Heavy Fermions Student Leland Harriger Professor Elbio Dagotto

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

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

Fermi Gas Theory n The simplest model: Particle in a Box

The Equation

The Solution

K-space n Fermi Surface

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

Heat Capacity n n n 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

Experimental Agreement Metal Ag Cu Rb Li ᵞγ(exp) 0. 646 0. 695 2. 41 1. 63 Source: N. E. Phillips γ 0 (free 0. 65 0. 50 1. 97 0. 75 electron) 1. 00 1. 39 1. 22 2. 17 γ/γ 0 *

Refining the model n Take into account the ion cores

Interaction with the cores

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

Fermi Fluid n n n Takes into account electron-electron interactions Complicated interactions treated as noninteracting quasiparticles above an inert Fermi-sea. Formulation:

Heavy Fermions n Begin by example: q q n f-electron system Ce. Al 3 Specific Heat is linear in T ~ 1000 times larger than expected by Fermi Gas Theory Implies m* ~ 1000 times larger Interesting Properties: q q Heavy Fermion Systems were the first display NFL behavior. They also are an example of “exotic superconductivity”

Rich Phase Diagrams Exhibiting both NFL behavior and superconductivity. Source: Sanchez Y 1 -x. Ux. Pd Heat Capacity C ~ -Tln(T) Conductivity ~ 0 + AT 1. 1 Magnetic Susceptibility m ~ - T 1/2 Fermi Liquid C = T = 0 + AT 2 m = Source: Seaman et al.

Phases and properties n n 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)

Kondo Effect

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

Competition between interactions. n Two different energy scales:

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

Attempting a Universal Model

NFL and QCP Scaling

References n n n 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/Users. And. Science/Publications/Highlights/2002/HRRS/H RRS 1 http: //en. wikipedia. org/wiki/Kondo_effect Kittel Solid State Physics