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) ~10 2 too big Quantum particles in a box (Fermi Gas) of same order

9. Experimental Agreement Metalγ (exp) γ 0 (free electron) γ/γ0γ/γ0 Ag0.6460.651.00 Cu0.6950.501.39 Rb2.411.971.22 Li1.630.752.17 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 >10 4 Å 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 CeAl 3  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. Y 1-x U x PdFermi Liquid Heat CapacityC ~ -Tln(T) C =  T Conductivity  ~  0 + AT 1.1  =  0 + AT 2 Magnetic Susceptibility  m ~  -  T 1/2  m =  Source: Seaman et al. Source: Sanchez

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

23. NFL and QCP Scaling

24. References Z. Fisk, et. al. PNAS 92, 6663 (1995). Yi-feng Yang, et. al. Nature 454, 611 (2007). V.V. Krishnamurthy, et. al. PRB 78 024413 (2008). J.P. Sanchez ESRF http://www.esrf.eu/UsersAndScience/Publications/Highlights/2002/HRRS/H RRS1 http://www.esrf.eu/UsersAndScience/Publications/Highlights/2002/HRRS/H RRS1 http://en.wikipedia.org/wiki/Kondo_effect Kittel Solid State Physics