Notes on Interactions - Introduction to Condensed Matter Physics | PHYS 231, Study notes of Physics

Download Notes on Interactions - Introduction to Condensed Matter Physics | PHYS 231 and more Study notes Physics in PDF only on Docsity! Lecture 16 Interactions 1 Phys-231, Fall 07, UCSC, (c) 2007, G.-H. Gweon 12/03/2007 Marx: Quantitative differences become qualitative ones. Fitzgerald: The rich are different from us. Hemingway: Yes, they have more money. Quotes in P. W. Anderson, “More is different” Why Electron-Electron Interaction? Everything that relates to magnetism (FM, AFM) originates from electron-electron interaction. Electron-Electron is dominant in TM and RE elements Without E-E, hydrogen molecules or hydrogen solid cannot be understood properly 12/03/2007Phys-231, Fall 07, UCSC, (c) 2007, G.-H. Gweon2 Screening Lindhard Susceptibility (Hartree approx, any q) Reduces to Thomas-Fermi for small q 12/03/2007Phys-231, Fall 07, UCSC, (c) 2007, G.-H. Gweon5 Thomas-Fermi Screening 12/03/2007Phys-231, Fall 07, UCSC, (c) 2007, G.-H. Gweon6 Very effective screening at long λ Screened Coulomb Very short screening length Lindhard-Specific Screening 12/03/2007Phys-231, Fall 07, UCSC, (c) 2007, G.-H. Gweon7 At short λ (~ 1/kF) χ (q) generally has singularity at q=2kF Friedel (or Ruderman-Kittel) Oscillations http://www.aip.org/png/images/stm2.jpg Don Eigler, IBM Why Mean-Field Theory Completely Breaks Down in One Dimension 12/03/2007Phys-231, Fall 07, UCSC, (c) 2007, G.-H. Gweon10 Mermin-Wagner Theorem : No long range order (i.e. no phase transition) in 1D or 2D with short range interactions Peierls Instability (Charge Density Wave) Analogous Physics in Spin Density Wave (Cr), and Spin Peierls (CuGeO3) Transitions 12/03/2007Phys-231, Fall 07, UCSC, (c) 2007, G.-H. Gweon11 Wait … What Really Happens in Peierls Systems 12/03/2007Phys-231, Fall 07, UCSC, (c) 2007, G.-H. Gweon12 This was a mean-field picture! And, we did not condier Mermin-Wagner theorem. Neutron Diffraction, X-ray Diffraction, Photoemission Spectroscopy, Pauli Susceptibility, Resistivity etc. can examine these strange behaviors on quasi-1D materials Hubbard Model and (A)FM Hubbard Model provides a basis for the Stoner FM (small U) Hubbard Model also provides a basis for an AFM in the opposite limit of large U 12/03/2007Phys-231, Fall 07, UCSC, (c) 2007, G.-H. Gweon15 AFM MH Insulator Electron-Phonon Interaction: BCS theory e +Z +Z +Z +Z e PHONON MEDIATED PAIRING Pairs of electrons: Cooper pairs Tc~ωph exp(-1/λ)~M -1/2 El-ph coupling constant: λ Superconducting gap: Δ e-ph wins e-e at low freq. (Slow Wins!) M Emergence of Debye Phonon in Metal 12/03/2007Phys-231, Fall 07, UCSC, (c) 2007, G.-H. Gweon17 Ion-Ion interaction without screening: Phonon Mode is NOT Debye-like! Ion-Ion interaction with screening: Phonon Mode is LIKE Debye, as observed. Electron Dispersion Change (“Kink”) Observed for simple metals such as Be, Mo, W, etc. Highly debated in HTSC 12/03/2007Phys-231, Fall 07, UCSC, (c) 2007, G.-H. Gweon20 Read: 519-521 of A&M or Schrieffer “Theory of Superconductivity” Heavy Quasi-Particle at Low Energy … Momentum EF Change of Velocity due to El-Ph Interaction Electron-Phonon Interaction 12/03/2007Phys-231, Fall 07, UCSC, (c) 2007, G.-H. Gweon22 Can interpret the energy lowering as being due to electron-phonon interaction (pages 522-523) Important element in giving Bloch T5 law of resistivity at low T (read A&M pages 525-526) E-Ph important for Peierls transition Compeition between Cooper channel and Peierls channel!