A%20New%20Frontier

1
A New Frontier
The quest to discover the self-organizing
principles that govern collective behavior in
matter is a new frontier,
2
(No Transcript)
3
Heavy Electrons and The Riddle of Quantum
CriticalityPiers Coleman, Rutgers CMT, NJ, USA
Cargese, August 2005.
Lectures will be given on the blackboard These
viewgraphs are supplementary.

1. Local moments and the Kondo effect
2. Heavy fermion metals, superconductors and
   magnets.
3. Break-up of the Heavy Electron at a quantum
   critical point.

Supported by NSF DMR
4
Heavy Electrons and The Riddle of Quantum
CriticalityPiers Coleman, Rutgers CMT, NJ, USA
Cargese, August 2005.
5
Detailed notes Local moment physics in heavy
electron systems, P, Coleman, Lectures in the
pysics of highly correlated electron systems VI,
editor F. Mancini, AIP (2002), 79-160,
cond-mat/0206003. General reading Many Body
Physics unfinished frontier, P. Coleman,
cond-mat 2002, Ann Henri Poincare 4, S559-S580
(2003), cond-mat/0307004. Quantum Criticality,
P. Coleman and Andrew Schofield, Nature, 433,
226-229 (2005), cond-mat/0503002. Quantum
Criticality How do Fermi liquids get heavy and
die? , P.C, C. Pépin, Q.Si ,R. Ramazashvili J.
Phys Cond Matt. 13. R723 (2001),
cond-mat/020?001 Schwinger boson approach to
the fully screened Kondo model, J. Rech et al,
cond-mat/0507001.
6
Local Moment Formation and the resistance minimum
7
Mathias and Clogston (1962)
8
Anderson Model of Moment Formation
9
Physics of Local Moments
10
Kondo Physics
Kondo Model
11
The Dense Kondo Lattice and the development of
coherence.
12
(No Transcript)
13
Heavy Fermion Metals Extreme Limit of Mass
Renormalization.
14
Interactions in the Lattice.
15
Kondo Lattice Physics in the 1-1-5 Compounds.
(Courtesy, J. Sarrao)
16
Frustration induced d-electron heavy fermion
system.
(Urano et al 00, Hopkinson and PC, 02)
17
Beyond the comparison of Energy Scales what do
we know about the detailed physics of the
Doniach phase diagram?

• How does the spin form the heavy quasiparticles-
• (and what about the Kondo screening cloud ?
  )
• When pairing develops how does the spin
  participate in the superconducting order
  parameter?
• What other forms of exotic order are possible?
• What is the physics of the Quantum Critical
  Point?

18
How does the spin form the heavy
quasiparticles- and is there a Kondo screening
cloud?
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
What kind of Fermi surface transformation
accompanies the development of antiferromagnetism
?
23

• When pairing develops how does the spin
  participate in the superconducting order
  parameter?

24
T(K)
25
Composite Pairing.
(Andrei and PC, 88 Miranda, PC, Tsvelik 94
Balatsky and Abrahams 95, Andrei, PC,
Kee,Tsvelik 97, Senthil et al 02)
Kondo Effect in the presence of a spin liquid
may drive superconductivity.
26

• What is the physics of the Quantum Critical
  Point?

27
Landau interactions can be turned on
adiabatically, preserving the excitation
spectrum.
Landau, JETP 3, 920 (1957)
28
(No Transcript)
29
When the interaction becomes too large.
what happens?
30
(No Transcript)
31
Quantum Criticality in 2 and 3 dimensions
(Gegenwart et al, 2001)
Anomalous normal state of cuprates
Heavy Electron Quantum Critical Point.
32
Gegenwart et al (2002)
33
Quantum Criticality divergent specific heat
capacity
34
E/T Scaling
Locality
35
Standard Model QSDW

• Moriya, Doniach,Schrieffer (60s)
• Hertz (76)
• Millis (93)

NO E/T SCALING , NO MASS DIVERGENCE IN 3D
36

• Local quantum criticality (1/d- dmft)
• (Si et al, Nature 2001) Spin is the critical
  mode,
• critical fluctuations are only critical in time.
• Deconfined Criticality
• ( Pepin et al, JCM 2001, Senthil et al, Science
  2004) QCP may involve two length-scales, two
  fixed points.
• Crossover to fluid of free spinons at ?1
• Confinement of spinons at ?2 gtgt ?1 (to form a
  valence bond fluid) by tunneling through monopole
  gauge fields configurations

37
Spins condensed
Spins bound to charge as composite fermions
38
Questions on QCP

• Assuming that the WFK paradigm still applies
  then what is the right mean-field theory to
  expand around?
• Assuming that locality is always unstable how
  does the electron mass diverge over the entire
  Fermi surface?
• What is the nature of the strange metal are the
  charge carriers electrons and are the charge
  carriers degenerate and quantum, or classical and
  Boltzmanian?

39
(No Transcript)
40
(No Transcript)
41
T. Namiki, H. Sato, J. Urakawa, H. Sugawara, Y.
Aoki, R. Settai and Y. Onuki, Physica B 281282
359-360 (2000).
42

• What new forms of order become possible?

43
New Forms of Order
Marston and Affleck (89)
Chandra et al (2002)
Hidden order? (Chakravarty et al., Varma 01)
Bernal et al, 2001 29Si NMR
44
Open Questions

• How do quasiparticles form from spins?
• How does spin form a superconducting order
  parameter?
• What is the nature of the QCP
• The Fermi surface transformation?
• What are the virtual quantum fluctuations that
  produce the
• mass renormalization?
• The nature of the coupling to magnetism?
• What new forms of order become possible in Kondo
  spin systems?