DOCSLIB.ORG

Kondo Effect in Quantum Dots

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Kondo Effect in Quantum Dots Kondo Effect in Quantum Dots Seminar: Nanoscopic Systems 29. 7. 2005 Gesa von Bornstaedt Gesa von Bornstaedt Kondo Effect in Quantum Dots Outline 1. What is the Kondo effect? 2. Calculation of the Kondo effect for a single magnetic impurity 3. ”Poor Man’s Scaling” - A renormalization group approach 4. Investigation of the Kondo effect in quantum dots 5. Conclusion Gesa von Bornstaedt Kondo Effect in Quantum Dots 1. What is the Kondo effect? • Resistivity is dominated by phonon scattering for T 0 • In most metals the resistivity decreases monotonically for T → 0 • But: resistance minimum in some metals for T → 0 • Kondo effect: Resonant spin flip scattering at local magnetic impurities • Influences transport properties Figure 1: Minimum in the resistivity of Au (de Haas, de Boer and van den Berg, 1934) Gesa von Bornstaedt Kondo Effect in Quantum Dots 2. Calculation for a single local magnetic impurity Hamiltonian Kondo’s assumption: a local magnetic moment associated with a spin S which is coupled via an exchange interaction with the conduction band electron. † 1 + − − + H = ∑kckσ ckσ + J(ω) S s + S s + Jz(ω)Szsz kσ 2 † 1 + † − † † † = ∑kckσ ckσ + ∑ J(ω) S ck↓ck0↑ + S ck↑ck0↓ + Jz(ω)Sz ck↑ck0↑ − ck↓ck0↓ kσ 2 k,k0 S = local impurity spin s = conduction electron spin Figure 2: Spin flip scattering of a localized impurity moment by a conduction electron Gesa von Bornstaedt Kondo Effect in Quantum Dots Perturbative approach • T > 0 =⇒ expectation values can’t be taken with respect to the ground state • Appropriate: Matsubara Method Starting point: H = H0 + V(t) with 1 V(t) = J (ω) S+s− + S−s+ + J (ω)S s 2 1 z z z Generalized Wick Theorem for n particle Green’s function: (0) hTτ (UVW...XYZ)i = { fully contracted terms} Problem: • Wick’s theorem only valid for operators, whose commutator is a c-number • Not the case for the impurity spin, obeying the standard commutation relations of angular momentum Gesa von Bornstaedt Kondo Effect in Quantum Dots Pseudo fermion method ± Representation of S , Sz through canonical field operators ~ †~ In formulas: S = ∑σσ0 fσ Sσσ0 fσ0 for example: 1 1 † † 1 Sz| ↑i = 2 | ↑i corresponds to 2 f↑ f↑ − f↓ f↓ | ↑i = 2 | ↑i Problem: artificially enlarged Fock space =⇒ project out the unphysical part with the following constraint † Q = ∑ fσ fσ = 1 σ All physical relevant quantities depend on the partition function : h −β(H+λ(Q−1))i Zc = lim tr Q e λ→ ∞ Gesa von Bornstaedt Kondo Effect in Quantum Dots Evaluation of Wick’s theorem Two particle interaction using the pseudo fermions: 1 † † V(t) = ∑ v(kl; nm) fk fl cmcn k, l, m, n ∈ {↑, ↓} klmn 2 Two particle correlation function looks like: D † † † † † † E ∝ Tτ Vb f f cm cn Vb f f cm cn f f cmcn k1 l1 1 1 k2 l2 2 2 k l Remember: • any contraction between a pseudo and a fermion operator = 0 † • contraction( fk fl ) ∝ δkl =⇒ just two fully contracted terms survive, corresponding to two diagrams Gesa von Bornstaedt Kondo Effect in Quantum Dots Diagrams The scattering matrix is defined as the sum of diagram (I) and (II) • Solid lines: bare electron operators • Dashed lines: impurity pseudo fermion operators Gesa von Bornstaedt Kondo Effect in Quantum Dots Evaluation of the diagrams Vertex part of the diagrams: 1 1 (I) = − ∑ J hτ|S+|σ ihσ|s−|σ i + hτ|S−|σ ihσ|s+|σ i + 2J hτ|Sz|σ ihσ|sz|σ i β 4 1 2 1 2 1 z 2 1 σ,τ,ωn,k + − − + z z · J1 hσ4|S |τihσ3|s |σi + hσ4|S |τihσ3|s |σi + 2Jzhσ4|S |τihσ3|s |σi ·Gkσ (iωn)gτ (iω − iωn) 1 1 (II) = − ∑ J hτ|S+|σ ihσ |s−|σi + hτ|S−|σ ihσ |s+|σi + 2J hτ|Sz|σ ihσ |sz|σi β 4 1 2 3 2 3 z 2 3 σ,τ,ωn,k + − − + z z · J1 hσ4|S |τihσ|s |σ1i + hσ4|S |τihσ|s |σ1i + 2Jzhσ4|S |τihσ|s |σ1i ·Gkσ (iωn)gτ (−iω + iωn) where the free Matsubara Green’s functions for electrons and pseudo fermions are : 1 1 G ν(iωn) = gτ (iνn) = k iωn−k iνn−λ Gesa von Bornstaedt Kondo Effect in Quantum Dots Simplifications • Sum over Matsubara Frequencies Fermionic Matsubara Frequencies correspond to singularities of Fermi distribution =⇒ The sum can be replaced by a contour integral: 1 1 1 I dz 1 1 f (−λ) − f ( ) (I) ∝ − ∑ · = f (z) · = k β ω − ω − ω − λ π − ω − − λ ω − − λ ωn i n k i i n 2 i z k i z i k 1 ∑ H dz Figure 3: β n F(iωn) = − 2πi F(z) f (z) Gesa von Bornstaedt Kondo Effect in Quantum Dots Further simplifications • Pseudo fermion energy is gauged to get rid of the λ in the denominator Constraint Q allows a U(1) gauge symmetry for this energy f 0 = eiα f ⇒ f 0† f 0 = f † f iω → ω + λ iω → ω − λ • Project out unphysical part by λ → , using limλ→ f (−λ) = 1 ∞ ∞ 1 − f ( ) (I) −→ ∑ k ω − k k f ( ) (II) −→ ∑ k ω − k k • Evaluation of the spin sum using – Completeness relations – Spin algebra Gesa von Bornstaedt Kondo Effect in Quantum Dots Second order term of the scattering matrix 1 1 − 2 f ( ) 3 1 t(2) = J2hσ |~S|σ ihσ |~s|σ i ∑ k + J2hσ |σ ihσ |σ i ∑ 4 2 3 1 ω − 4 2 3 1 ω − 2 k k 16 k k • Evaluation of the k-sum (assuming a constant density N(0) for the conduction electrons): 1 − 2 f ( ) Z D tanh(/2T) − ∑ k = N(0) d ω − − ω k k −D D =∼ 2N(0) ln max(|ω| , T) For electrons near the Fermi surface (ω = 0) and small temperatures T the result is: D t(2) = N(0)J2hσ |~S|σ ihσ |~s|σ iln 4 2 3 1 T Gesa von Bornstaedt Kondo Effect in Quantum Dots Scattering matrix and resistivity • The resistivity is connected to the scattering matrix via: ρ(T) ∝ |t|2 Scattering matrix: D t = J ~S~s 1 + N(0) J ln T D =⇒ ρ(T) ∝ 1 + 2N(0) J ln T • Problem: This term for the resistivity is divergent for T → 0 • Perturbation theory breaks down, when the 2nd order term becomes ' 1st order term • This limit defines the so called Kondo temperature: − 1 2N(0)J Tk = De Gesa von Bornstaedt Kondo Effect in Quantum Dots 3. ”Poor Man’s Scaling” - A renormalization group approach • Anderson’s idea: Use scaling to continue the perturbative approach to small temperatures (T < TK) • Idea: reduce the bandwidth D of the conduction band • Constraint: The underlying physical quantity, the scattering matrix t, stays invariant • =⇒ Coupling constants (J1, Jz) change with bandwidth D t = V + VPdDG0t + V(1 − PdD)G0t 0 0 0 ⇒ t = V + V (1 − PdD)G0t with V = V + PdDG0V = V + dV Gesa von Bornstaedt Kondo Effect in Quantum Dots Renormalization Evaluating the integral for the reduced bandwidth: Z tanh(/2T) Z D tanh(/2T) Z D−dD tanh(/2T) d = d − d = 2d(lnD) int − ω −D − ω −(D−dD) − ω Change of the potential term 1 dV = −2N(0) J J S+s− + S−s+ + J2 Szsz d(lnD) 2 z 1 1 Renormalization Group Equations: dJ dJ z = −2N(0)J2 1 = −2N(0)J J d lnD 1 d lnD z 1 In the physical state (J1 = Jz) this leads to one analytically soluble differential equation: 1 J(D) = 1 + 2N(0)ln( D ) J0 D0 → Divergent for T = TK Gesa von Bornstaedt Kondo Effect in Quantum Dots Physical consequences • Low temperature regime corresponds to diverging coupling constant • Since J → the impurity and conduction electron spin have to allign antiparallel to minimize the total energy • For T → 0∞ local impurity spin forms a singlet with a conduction electron • Local impurity spin is screened by the conduction electrons • Behaves like a non-magnetic one • Saturation of the resistivity becomes explicable Figure 4: Sketch of the coupling constant and the resistance minimum versus temperature Gesa von Bornstaedt Kondo Effect in Quantum Dots 4. Investigation of the Kondo effect in quantum dots Quantum Dot • Small solid-state device • Single electron transistor (SET) • Contains confined ’droplet’ of electrons • Integer number of electrons N • Artificial atom Figure 5: Scanning electron microscope image of a SET (Picture taken from: D. Goldhaber-Gordon, H. Shtrikman et al.: ”Kondo effect in a single-electron transistor”, Nature vol 391, 156 (1998).) Gesa von Bornstaedt Kondo Effect in Quantum Dots Transport in detail • Tunable tunnel coupling to the leads • Has a single spin-degenerate energy state 0 • Occupied by one electron with spin up or down • First order tunneling is blocked by the coulomb blockade • Virtual tunnel events with an effective spin-flip are possible • Successive spin-flip processes screen the local spin on the dot Figure 6: Possible virtual tunnel event Gesa von Bornstaedt Kondo Effect in Quantum Dots Why is a quantum dot a Kondo system? • For an odd number of electrons the dot has a net spin magnetic moment For an even number of electrons it is no Kondo system • Individual artificial magnetic impurity • Spin singlet state is formed between the unpaired localized electron and delocalized electrons in the leads • Quantum dot has a narrow-resonance in the density-of-states (DOS) • This Kondo resonance gives rise to enhanced conductance through the dot Figure 7: Kondo resonance (Lower energy bump: broadened single-particle state 0) Gesa von Bornstaedt Kondo Effect in Quantum Dots Minimum in the conductance • Minimum in δG strongly resembles the resistance minimum for magnetic impurities • 3, 5, 7 show Kondo behavior (odd number of electrons) • 2, 4, 6 are no Kondo systems (even number of electrons) Figure 8: Conductance versus temperature (Data taken from: Sara M.
Load more

Recommended publications
  • Many-Body Effects in Optical Excitations of Transition Metal Dichalcogenides
    Research Collection Doctoral Thesis Many-Body Effects in Optical Excitations of Transition Metal Dichalcogenides Author(s): Sidler, Meinrad Publication Date: 2018-02 Permanent Link: https://doi.org/10.3929/ethz-b-000290909 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library DISS. ETH NO. 24988 Many-Body Effects in Optical Excitations of Transition Metal Dichalcogenides A thesis submitted to attain the degree of DOCTOR OF SCIENCES of ETH ZURICH (Dr. sc. ETH Zurich) presented by MEINRAD SIDLER MSc ETH Physics, ETH Zurich born on 21.06.1989 citizen of Grosswangen LU accepted on the recommendation of: Prof. Ata¸cImamo˘glu,examiner Prof. Bernhard Urbaszek, co-examiner 2018 c Summary This dissertation treats a quantum impurity problem in a semiconductor system. Quantum impurity problems describe the interaction between a single quantum object and a complex environment. They are ubiquitous in physical systems and represent a fundamental field of research in many-body physics. Prominent examples are the Anderson orthogonality catastrophe and the Kondo effect. In both cases, the impurity is much heavier than the constituents of the interacting environment. If the mass of the impurity is comparable to the surrounding particles, we have a mobile impurity. These systems are usually harder to solve, as evident in the case of lattice polarons, which were first proposed in 1933 by Lev Landau. A complex but accurate description was found years later in 1955 by Richard Feynman. In recent years, strong coupling between single, mobile quantum impurities and a fermionic bath was realized in cold atoms.
    [Show full text]
  • A New View on the Origin of Zero-Bias Anomalies of Co Atoms Atop Noble Metal Surfaces ✉ ✉ Juba Bouaziz 1 , Filipe Souza Mendes Guimarães 1 & Samir Lounis 1
    ARTICLE https://doi.org/10.1038/s41467-020-19746-1 OPEN A new view on the origin of zero-bias anomalies of Co atoms atop noble metal surfaces ✉ ✉ Juba Bouaziz 1 , Filipe Souza Mendes Guimarães 1 & Samir Lounis 1 Many-body phenomena are paramount in physics. In condensed matter, their hallmark is considerable on a wide range of material characteristics spanning electronic, magnetic, thermodynamic and transport properties. They potentially imprint non-trivial signatures in 1234567890():,; spectroscopic measurements, such as those assigned to Kondo, excitonic and polaronic features, whose emergence depends on the involved degrees of freedom. Here, we address systematically zero-bias anomalies detected by scanning tunneling spectroscopy on Co atoms deposited on Cu, Ag and Au(111) substrates, which remarkably are almost identical to those obtained from first-principles. These features originate from gaped spin-excitations induced by a finite magnetic anisotropy energy, in contrast to the usual widespread inter- pretation relating them to Kondo resonances. Resting on relativistic time-dependent density functional and many-body perturbation theories, we furthermore unveil a new many-body feature, the spinaron, resulting from the interaction of electrons and spin-excitations loca- lizing electronic states in a well defined energy. ✉ 1 Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, Jülich 52425, Germany. email: [email protected]; [email protected] NATURE COMMUNICATIONS | (2020) 11:6112 | https://doi.org/10.1038/s41467-020-19746-1 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-19746-1 ignatures of many-body phenomena in solid state physics theoretical transport spectra are nearly identical to the experi- Sare diverse1–5.
    [Show full text]
  • Kondo Effect in Mesoscopic Quantum Dots
    1 Kondo Effect in Mesoscopic Quantum Dots M. Grobis,1 I. G. Rau,2 R. M. Potok,1,3 and D. Goldhaber-Gordon1 1 Department of Physics, Stanford University, Stanford, CA 94305 2 Department of Applied Physics, Stanford University, Stanford, CA 94305 3 Department of Physics, Harvard University, Cambridge, MA 02138 Abstract A dilute concentration of magnetic impurities can dramatically affect the transport properties of an otherwise pure metal. This phenomenon, known as the Kondo effect, originates from the interactions of individual magnetic impurities with the conduction electrons. Nearly a decade ago, the Kondo effect was observed in a new system, in which the magnetic moment stems from a single unpaired spin in a lithographically defined quantum dot, or artificial atom. The discovery of the Kondo effect in artificial atoms spurred a revival in the study of Kondo physics, due in part to the unprecedented control of relevant parameters in these systems. In this review we discuss the physics, origins, and phenomenology of the Kondo effect in the context of recent quantum dot experiments. After a brief historical introduction (Sec. 1), we first discuss the spin-½ Kondo effect (Sec. 2) and how it is modified by various parameters, external couplings, and non-ideal conduction reservoirs (Sec. 3). Next, we discuss measurements of more exotic Kondo systems (Sec. 4) and conclude with some possible future directions (Sec. 5). Keywords Kondo effect, quantum dot, single-electron transistor, mesoscopic physics, Anderson model, Coulomb blockade, tunneling transport, magnetism, experimental physics 2 1 Introduction At low temperatures, a small concentration of magnetic impurities — atoms or ions with a non-zero magnetic moment — can dramatically affect the behavior of conduction electrons in an otherwise pure metal.
    [Show full text]
  • Kondo Effect in Real Metals Ph
    Kondo effect in real metals Ph. Nozières, Annie Blandin To cite this version: Ph. Nozières, Annie Blandin. Kondo effect in real metals. Journal de Physique, 1980, 41 (3), pp.193- 211. 10.1051/jphys:01980004103019300. jpa-00209235 HAL Id: jpa-00209235 https://hal.archives-ouvertes.fr/jpa-00209235 Submitted on 1 Jan 1980 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. J. Physique 41 (1980) 193-2111 MARS 1980, 193 Classification Physics Abstracts 75.20H Kondo effect in real metals Ph. Nozières Institut Laue-Langevin, 156X, 38042 Grenoble Cedex, France and A. Blandin Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France (Reçu le 21 septembre 1979, accepte le 30 octobre 1979) Résumé. 2014 Dans le cadre d’un hamiltonien d’Anderson généralisé, nous étudions le comportement d’une impureté magnétique dans un métal réel, compte tenu de la structure orbitale des électrons localisés sur l’impureté, du champ cristallin et du couplage spin-orbite. Nous nous limitons à un schéma atomique, dans lequel l’impureté a une valeur bien définie entière (une transformation de Schrieffer Wolff est alors possible). Les principales étapes d’une procédure de renormalisation sont décrites en détail.
    [Show full text]
  • Heavy Fermions: Electrons at the Edge of Magnetism
    Heavy Fermions: Electrons at the Edge of Magnetism Piers Coleman Rutgers University, Piscataway, NJ, USA Mathur et al., 1998). The ‘quantum critical point’ (QCP) that 1 Introduction: ‘Asymptotic Freedom’ in a Cryostat 95 separates the heavy-electron ground state from the AFM rep- 2 Local Moments and the Kondo Lattice 105 resents a kind of singularity in the material phase diagram 3 Kondo Insulators 123 that profoundly modifies the metallic properties, giving them a a predisposition toward superconductivity and other novel 4 Heavy-fermion Superconductivity 126 states of matter. 5 Quantum Criticality 135 One of the goals of modern condensed matter research 6 Conclusions and Open Questions 142 is to couple magnetic and electronic properties to develop Notes 142 new classes of material behavior, such as high-temperature Acknowledgments 142 superconductivity or colossal magnetoresistance materials, References 143 spintronics, and the newly discovered multiferroic materials. Further Reading 148 Heavy-electron materials lie at the very brink of magnetic instability, in a regime where quantum fluctuations of the magnetic and electronic degrees are strongly coupled. As such, they are an important test bed for the development of 1 INTRODUCTION: ‘ASYMPTOTIC our understanding about the interaction between magnetic FREEDOM’ IN A CRYOSTAT and electronic quantum fluctuations. Heavy-fermion materials contain rare-earth or actinide The term heavy fermion was coined by Steglich et al. (1976) ions, forming a matrix of localized magnetic moments. The in the late 1970s to describe the electronic excitations in active physics of these materials results from the immersion a new class of intermetallic compound with an electronic of these magnetic moments in a quantum sea of mobile con- density of states as much as 1000 times larger than copper.
    [Show full text]
  • A High-Temperature Silicon Qubit and Its Quantum Interference Tunable
    Abstracts from Invited Speakers Keiji Ono (RIKEN) A High-temperature Silicon Qubit and its Quantum Interference Spin qubits are attractive building blocks for quantum computers. Si is a promising host material for spin qubits since it could enable long coherence, high-density integration, and high compatibility with classical computers. Spin qubits have been implemented in Si using gate-defined quantum dots or shallow impurities. However, these qubits must be operated at temperatures <0.1 K, limiting the expansion of qubit technology. We used deep impurities in Si to achieve room-temperature single- electron tunnelling and spin qubit operation at 5–10 K [1]. We employed tunnel field-effect transistors (TFETs) instead of conventional metal–oxide–semiconductor field-effect transistors and achieved strong confinement of the single quantum dots embraced in TFETs up to 0.3 eV. Furthermore, double- quantum-dot devices were operated as spin qubits, and read-out was realized using a spin blockade. These results will enable broadening of the range of spin qubit applications such as sensing, security, and quantum computing. We also study quantum interference effects of a qubit whose energy levels are continuously modulated [2]. The qubit energy levels are modulated via its gate-voltage-dependent g-factors, with either rectangular, sinusoidal, or ramp radio-frequency waves. The energy-modulated qubit is probed by the electron spin resonance. Our results demonstrate the potential of spin qubit interferometry that is implemented in a Si device and is operated at a relatively high temperature. [1] K. Ono, T. Mori, S. Moriyama, High-Temperature Operation of Spin Qubits based on Silicon Tunnel Field-Effect Transistors, arXiv:1804.03364, Scientific reports, in print.
    [Show full text]
  • Arxiv:1102.2798V1 [Cond-Mat.Mes-Hall] 14 Feb 2011 Ipysprse Yculn Ftesi Omolecu- to Spin the of One Be Coupling to by [8]
    Interaction of spin and vibrations in transport through single-molecule magnets F. May(1,2), M. R. Wegewijs(3,4), and W. Hofstetter(1) (1) Institut f¨ur Theoretische Physik, Johann Wolfgang Goethe-Universit¨at, 60438 Frankfurt/Main, Germany (2) Max Planck Institute for Polymer Research, 55128 Mainz, Germany (3) Institut f¨ur Theorie der Statistischen Physik, RWTH Aachen, 52056 Aachen, Germany and (4) Peter Gr¨unberg Institut and JARA - Fundamentals of Information Technology, Forschungszentrum J¨ulich, 52425 J¨ulich, Germany We study linear electron transport through a single-molecule magnet (SMM) and the interplay of its anisotropic spin with quantized vibrational distortions of the molecule. We show that, despite the longitudinal anisotropy barrier and small transverse anisotropy, vibrational fluctuations can induce quantum spin-tunneling (QST) and a QST-Kondo effect. The interplay of spin scattering, QST and molecular vibrations can strongly enhance the Kondo effect and induce an anomalous magnetic field dependence of vibrational Kondo side-bands. PACS numbers: 85.65.+h, 73.63.Kv, 85.35.-p Transport measurements on nanometer-sized magnetic lar vibrations as this tends to increase the anisotropy systems address the fundamental problem of how a few barrier [7]. However, the dynamical effect of vibrational magnetic atoms in an anisotropic environment respond to fluctuations and the possible competition between longi- an electron current [1]. Such an environment is provided, tudinal and transverse spin-vibration coupling have not for instance, by ligand groups holding such atoms to- been studied so far, even though coupling to vibrations in gether in a single magnetic molecule contacted in a break the Kondo regime has been considered for spin-isotropic junction [2, 3].
    [Show full text]
  • Interplay Between Charge, Magnetic and Superconducting Order in a Kondo Lattice with an Attractive Hubbard Interaction
    Interplay between charge, magnetic and superconducting order in a Kondo lattice with an attractive Hubbard interaction Benedikt Lechtenberg,1 Robert Peters,1 and Norio Kawakami1 1Department of Physics, Kyoto University, Kyoto 606-8502, Japan (Dated: May 8, 2019) We investigate the competition between superconductivity, charge-ordering, magnetic-ordering, and the Kondo effect in a heavy fermion s-wave superconductor described by a Kondo lattice model with an attractive on-site Hubbard interaction. The model is solved using the real-space dynamical mean field theory. For this purpose, we develop a numerical renormalization group (NRG) framework in Nambu space, which is used to solve the superconducting impurity problem. This extended NRG scheme also allows for SU(2) spin symmetry broken solutions, enabling us to examine the competition or cooperation between s-wave superconductivity and incommensurate spin-density waves (SDWs). At half filling, we find an intriguing phase where the magnetic ordering of the f-electrons lifts the degeneracy between the charge density wave (CDW) state and the superconducting state, leading to a strong suppression of superconductivity. In addition, the system may also become a half metal in this parameter regime. Away from half filling, the CDWs vanish and are replaced by superconductivity combined with incommensurate SDWs up to moderate Kondo couplings to the f-electrons. We find that both CDWs as well as superconductivity enhance magnetic ordering due to the suppression of Kondo screening. I. INTRODUCTION the interplay between superconductivity, magnetic order- ing, charge ordering, and the Kondo effect. One of the simplest models comprising all these effects Strongly correlated electron systems attract enormous is a Kondo lattice [37{41] with an additional attractive attention because of the multitude of remarkable phe- Hubbard interaction U < 0 [42]: nomena they exhibit, such as the Kondo effect, mag- netic or charge ordering, and unconventional supercon- X y X H =t c c + H:c: µ ni,σ ductivity.
    [Show full text]
  • Tuning the Kondo Effect in Yb (Fe1−X Cox)2 Zn20
    Physics and Astronomy Publications Physics and Astronomy 4-15-2017 Tuning the Kondo effect in Yb (Fe1−x Cox)2 Zn20 Tai Kong Iowa State University and Ames Laboratory Valentin Taufour Iowa State University and Ames Laboratory Sergey L. Bud’ko Iowa State University and Ames Laboratory, [email protected] Paul C. Canfield Iowa State University and Ames Laboratory, [email protected] Follow this and additional works at: https://lib.dr.iastate.edu/physastro_pubs Part of the Condensed Matter Physics Commons The complete bibliographic information for this item can be found at https://lib.dr.iastate.edu/physastro_pubs/523. For information on how to cite this item, please visit http://lib.dr.iastate.edu/howtocite.html. This Article is brought to you for free and open access by the Physics and Astronomy at Iowa State University Digital Repository. It has been accepted for inclusion in Physics and Astronomy Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Tuning the Kondo effect in Yb (Fe1−x Cox)2 Zn20 Abstract We study the evolution of the Kondo effect in heavy fermion compounds, Yb(Fe1−xCox)2Zn20 (0≤x≤1), by means of temperature-dependent electric resistivity and specific heat. The ground state of YbFe2Zn20 can be well described by a Kondo model with degeneracy N = 8 and a TK∼30 K. The ground state of YbCo2Zn20 is close to a Kondo state with degeneracy N = 2 and a much lower TK∼ 2 K, even though the total crystalline electric field (CEF) splittings are similar for YbFe2Zn20 and YbCo2Zn20.
    [Show full text]
  • A Holographic Model of the Kondo Effect
    A holographic model of the Kondo effect Johanna Erdmenger Max-Planck-Institut für Physik, München Based on joint work with C. Hoyos (Tel Aviv Univ.), A. O’Bannon (DAMTP Cambridge), J. Wu (NCTS Taiwan) 1309.xxxx, to appear Outline • 1. Kondo effect: Physics, CFT approach, large N • 2. Holographic model: Similarities and differences Kondo effect Screening of a magnetic impurity by conduction electrons at low temperatures Metals: Fermi liquid + impurities: In the presence of magnetic impurities: UV Free electrons + impurity spin IR Impurity screened Kondo model Kondo ’64, Affleck+Ludwig ‘90s Free electrons Local interaction with magnetic impurity Logarithmic behaviour at low temperatures Jun Kondo: • Progress of Theoretical Physics • Volume 32, Issue 1 • Pp. 37-49 TK : Kondo temperature IR theory is strongly coupled! TK ~ ΛQCD RG flow The Kondo model was decisive in the development of the RG formalism. (Wilson) Negative beta function: β λ2 + (λ3) λ ∝− O UV fixed point: Free theory Asymptotic freedom In some cases, the model flows to a strongly coupled IR fixed point. UV IR CFT approach Affleck+Ludwig, 90’s • One-impurity problem: Spherical symmetry • Reduces to 1+1-dimensional system with boundary • Consider only left-movers ψL ψL ψL ψR CFT approach Compare CFT’s at UV and IR fixed points UV: Free fermions, boundary condition ψ = ψ+ − IR: Free fermions, boundary condition ψ = ψ+ − − Change in boundary condition induces change in spectrum Generalizations Sugawara construction: Separation of spin, channel and charge currents IR CFT Critical, under- and overscreening Example of SU(2) k : Large N: Slave fermions χ†χ = q, Q = q/N Large N: Slave fermions Sachdev, Senthil, Voijta cond-mat/0209144 Kondo effect corresponds to condensation of = ψ† χ O L 2.
    [Show full text]
  • Topics in Kondo Insulators
    TOPICS IN KONDO INSULATORS By ARI WUGALTER A dissertation submitted to the School of Graduate Studies Rutgers, The State University of New Jersey In partial fulfillment of the requirements For the degree of Doctor of Philosophy Graduate Program in Physics and Astronomy Written under the direction of Piers Coleman And approved by New Brunswick, New Jersey October, 2020 ABSTRACT OF THE DISSERTATION Topics in Kondo Insulators By ARI WUGALTER Dissertation Director: Piers Coleman We have studied Kondo insulator states in the single and two-channel Kondo models. The Kondo insulator state shows remarkable optical properties. Specifically, a dielec- tric constant which is 100 times higher than for a regular insulator. Moreover, the ≈ diamagnetic permeability does not seem to be affected by the onset of the Kondo effect. This suggest that while the Kondo effect is very effective in suppressing the longitudinal current fluctuations, it is largely ineffective in its influence on diamag- netic currents. In the two channel Kondo model, we observe the formation of a half-Kondo insula- tor, where the spontaneous breaking of channel symmetry leads to the formation of a Kondo insulator in one channel, while the other channel remains metallic. We discuss, how this phenomenon can be understood using the concept of order fractionalization, in which the channel magnetization breaks up into an emergent spinor order para- meter. By integrating out the fermions we derive an effective action that describes this symmetry breaking and its emergent collective modes. A remarkable observation ii is that topological defects in the order parameter carry a U(1) flux, manifested in the Aharonov-Bohm phase picked by electrons that orbit the defect.
    [Show full text]
  • Arxiv:Cond-Mat/9704103 V3 28 Aug 1997 Exotic P Ev Formation Regime Kondo Pro Nanoscale Non-F B for W Trons Energetic Ing Explaining Y Erconductors
    Exotic Kondo Effects in Metals: Magnetic Ions in a Crystalline Electric Field and Tunneling Centers D.L. Cox, Department of Physics, The Ohio State University, Columbus, Ohio, 43210 and Department of Physics, University of California, Davis, California, 95616 and A. Zawadowski, Institute of Physics, and Research Group of Hungarian Academy of Sciences, Technical University of Budapest, Budafoki ut 8, H1521, and Research Institute for Solid State Physics, Hungarian Academy of Sciences, P.O.B. 49, H-1525, Budapest, Hungary January 24, 2002 arXiv:cond-mat/9704103 v3 28 Aug 1997 Abstract The ordinary single channel Kondo model consists of one or more spin 1/2 local moments interact- ing antiferromagnetically with conduction electrons in a metal. This model has provided a paradigm for understanding many phenomena of strongly correlated electronic materials, ranging from the formation of heavy fermion fermi liquids to the mapping to a one-band model in the cuprate su- perconductors. The simplest extension of this ordinary Kondo model in metals which yields exotic non-Fermi liquid physics is the multichannel Kondo impurity model in which the conduction elec- trons are given an extra quantum label known as the channel or flavor index. In the overcompensated regime of this model non-Fermi liquid physics is possible, in contrast to the single channel model. We overview here the multichannel Kondo impurity model candidates most extensively studied for explaining real materials, specifically the two level system Kondo model relevant for metallic glasses, nanoscale devices, and some doped semiconductors, and the quadrupolar and magnetic two-channel Kondo models developed for rare earth and actinide ions with crystal field splittings in metals.
    [Show full text]