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Phys 460 Lecture 22

( pdf version - 6 slides/page )
Monday, November 13, 2006
Lecturer: Richard Martin 		No new homework

Reading:
Kittel, Ch. 9 (brief parts), Ch 10

Metals (brief review) and Superconductivity I
Outline

  1. From previous lectures:
    • Part I: Crystal Structures, Diffraction, Reciprocal Lattice, Crystal binding
      Phonons, Dispersion curves, Thermal properties
    • Part II: Free electron gas, Energy bands for electrons in crystals Ekn, gaps, metals vs. insulators, semiconductors
    • Part III:
      • Semiconductor devices - inhomogeneous semiconductors - heterostructures
      • Semiconductor nanostructures
  2. Very brief overview of metals
    • Review of homogeneous electron gas
      • Fermi surface is the key idea for electrons
      • The states are filled for En(k) < EFermi
        The states are empty for En(k) > EFermi
      • Defines Fermi surface in k space: set of k values where En(k) = EFermi
      • Fermi function, Heat capacity, conductivity
    • ALL the ideas apply to metallic crystals! The application is more complicated because the Fermi surface is not a sphere, but the ideas are the same!
    • Example of the Fermi Surface of Cu - see also Kittel
  3. Superconductivity I - Experimental Facts
    • Discovered in 1911 in Hg - 4.6 K - R apparently drops to ZERO suddenly li> Occurs for temperature T < Tc, where Tc is the transition temperature (also called the critical temperature)
    • Which materials?
      NOT magnetic material like Fe
      NOT the "best" metals like Cu
    • Exclusion of magnetic fields
      Meisner Effect shows a superconductor is not just a perfect conductor
      NEW PHASE OF MATTER
      Magnetic field excluded for applied field H < Hc
    • Heat Capacity shows there is a phase transition
      Below Tc< there is a gap (like an insulator!)
    • Transition is reversible - no hysteresis
    • Isotope effect - something to do with MOTION of nuclei
    • Type I and Type II
      • Type I: Magnetic field excluded for applied field H < Hc for any temperature T < Tc
      • Type II: Magnetic field excluded for applied field H < Hc1. The field penetrates in flux quants for fields < Hc1 < H < Hc2, where Hc1 and Hc2 are functions of T for T < Tc
Email clarification questions and corrections to rmartin@uiuc.edu
Email questions on solving problems to xin2@.uiuc.edu