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Heavy Fermions

Heavy Fermions. Student: Leland Harriger Professor: Elbio Dagotto Class: Solid State II, UTK Date: April 23, 2009. Structure of Presentation. Fermi Gas Modifications to Fermi Gas Examples and Properties of Heavy Fermions Interactions Important to Heavy Fermions

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Heavy Fermions

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  1. Heavy Fermions Student: Leland Harriger Professor: Elbio Dagotto Class: Solid State II, UTK Date: April 23, 2009

  2. Structure of Presentation • Fermi Gas • Modifications to Fermi Gas • Examples and Properties of Heavy Fermions • Interactions Important to Heavy Fermions • Common Features within Heavy Fermions

  3. Fermi Gas Theory • The simplest model: Particle in a Box

  4. The Equation

  5. The Solution

  6. K-space • Fermi Surface

  7. Density of States and Fermi-Dirac Distribution • Note that the systems energy is directly related to the number of orbitals: • Gives us the number of orbitals per unit energy. • Combine this with the probability of occupation:

  8. Heat Capacity • How reliable is this model? • Classical particles in a box (Ideal Gas) • ~102 too big • Quantum particles in a box (Fermi Gas) • of same order

  9. Experimental Agreement Source: N.E. Phillips *

  10. Refining the model • Take into account the ion cores

  11. Interaction with the cores

  12. Electron-Electron Interactions • For Metals: • Conduction electrons are 2Å apart. • Mean free paths are >104Å at room temp. • Why: • Coulomb Screening • Exclusion Principle

  13. Fermi Fluid • Takes into account electron-electron interactions • Complicated interactions treated as non-interacting quasiparticles above an inert Fermi-sea. • Formulation:

  14. Heavy Fermions • Begin by example: • f-electron system CeAl3 • Specific Heat is linear in T • ~ 1000 times larger than expected by Fermi Gas Theory • Implies m* ~ 1000 times larger • Interesting Properties: • Heavy Fermion Systems were the first display NFL behavior. • They also are an example of “exotic superconductivity”

  15. Rich Phase Diagrams Exhibiting both NFL behavior and superconductivity. Source: Sanchez Source: Seaman et al.

  16. Phases and properties • Heavy Fermion is NOT synonymous with Non-Fermi Liquid. • However, in the Fermi Liquid phase heavy fermions have anonymously large electronic specific heat coefficient and Sucseptibility. (2-4 orders of magnitude larger than Cu)

  17. Kondo Effect

  18. RKKY Interaction • Magnetic impurities replaced by magnetic lattice. • Indirect exchange coupling established between magnetic ions.

  19. Competition between interactions. • Two different energy scales:

  20. Coherence and Delocalization • T* = coherence temperature • We see: reduced resistivity, modified spin sucseptibility, observed Knight shift, sudden entropy change, and more. • Why: delocalization of the f-electrons.

  21. Attempting a Universal Model

  22. NFL and QCP Scaling

  23. References • Z. Fisk, et. al. PNAS92, 6663 (1995). • Yi-feng Yang, et. al. Nature454, 611 (2007). • V.V. Krishnamurthy, et. al. PRB78 024413 (2008). • J.P. Sanchez ESRFhttp://www.esrf.eu/UsersAndScience/Publications/Highlights/2002/HRRS/HRRS1 • http://en.wikipedia.org/wiki/Kondo_effect • Kittel Solid State Physics

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