1. Quantum criticality of Fermi points:

1
(No Transcript)
2
(No Transcript)
3
Outline
1. Quantum criticality of Fermi points
Dirac fermions in d-wave superconductors
2. Quantum criticality of Fermi surfaces
Onset of spin density wave order in the
cuprates
4
Outline
1. Quantum criticality of Fermi points
Dirac fermions in d-wave superconductors
2. Quantum criticality of Fermi surfaces
Onset of spin density wave order in the
cuprates
5
The cuprate superconductors
6
Square lattice antiferromagnet
Ground state has long-range Néel order
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
d-wave superconductivity in cuprates
4 two-component Dirac fermions
12
Nematic order in YBCO
V. Hinkov, D. Haug, B. Fauqué, P. Bourges, Y.
Sidis, A. Ivanov, C. Bernhard, C. T. Lin, and B.
Keimer , Science 319, 597 (2008)
13
Broken rotational symmetry in the pseudogap phase
of a high-Tc superconductor
R. Daou, J. Chang, David LeBoeuf, Olivier
Cyr-Choiniere, Francis Laliberte, Nicolas
Doiron-Leyraud, B. J. Ramshaw, Ruixing Liang, D.
A. Bonn, W. N. Hardy, and Louis Taillefer arXiv
0909.4430
S. A. Kivelson, E. Fradkin, and V. J. Emery,
Nature 393, 550 (1998).
14
d-wave superconductivity in cuprates
15
d-wave superconductivity in cuprates
16
Lattice rotation symmetry breaking
17
Time-reversal symmetry breaking
18
M. Vojta, Y. Zhang, and S. Sachdev, Phys. Rev.
Lett. 85, 4940 (2000) E.-A. Kim, M. J. Lawler, P.
Oreto, S. Sachdev, E. Fradkin, S.A. Kivelson,
Phys. Rev. B 77, 184514 (2008).
19
Discrete symmetry breaking in d-wave
superconductors
4 two-component Dirac fermions
20
Discrete symmetry breaking in d-wave
superconductors
4 two-component Dirac fermions
Ising field theory
21
Ising order and Dirac fermions couple via a
Yukawa term.
Nematic ordering
Time reversal symmetry breaking
M. Vojta, Y. Zhang, and S. Sachdev, Physical
Review Letters 85, 4940 (2000)
22
Ising order and Dirac fermions couple via a
Yukawa term.
Nematic ordering
Time reversal symmetry breaking
M. Vojta, Y. Zhang, and S. Sachdev, Physical
Review Letters 85, 4940 (2000)
23
Expansion in number of fermion spin components Nf
Integrating out the fermions yields an effective
action for the scalar order parameter
Y. Huh and S. Sachdev, Physical Review B 78,
064512 (2008).
24
Expansion in number of fermion spin components Nf
Integrating out the fermions yields an effective
action for the nematic order parameter
E.-A. Kim, M. J. Lawler, P. Oreto, S. Sachdev, E.
Fradkin, S.A. Kivelson, arXiv0705.4099
25
Expansion in number of fermion spin components Nf
Integrating out the fermions yields an effective
action for the T-breaking order parameter
E.-A. Kim, M. J. Lawler, P. Oreto, S. Sachdev, E.
Fradkin, S.A. Kivelson, arXiv0705.4099
26
(No Transcript)
27
Outline
1. Quantum criticality of Fermi points
Dirac fermions in d-wave superconductors
2. Quantum criticality of Fermi surfaces
Onset of spin density wave order in the
cuprates
28
Outline
1. Quantum criticality of Fermi points
Dirac fermions in d-wave superconductors
2. Quantum criticality of Fermi surfaces
Onset of spin density wave order in the
cuprates
29
(No Transcript)
30
Spin density wave theory
31
Spin density wave theory
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
Quantum oscillations
Nature 450, 533 (2007)
38
Quantum oscillations
Nature 450, 533 (2007)
39
(No Transcript)
40
Evidence for connection between linear
resistivity and stripe-ordering in a cuprate with
a low Tc
Linear temperature dependence of resistivity and
change in the Fermi surface at the pseudogap
critical point of a high-Tc superconductor R.
Daou, Nicolas Doiron-Leyraud, David LeBoeuf, S.
Y. Li, Francis Laliberté, Olivier Cyr-Choinière,
Y. J. Jo, L. Balicas, J.-Q. Yan, J.-S. Zhou, J.
B. Goodenough Louis Taillefer, Nature Physics
5, 31 - 34 (2009)
41
(No Transcript)
42
Theory of quantum criticality in the cuprates
43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
(No Transcript)
47
(No Transcript)
48
(No Transcript)
49
(No Transcript)
50
(No Transcript)
51
(No Transcript)
52
(No Transcript)
53
V. Galitski and S. Sachdev, Physical Review B
79, 134512 (2009).
Eun Gook Moon and S. Sachdev, Physical Review B
80, 035117 (2009).
54
Similar phase diagram for CeRhIn5
G. Knebel, D. Aoki, and J. Flouquet,
arXiv0911.5223
55
(No Transcript)
56
(No Transcript)
57
(No Transcript)
58
(No Transcript)
59
(No Transcript)
60
(No Transcript)
61
(No Transcript)
62
Hertz-Moriya-Millis (HMM) theory
63
Hertz-Moriya-Millis (HMM) theory
Ar. Abanov and A.V. Chubukov, Phys. Rev. Lett.
93, 255702 (2004).
64
(No Transcript)
65
(No Transcript)
66
(No Transcript)
67
(No Transcript)
68
Max Metlitski
M. Metlitski and S. Sachdev, to appear Ar.
Abanov, A.V. Chubukov, and J. Schmalian,
Advances in Physics 52, 119 (2003)
Sung-Sik Lee, arXiv0905.4532.
69
(No Transcript)
70
(No Transcript)
71
(No Transcript)
72
(No Transcript)
73
(No Transcript)
74
Y. Huh and S. Sachdev, Phys. Rev. B 78, 064512
(2008).
75
(No Transcript)
76
RG-improved Migdal-Eliashberg theory
77
RG-improved Migdal-Eliashberg theory
78
RG-improved Migdal-Eliashberg theory
79
(No Transcript)
80
(No Transcript)
81
(No Transcript)
82
(No Transcript)
83
RG-improved Migdal-Eliashberg theory
84
(No Transcript)
85
(No Transcript)
86
(No Transcript)
87
(No Transcript)
88
(No Transcript)
89
(No Transcript)
90
(No Transcript)
91
(No Transcript)
92
Theory for the onset of spin density wave order
in metals is strongly coupled in two dimensions
93
(No Transcript)
94
Naturally formulated in route B theory of
fluctuating Fermi pockets
95
VBS and/or nematic
Onset of superconductivity induces confinement
R. K. Kaul, M. Metlitksi, S. Sachdev, and Cenke
Xu, Physical Review B 78, 045110 (2008).