regard. In this paper we discuss practical steps for a realization of TKE with a relatively high Kondo temperature T K . Its central feature is the so-called Majorana-Cooper box (MCB) and we argue that a particular type of iron-based topological superconductor is especially suitable for realization of TKE. Once MCB is available one needs to connect it to external metallic leads to produce TKE. A relatively high value of the Kondo temperature T K is then aided by a large superconducting gap of the iron-based superconductor. We give estimates for T K , for the cases of both isotropic and anisotropic exchange couplings of MCB with the leads.

Many-Body Quantum Interference Route to the Two-Channel Kondo Effect: Inverse Design for Molecular Junctions and Quantum Dot Devices.

Molecular junctions-whether actual single molecules in nanowire break junctions or artificial molecules realized in coupled quantum dot devices-offer unique functionality due to their orbital complexity, strong electron interactions, gate control, and many-body effects from hybridization with the external electronic circuit. Inverse design involves finding candidate structures that perform a desired function optimally. Here we develop an inverse design strategy for generalized quantum impurity models describing molecular junctions, and as an example, use it to demonstrate that many-body quantum interference can be leveraged to realize the two-channel Kondo critical point in simple 4- or 5-site molecular moieties. We show that remarkably high Kondo temperatures can be achieved, meaning that entropy and transport signatures should be experimentally accessible.

Theoretical Studies on Off-Axis Phase Diagrams and Knight Shifts in UTe2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}: Tetra-Critical Point, d-Vector Rotation, and Multiple Phases

Inspired by recent remarkable sets of experiments on UTe2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}: discoveries of the fourth horizontal internal transition line running toward a tetra-critical point (TCP) at H = 15 T, the off-axis high-field phases, and abnormally large Knight shift (KS) drop below Tc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_\ extrm{c}$$\\end{document} for H‖a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H \\parallel a$$\\end{document}-magnetic easy axis, we advance further our theoretical work on the field (H)-temperature (T) phase diagram for H‖b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H \\parallel b$$\\end{document}-magnetic hard axis which contains a positive sloped Hc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_\ extrm{c2}$$\\end{document} departing from TCP. A nonunitary spin-triplet pairing with three components explains these experimental facts simultaneously and consistently by assuming that the underlying normal electron system with a narrow bandwidth characteristic to the Kondo temperature ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim$$\\end{document}30 K unsurprisingly breaks the particle-hole symmetry. This causes a special invariant term in Ginzburg–Landau (GL) free energy functional which couples directly with the 5f magnetic system, giving rise to the Tc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_\ extrm{c}$$\\end{document} splitting and ultimately to the positive sloped Hc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_\ extrm{c2}$$\\end{document} and the horizontal internal transition line connected to TCP. The large KS drop can be understood in terms of this GL invariance whose coefficient is negative and leads to a diamagnetic response where the Cooper pair spin is antiparallel to the applied field direction. The present scenario also accounts for the observed d-vector rotation phenomena and off-axis phase diagrams with extremely high Hc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_\ extrm{c2}$$\\end{document}≳\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gtrsim$$\\end{document}70 T found at angles in between the b- and c-axes and between the bc-plane and a-axis, making UTe2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} a fertile playground for a possible topological superconductor.

Probing magnetic and triplet correlations in spin-split superconductors with magnetic impurities

A superconductor (SC) in proximity to a ferromagnetic insulator (FMI) is predicted to exhibit mixed singlet and triplet correlations. The magnetic proximity effect of FMI spin splits the energy of Bogoliubov excitations and leads to a spin polarization at the surface for superconducting films that are thinner than the superconducting coherence length. In this work, we study manifestations of these phenomena in the properties of a magnetic impurity coupled via Kondo coupling to this FMI/SC system. Using the numerical renormalization group (NRG) method, we compute the properties of the ground state and low-lying excited states of a model that incorporates the Kondo interaction and a Ruderman-Kittel-Kasuya-Yosida (RKKY)-like interaction with the surface spin polarization. Our main finding is an energy splitting of the lowest even fermion-parity states caused by the proximity to the FMI. As the Kondo coupling increases, the splitting grows and saturates to a universal value equal to twice the exchange field of the FMI. We introduce a two-site model that can be solved analytically and provides a qualitative understanding of this and other NRG results. In addition, using perturbation theory, we demonstrate that the mechanism behind the splitting involves the RKKY field and the triplet correlations of the spin-split superconductor. A scaling analysis combined with NRG shows that the splitting can be written as a single-parameter scaling function of the ratio of the Kondo temperature and the superconducting gap, which is also numerically obtained. Published by the American Physical Society 2024

Coexistence of near- EF Flat Band and Van Hove Singularity in a Two-Phase Superconductor

Quantum many-body systems, particularly, the ones with large near-EF density states, are well known for exhibiting rich phase diagrams as a result of enhanced electron correlations. The recently discovered locally noncentrosymmetric heavy fermion superconductor CeRh2As2 has stimulated extensive attention due to its unusual H−T phase diagram consisting of two-phase superconductivity, antiferromagnetic order, and possible quadrupole-density wave orders. However, the critical near-EF electronic structure remains experimentally elusive. Here, we provide this key information by combining soft-x-ray and vacuum ultraviolet (VUV) angle-resolved-photoemission-spectroscopy measurements and atom-resolved density-functional-theory (DFT)+U calculations. With bulk-sensitive soft x ray, we reveal quasi-2D hole and electron pockets near the EF. On the other hand, under VUV light, the Ce flat bands are resolved with the c−f hybridization persisting up to well above the Kondo temperature. Most importantly, we observe a symmetry-protected fourfold Van Hove singularity (VHS) coexisting with the Ce 4f5/21 flat bands at the X point, which, to the best of our knowledge, has never been reported before. Such a rare coexistence is expected to lead to a large density of states at the zone edge, a large upper critical field of the odd-parity phase, as well as spin and/or charge instabilities with a vector of (1/2, 1/2, 0). Uniquely, it will also result in a new type of f-VHS hybridization that alters the order and fine electronic structure of the VHS and flat bands. Our findings provide not only key insights into the nature of multiple phases in CeRh2As2 but also open up new prospects for exploring the novelties of many-body systems with f-VHS hybridization. Published by the American Physical Society 2024

Kondo effects in variable-valence manganese-substituted thulium selenide

Kondo effects in variable-valence manganese-substituted thulium selenide

Concurrence of directional Kondo transport and incommensurate magnetic order in the layered material AgCrSe2

In this work, we report on the concurrent emergence of the directional Kondo behavior and incommensurate magnetic ordering in a layered material. We employ temperature- and magnetic field-dependent resistivity measurements, susceptibility measurements, and high resolution wavelength X-ray diffraction spectroscopy to study the electronic properties of AgCrSe2. Impurity Kondo behavior with a characteristic temperature of TK = 32 K is identified through quantitative analysis of the in-plane resistivity, substantiated by magneto-transport measurements. The excellent agreement between our experimental data and the Schlottmann’s scaling theory allows us to determine the impurity spin as S = 3/2. Furthermore, we discuss the origin of the Kondo behavior and its relation to the material’s antiferromagnetic transition. Our study uncovers a rare phenomenon—the equivalence of the Néel temperature and the Kondo temperature—paving the way for further investigations into the intricate interplay between impurity physics and magnetic phenomena in quantum materials, with potential applications in advanced electronic and magnetic devices.

An impurity model in a random magnetic field

An impurity model in a random magnetic field

Thermopower of the CeNi4Cu compound with unstable valence of Ce

Thermopower of the CeNi4Cu compound with unstable valence of Ce

Atomic-scale magnetic doping of monolayer stanene by revealing Kondo effect from self-assembled Fe spin entities

Atomic-scale spin entity in a two-dimensional topological insulator lays the foundation to manufacture magnetic topological materials with single atomic thickness. Here, we have successfully fabricated Fe monomer, dimer and trimer doped in the monolayer stanene/Cu(111) through a low-temperature growth and systematically investigated Kondo effect by combining scanning tunneling microscopy/spectroscopy (STM/STS) with density functional theory (DFT) and numerical renormalization group (NRG) method. Given high spatial and energy resolution, tunneling conductance (dI/dU) spectra have resolved zero-bias Kondo resonance and resultant magnetic-field-dependent Zeeman splitting, yielding an effective spin Seff = 3/2 with an easy-plane magnetic anisotropy on the self-assembled Fe atomic dopants. Reduced Kondo temperature along with attenuated Kondo intensity from Fe monomer to trimer have been further identified as a manifestation of Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between Sn-separated Fe atoms. Such magnetic Fe atom assembly in turn constitutes important cornerstones for tailoring topological band structures and developing magnetic phase transition in the single-atom-layer stanene.

The Kondo scaling for spin thermocurrent in strongly correlated electron systems

One of the most important feature in the Kondo physics is the universal scaling behavior. In this study, we analyze the transport behavior of the spin thermocurrent driven by a small temperature bias and under a weak magnetic field. We conclude that the spin thermocurrent exhibits a universal scaling behavior, similar to the spin susceptibility. The validity of our conclusion is also checked by using the numerically exact hierarchical equations of motion approach. From our fitting result of the scaling function, it is found that the Kondo temperature can be determined by the maximum of the spin thermocurrent at T/TK=0.383 .

Non-perturbative intertwining between spin and charge correlations: A ``smoking gun'' single-boson-exchange result

We study the microscopic mechanism controlling the interplay between local charge and local spin fluctuations in correlated electron systems via a thorough investigation of the generalized on-site charge susceptibility of several fundamental many-electron models, such as the Hubbard atom, the Anderson impurity model, and the Hubbard model. By decomposing the numerically determined generalized susceptibility in terms of physically transparent single-boson exchange processes, we unveil the microscopic mechanisms responsible for the breakdown of the self-consistent many-electron perturbation expansion. In particular, we unambiguously identify the origin of the significant suppression of its diagonal entries in (Matsubara) frequency space and the slight increase of the off-diagonal ones which cause the breakdown. The suppression effect on the diagonal elements originates directly from the electronic scattering on local magnetic moments, reflecting their increasingly longer lifetime as well as their enhanced effective coupling with the electrons. Instead, the slight and diffuse enhancement of the off-diagonal terms can be mostly ascribed to multiboson scattering processes. The strong intertwining between spin and charge sectors is partly weakened at the Kondo temperature due to a progressive reduction of the effective spin-fermion coupling of local magnetic fluctuations in the low frequency regime. Our analysis, thus, clarifies the precise mechanism through which the physical information is transferred between different scattering channels of interacting electron problems and highlights the pivotal role played by such an intertwining in the physics of correlated electrons beyond the perturbative regime.

The study of electronic structure and magnetic properties of ferromagnetic Kondo-lattice CePd2P2 from the first-principles

The study of electronic structure and magnetic properties of ferromagnetic Kondo-lattice CePd2P2 from the first-principles