1 / 44

A Series of Ten Lectures at XVI Training Course on Strongly Correlated Systems, October 2011

From Kondo and Spin Glasses to Heavy Fermions, Hidden Order and Quantum Phase Transitions. A Series of Ten Lectures at XVI Training Course on Strongly Correlated Systems, October 2011 J. A. Mydosh Kamerlingh Onnes Laboratory and Institute Lorentz Leiden University

hiroshi-miura
Download Presentation

A Series of Ten Lectures at XVI Training Course on Strongly Correlated Systems, October 2011

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. From Kondo and Spin Glasses to Heavy Fermions, Hidden Order and Quantum Phase Transitions A Series of Ten Lectures at XVI Training Course on Strongly Correlated Systems, October 2011 J. A. Mydosh Kamerlingh Onnes Laboratory and Institute Lorentz Leiden University The Netherlands

  2. Lecture schedule October 3 – 7, 2011 • #1 Kondo effect • #2 Spin glasses • #3 Giant magnetoresistance • #4 Magnetoelectrics and multiferroics • #5 High temperature superconductivity • #6 Applications of superconductivity • #7 Heavy fermions • #8 Hidden order in URu2Si2 • #9 Modern experimental methods in correlated electron systems • #10 Quantum phase transitions Present basic experimental phenomena of the above topics Present basic experimental phenomena of the above topics

  3. Lecture schedule October 3 – 7, 2011 • #1 Kondo effect • #2 Spin glasses • #3 Giant magnetoresistance • #4 Magnetoelectrics and multiferroics • #5 High temperature superconductivity • #6 Applications of superconductivity • #7 Heavy fermions • #8 Hidden order in URu2Si2 • #9 Modern experimental methods in correlated electron systems • #10 Quantum phase transitions Present basic experimental phenomena of the above topics Present basic experimental phenomena of the above topics

  4. #1] The Kondo Effect: Experimentally Driven 1930/34; Theoretically Explained 1965 as magnetic impurities in non-magnetic metals. Low temperature resistivity minimum in AuFe and CuFe alloys. Increased scattering. Strange decrease of low temperature susceptibility, deviation from Curie-Weiss law. Disappearance of magnetism. Broad maximum in specific heat. Accumulation of entropy. Not a phase transition but a crossover behavior! Virtual bond state of impurity in metal. Magnetic or non-magnetic? s – d exchange model forĤsd= ΣJ s ·S Kondo’s calculation (1965) using perturbation theory for ρ. Wilson’s renormalization group method (1974) and χ(T)/C(T) ratio. Bethe ansatz theory (1981) for χ, M and C: thermodynamics. Modern Kondo behavior: Quantum dots, Kondo resonance & lattice.

  5. Interaction between localized impurity spin and conduction electrons – temperature dependent.Many body physics, strongly correlated electron phenomena yet Landau Fermi liquid. Not a phase transition but crossover in temperature

  6. Kondo effect: scattering of conduction electron on a magnetic imputity via a spin-flip (many-body) process. Kondo cloud

  7. Magnetic resistivity Δρ(T) = ρmag(T) + ρ0 = ρtotal(T)- ρphon(T) AuFe alloys. Note increasing ρ0 and ρ(max) as concentration is increased

  8. Concentration scaled magnetic resistivity Δρ(T)/c vs lnT CuAuFe alloys.Note lnT dependences (Kondo) and deviations from Matthiessen’s rule.

  9. Now Δρspin/c vs ln(T/TK) corrected for DM’sR Note decades of logarithmic behavior in T/TK and low T  0 Δρspin/c = ρun[1 – (T/TK)2], i.e., Fermi liquid behavior of Kondo effect

  10. Quantum dots – mesoscopically fabricated, tunneling of single electrons from contact reservoir controlled by gate voltage This is Kondo!

  11. Schematic energy diagram of a dot with one spin-degenerate energy level Ɛ0 occupied by a single electron; U is the single-electron charging energy, and ΓL and ΓR give the tunnel couplings to the left and right leads. S M Cronenwett et al., Science 281(1998) 540.

  12. Quantized conductance vs temperature Gate voltage is used to tune TK; measurements at 50 to 1000 mK.

  13. Kondo – quantum dot universality when scaled with TK

  14. Inverse susceptibility (χ= M/H) scaled with the concentration for CuMn with TK = 10-3K

  15. Inverse susceptibility and concentration scaled inverse susceptibility (c/χi)for CuFe with TK = 30K XXXX CuFe

  16. Excess specific heat ΔC/c on logarithmic scaleCuCr alloyswith TK = 1K

  17. Place a 3d (4f) impurity in a noble (non-magnetic) metal Virtual bound state (vbs) model-See V.Shenoy lecture notes

  18. e e

  19.  - U -  down-spin up-spin

  20. U splits the up and down vbs’, note different DOS’ Net magnetic moment of non-half integral spin  U 

  21. transition”

  22. ( J = V2/U; antiferromagnetic)

  23. 1st order perturbation theory processes ●S(S+1) Spin disorder scattering

  24. 2nd order perturbation non-spin flip

  25. Spin flip 2nd order perturbation

  26. Calculation of the logarithmic – T resistivity behavior

  27. Calculation of the resistivity minimum with phonons added

  28. Clean resistivity experiments on known concentrations of magnetic impurities, AuFe withTK = 0.5 K.

  29. Collection of Kondo temperatures

  30. Wilson renormalization group method (1974): scaletransformation of Kondo Hamiltonian to be diagonalized Spherical wave packets localized around impurity Shell parameter Λ > 1; E~Λ-n/2 for n states Calculate via numerical iteration χ(T) as a universal function and C(T) over entire T-range Lim(T0): χ(T)/[C(T)/T] =3R(gµB)2/(2∏kB)2 Wilson ratio R = 2 for Kondo, 1 for heavy fermions Determination of Kondo temperature TK = D|2Jρ|1/2exp{-1/2Jρ} where J is exchange coupling and ρ the host metal density of states K. Wilson, RMP 47(1975)773.

  31. Bethe Ansatz (1980’s) - Andrei et al., RMP 55, 331(1983). “Bethe ansatz” method for finding exact solution of quantum many-body Kondo Hamiltonian in 1D. Many body wave function is symmetrized product of one-body wave functions. Eigenvalue problem. Allows for exact (diagonalization) solution of thermodynamic propertries: χ, M and C as fct(T,H). Does not give the transport properties, e.g. ρ(T,H). “1D” Fermi surface TK << D

  32. Impurity susceptibility χi(T) Agrees withexperiment Low T χiis constant: Fermi liquid; C-W law at high T with To ≈ TK

  33. Impurity magnetization as fct(H) Agrees with experiment M ~ H at low H; M free moment at large H (Kondo effect broken)

  34. Specific heat vs log(T/TK)for different spin values Agrees with experiment Note reduced CiV as the impurity spin increases.

  35. Kondo cloud - wave packet but what happens with a Kondo lattice? Never unambiguously found!

  36. Kondo resonance - how to detect? Photoemission spectroscopy (PES) Still controversial

  37. Kondo effect ( Kondo lattice) gives an introduction to forthcoming topics, e.g., SG, GMR, HF; QPT. • #1 Kondo effect • #2 Spin glasses • #3 Giant magnetoresistance • #4 Magnetoelectrics and multiferroics • #5 High temperature superconductivity • #6 Applications of superconductivity • #7 Heavy fermions • #8 Hidden order in URu2Si2 • #9 Modern experimental methods in correlated electron systems • #10 Quantum phase transitions

  38. Kondo resonance to be measured via PES

  39. ??? To use ???

More Related