Quantum Criticality

Condensed Matter Physics(Lee)

Complexity causes new physics

Range for CMP

Classical PhaseTransitions

Classical example:Phase diagram of H2O

Notice: 1st order and2nd order transitions

Experimental Evidence forPhase Transitions

Specific heat

The ‘Standard Model’Fermi Liquid Theory and Metals

Non-classical ‘sharing’ of e- in ‘cond. band’

Band theory:

… more on metals

DOS – density of states

cV ~ T, ~ T2

Fermi Liquid Theory (Landau):

quasi-particles (excitations)in ‘sea’ of fermions

Metal-insulator transitions; Mott insulators

What is a Quantum Phase Transition?

Quantum fluctuationsb/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)

Quantum Criticality

Steglich 2003

Hertz 1976

… more examples

Hill 2001, (T) at high B

CV in HF, Steglich

… more examples – Heavy Fermions

… more examples - HTSC

Laughlin etal Adv PhysThe bigger picture: HF vs SC phase diagrams

Lee, CQP AFM vs SC

… more examples: fract. QH Eff.

Hall Effect:Lorentz force causesdrift F= q(E+v x B)

Quantum Hall Effect(1994):Quantized ~ h/e2

Fractional QHEquantized in non-integersteps

Comprehensive Literature List

Monographs:In Physics and Electronics ed. JMT ThompsonDKK 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 QCPNature 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?’