Foundations of Condensed Matter Physics PHY1850F 2005 www.physics.utoronto.ca/~wei/phy1850f.html
Physics 1850F Foundations of Condensed Matter Physics Webpage: www.physics.utoronto.ca/~wei/phy1850f.html Prerequisites: Quantum Mechanics, Statistical Mechanics, Classical Mechanics, Electricity & Magnetism (at the upper-division undergraduate level). Textbooks: C. Kittel, Introduction to Solid State Physics (8th Edition) J. M. Ziman, Principles of the Theory of Solids (2nd Edition) Course Topics: 1. Crystal Structures & Binding 2. Phonons I: Lattice Vibrations 3. Phonons II: Thermal Properties 4. Electron Kinetics: Transport & Thermal Properties 5. Electron Dynamics: Dispersion & Fermiology 6. Elementary Excitations: Quasiparticles & Screening 7. Superconductivity 8. Magnetism 9. Tunneling & Photoemission 10. Mesoscopic Transport & Nanoscale Phenomena Grading Policy: Homework: 1/3 Exam: 1/3 Presentation*: 1/3
Why is this frog Condensed Matter? Credit: www.hfml.ru.nl/froglev.html
Levitating Frog: The Movie Credit: www.hfml.ru.nl/froglev.html
Other Levitating Objects Credit: www.hfml.ru.nl/froglev.html
Levitating YBa 2 Cu 3 O 7 : The Movie Credit: www.fys.uio.no/super/levitation/
Elemental Magnets & Superconductors [from: LANL website]
Physics of Materials Conductivity Insulator: diamond, quartz, Al 2 O 3 Semicond.: Si, Ge, GaAs (doped) Metal: Au, Fe, Cu, Al Supercond.: Hg, Pb, Nb 3 Sn Superconductivity Magnetism Dia- : graphite, Au, NaCl Para- : Al, Ti, Cr (ambient) Antiferro- : MnO, La 2 CuO 4 Ferro- : Fe, Ni, SmCo 5 Ferromagnetism R (W) M/M s T c [Kamerlingh Onnes, 1911] T(K) [C. Kittel textbook] T/T m
Electrons in a Crystal Charge Quantized: -e or +e Electrostatic repulsion Coulomb interaction with lattice Cooperative behavior (e.g. Pairing) Charge-excitations Quasiparticles Spin Quantized: +1/2 or -1/2 Magnetic dipole moment Exchange interaction between spins Collective alignment (FM or AFM) Spin-excitations Spinons Ferromagnetism (parallel spins): Exchange > 0 => Net moment Cooper pair (Charge=2e, Spin=0): Opposite momenta; Coherence length x Antiferromagnetism (antiparallel): Exchange < 0 => Zero moment
Band Theory of Solids (100% spin-polarized!)
Order Parameter Superconductivity Ferromagnetism D/D o M/M s T/T c T/T m Superconductivity & Magnetism have formal similarities Characterized by degree of QM order Y represents either D or M They generally compete, but may cooperate Quantum Critical Phenomena (QCP) Ψ = e i?
Exotic Magnets & Superconductors [Krauss et al. 01] La 0.7 Ca 0.3 MnO 3 Colossal Magnetoresistivity (CMR) Half-metallic ferromagnetism (HMF) YBa 2 Cu 3 O 6+x High-T c Superconductivity (HTS) Novel spin & charge ordering (Stripes)
Half-Metallic Ferromagnets % Spin Polarization (measured) Conventional Half-Metallic NiFe 37% Co 40 Ni 42 Fe 45 NiMnSb 58% La 0.7 Ca 0.3 MnO 3 78 Fe 3 O 4 84 CrO 2 90 [Source: Coey et al, 02]
Copper Oxide Superconductors La 2-x Sr x CuO 4 T c =40K YBa 2 Cu 3 O 6+x T c =90K Tl 1 Ba 2 Ca n-1 CuO 3+2n T c =80K T c =110K T c =125K Note: complexity tends to increase T c
On the slippery slope to High T c MgB 2 K 3 C 60 (Ba,K)BiO 3 the quantum leap Note: x tends to decrease with T c, thus increasing fluctuations
Quasi-2D Superconductors YBa 2 Cu 3 O 6+x MgB 2 T c =90K T c = 39K Note: reduced dimensionlity can enhance pairing
Hydrated Cobaltite T c ~ 5K [Physics World, March 2003] Note: Cobaltite layer has triangular lattice
Carbon Nanoballs & Nanotubes d ~ 1 nm d ~ 10 nm K 3 C 60 T c ~ 10 40 K SWNT, MWNT & bundles T c >> ~1K? Room-temp conductors Low-temp superconductors Reduced dimensionality: a whole new ball game!
Pressure-Induced Superconductivity
Intermetallic Superconductors Complex bandstructure, multiple-sheeted FS CeCoIn 5 ZrZn 2 PrOs 4 Sb 12 T c ~ 2.3K m*~ 1 100 m 0 T c ~ 0.3K SC coexists with FM both pressure-sensitive T c ~ 1.8K m*~ 1 100 m 0
Superconductivity x [BCS theory, 1957] Electrons form pairs Attraction via phonons (lattice) Pairs condense into SC ground-state Condensate is a coherent QM state zero resistance perfect diamagnetism Order Parameter Ψ = Amplitude e i? Phase
High-T c Phase Diagram Temperature insulator m ag n e ti Stripes Strange metal metal Spinon/Holon Stripes Magnetic field s m superconductor QCP? doping chargeon spin-charge separation? How do the electrons pair? spinon