1. Quantum Criticality

2. Condensed Matter Physics (Lee) Complexity causes new physics Range for CMP

3. Classical Phase Transitions Classical example: Phase diagram of H 2 O Notice: 1 st order and 2 nd order transitions

4. Experimental Evidence for Phase Transitions Specific heat

5. The ‘Standard Model’ Fermi Liquid Theory and Metals Non-classical ‘sharing’ of e - in ‘cond. band’ Band theory:

6. … more on metals DOS – density of states c V ~ T,  ~ T 2 Fermi Liquid Theory (Landau): quasi-particles (excitations) in ‘sea’ of fermions Metal-insulator transitions; Mott insulators

7. What is a Quantum Phase Transition? Quantum fluctuations b/c of Heisenberg uncertainty relation: no v=0 at T=0 can cause disruptions Examples: magnetism in metals (FM / AFM) superconductivity (‘pairing’ of electrons) often combined with low dimensionality (constrained motion)

8. Quantum Criticality Steglich 2003 Hertz 1976

9. … more examples Hill 2001,  (T) at high B C V in HF, Steglich

10. … more examples – Heavy Fermions

11. … more examples - HTSC Laughlin etal Adv Phys The bigger picture: HF vs SC phase diagrams Lee, CQP AFM vs SC

12. … more examples: fract. QH Eff. Hall Effect: Lorentz force causes drift F= q(E+v x B) Quantum Hall Effect (1994): Quantized ~ h/e 2 Fractional QHE quantized in non-integer steps

13. Comprehensive Literature List Monographs: In Physics and Electronics ed. JMT Thompson DKK Lee AJ Schofield ‘Metals without Electrons: The Physics of Exotic Quantum Fluids’ Some figures taken from Kittel and from Omar Review Articles: Coleman Schofield Nature 433 2005, Quantum Criticality’ Laughlin, Longzarich, Monthoux, Pines Adv Phys 50(361) Hertz 1976 PRB 14 Research Articles: Nature 425 2003 Doiron-Leyraud et al (Longzarich) Nature 424 2003 Custers (Steglich) The break up of heavy electrons at a QCP Nature 414 2001 Hill Breakdown of FL theory in a cuprate SC Nature 441 2006 Sebastian Nature 441 2006 Erwin ‘When is a metal not a metal?’