nodal/anti-nodal dichotomy and the energy-gaps of a doped mott …corpes07/beitraege/civelli.pdf ·...
TRANSCRIPT
![Page 1: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/1.jpg)
Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott Insulator
arXiv:0704.1486v1 [cond-mat.str-el]
Marcello CivelliApril 2007
Collaborators:
B.G. Kotliar, T.D Stanescu, M. Capone, A. Georges, K. Haule, O. Parcollet
![Page 2: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/2.jpg)
OUTLINEH-Tc Superconductors:
Strongly correlated many-body physics DMFTfundamental anisotropic properties DMFT not enough !
DMFT Cellular –DMFT
2D Hubbard Model: Normal state- Mott transitiond-wave SC statenodal/antinodal dichotomytwo nodal/antinodal energy-scales
![Page 3: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/3.jpg)
H-Tc Superconductors Materials1986 Bednorz and Muller
L a, S r
O
C u
No FL
FL
SC
PG
AF
Tc
T*
x0.150.0 under doped over doped
T
doping0
T
SC
TC
AF
pgFL
FL?
15%
Reservoir:La, Sr
OCu
2D physics! Simple theoretical Hubbard Model
MO
TT in
sula
tor
![Page 4: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/4.jpg)
Strongly Correlated Mott Physics
Kinetic term Local repulsionCompeting!
t U
Uk k
εk εk
εFεF
![Page 5: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/5.jpg)
Why Dynamics so important?e.g. Density of states- Halfilling-vary interaction U
metal
insulator
HOW?
CompetitionHigh-low energy physics!
Density ofStates A(ω)
ω
![Page 6: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/6.jpg)
Dynamical Mean Field Theory
Selfconsistency
AndersonImpurityModel
For a review: A. Georges et al. Rev. Mod. Phys. 68, 13 1996
non-interacting interacting
![Page 7: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/7.jpg)
Remarks DMFT:
What if Σ is k dependent?(finite D..)
DMFT is exact for Dimension =∞:i) Mapping to Impurity model exactii) Local Self-energy Σ≠Σ(k)
exact self-consistency conditionBUT
![Page 8: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/8.jpg)
Experimental Evidence: ARPES
D.S Marshall et al Phys. Rev. Lett. 76, 4841 (1996)
(π,0)
(π,π)
(0,0)
FS
Quasiparticle !
?!
Simple FLbreaks!
Density ofStates A(ω)
ω
ky
kx
QuasiparticlePeak
![Page 9: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/9.jpg)
ARPES in the first quadrant of BZ
hole doped
e- doped
*ARPES:Armitage, Damacelli, Z. Shen, K. Shen, Hussain,Campuzano, Norman, Randeira
A(k,ω→0)= -1/π G(k,ω→0) *
!Quasiparticle
Peak
K-dependent Properties
Local correlations
needed
DMFTNot
Enough !
![Page 10: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/10.jpg)
Describing K-dependence is a fundamental ingredient
Can we improve a LOCAL DMFT?
![Page 11: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/11.jpg)
Cellular Dynamical Mean Field Theory
Selfconsistency
AIM
G. Kotliar et al. Phys. Rev Let. 87, 186401 (2001)
Lattice→ Superlattice
ClusterImpurity
![Page 12: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/12.jpg)
Remarks CDMFT:Good:
Σ=Σ(k) Real SystemsD finite
Price: i) Mapping to Impurity Model not exactii) Self-energy Σ(k) approx.
![Page 13: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/13.jpg)
OUTLINEH-Tc Superconductors:
Strongly correlated many-body physics DMFTfundamental anisotropic properties DMFT not enough !
DMFT Cellular –DMFT
2D Hubbard Model: Normal state- Mott transitiond-wave SC statenodal/antinodal dichotomytwo nodal/antinodal energy-scales
![Page 14: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/14.jpg)
2D Hubbard Model with next-nearest neighbor hopping t’Impurity considered:
CMFT output few parameters: cluster self-energy Σ11, Σ12, Σ13
Σano→ < c1↑ c2↓ >
Preserve square lattice symmetries
Allows to describe d-wave superconductorbroken simmetry
![Page 15: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/15.jpg)
EigenValues of the cluster ImΣµν
kY
(0,0) π
π ΣA ΣB
ΣC ΣA
kx
eigenvaluesh-doped e-doped
![Page 16: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/16.jpg)
All information in the Green’s function
Extracting k-dependence ---- for example Σk
![Page 17: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/17.jpg)
A(k,ω→0)= -1/π G(k,ω)Experiments Theory
Mott transition in the Normal State:hot/cold Spots
![Page 18: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/18.jpg)
CDMFT cluster-local
theory
USE most localquantities to
extract k-quantities!
How do we extract k-quantities?
Truncated Fourier Expansion
e.g.
![Page 19: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/19.jpg)
T.Stanescu et al. Ann. of Phys., Vol. 321, 2006, p.1682 T. Stanescu and G. Kotliar, Phys. Rev. B 74, p.125110
cumulant
Σ1) candidate
2) candidate Mcluster lattice
![Page 20: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/20.jpg)
QMC TEST ON 1D CHAINcourtesy of B. Kyung 0 1 2 3
MGreen’s function
Σ
24 sites!
![Page 21: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/21.jpg)
TEST: insulating state 2D
ω
DOS
M
Σ
ΣStatesIn the
Mott gap!
ΣM Gk(ω)periodize
localK-spacecluster
INSULATOR
![Page 22: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/22.jpg)
Normal state at small doping
Den
sity M
Σ
M works better!
5% doping
MΣ
G
![Page 23: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/23.jpg)
CONSEQUENCE IS A
PSEUDO-GAP STATE!
![Page 24: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/24.jpg)
A
A
C
C
B
A(k,ω)Exp.
Pseudogapδ=0.05t~ 0.015 eV
δ
D.S Marshall et al Phys. Rev. Lett. 76, 4841 (1996)
T.Stanescu et al. Ann. of Phys., Vol. 321, 2006, p.1682
T. Stanescu and G. KotliarPhys. Rev. B 74, p.125110
G=0
poles
![Page 25: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/25.jpg)
Simple case: 2D Hubbard Model t’=0
High doping
Occup.
empty
(0,0)
(π,π)(0,π)
Insulator
Occup.
empty
(0,0)
(π,π)(0,π)
FS Polesin G(k,0+)
G(k,0+)=0!
A(ω)
A(ω)
ω
ω
![Page 26: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/26.jpg)
Line of G(k,0+)=0 at halffillingT.Stanescu et al. cond-mat/0602280
ω
A(ω)
-∆ ∆
ReG(k,0)=0 A(k,ω) is even
Half-filling nholes=1-ne-=1/2 + particle/hole symmetry
A(k,ω) = A(π-k,-ω)
(0,0)
(π,π)(0,π)
ky= π- ky
![Page 27: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/27.jpg)
Natural continuity into a doped Mott insulator
Occup.
empty
(0,0)
(π,π)(0,π)
(0,0)
(π,π)
(0,0)
(π,π)
�����2
Π
�����2
Π
Topol.FS transit.
G(k,0+)=0!
FS Polesin G(k,0+)
A(k,0)
A(k,0)Coexistence of
poles and zeroesBROKEN FS IN A(k,0)
doping
![Page 28: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/28.jpg)
OUTLINEH-Tc Superconductors:
Strongly correlated many-body physics DMFTfundamental anisotropic properties DMFT not enough !
DMFT Cellular –DMFT
2D Hubbard Model: Normal component- Mott transitiond-wave SC statenodal/antinodal dichotomytwo nodal/antinodal energy-scales
![Page 29: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/29.jpg)
d-wave SC with CDMFTKancharla et al. cond-mat/0508205
AIM with d-wave SC bath
SC
Self-consistency
+
+--
![Page 30: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/30.jpg)
d-wave SC state supported !
dSc non-zero Pd=<c↑c↓> in the 2D Hubbard Model
Pd
U=12t, t’=-0.3t
Anomalous Σano≠0, low energynon-momotonic in doping δ
0.25 0.20 0.15 0.10 0.05 0 δ
0
S.S Kancharla et al, cond-mat/0508205M. Civelli et al. cond-mat/0704.1486v1 Very important!
t’=0.0 Kancharla
![Page 31: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/31.jpg)
Σ cluster-Eigenvalues
Im Σ→0Fermi Liquid
superconducting normal
![Page 32: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/32.jpg)
Superconducting Green’s functionNambu’s notation
quasi-particle particle band
kx
ky
0
(π,π)
![Page 33: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/33.jpg)
Periodization procedureNormal component set Σano=0
Better M
5% doping
![Page 34: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/34.jpg)
Periodization procedure2 Σano≠0superconducting component
Only the nodal point is gapless
SpectrumLinearized!
Sum selectsNodal area only
Better Σ!
![Page 35: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/35.jpg)
Periodizing recipe:
Nodal point→ periodize Σ
Anti-nodal point → periodize Mas in the normal state case
In particular d-wave gap
![Page 36: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/36.jpg)
EXPERIMENTS: ARPES SPECTRA Tanaka et al. Science 314, 1910 (2006) doping
Optimal doping
![Page 37: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/37.jpg)
Question: one or two energy-gaps?Tanaka et al. Science 314, 1910 (2006)
See e.g. discussion Science Dec 2006A. J. Millis, Science 314, 1888 (2006).
T. Valla et al. Science 314, 1914 (2006)
e.g. e.g.
![Page 38: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/38.jpg)
-0.2 0 0.2ω/t
0
1
2
3
-0.2 0 0.2ω/t
1
2
3 δ=0.16δ=0.13δ=0.08δ=0.06δ=0.05δ=0.04δ=0.02
-0.2 0 0.2ω/t
0
0.5
1
1.5
2
0 0.08 0.16δ
0
0.05
0.1
0.15
0.2
Znod
Zanod
antinodal
antinodal
nodalΣano
=0AB
C
D
nodal
kx
ky
antinodal(π,π)(0,π)
(0,0)
0 0.08 0.16δ
kanod
knod
kx
2π
π4
2π
Quasi-particle Spectra CDMFT
pseudo-gap!
asimmetry
Σano=0
Σano≠0
![Page 39: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/39.jpg)
At the node I have a quasiparticle
We can attempt a standard Fermi-Liquid Expansion at low energy
vnod
v∆
![Page 40: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/40.jpg)
Nodal velocities- standard Fermi Liquid Analysis
lattice spacing X.J. Zhou et al.,
Nature 423, 398 (2003)
doping
EXP
Tanaka et al. Science 314, 1910 (2006)
![Page 41: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/41.jpg)
K. McElroy et al., Phys. Rev. Lett. 94, 197005 (2005).
Local density of states
![Page 42: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/42.jpg)
0.05 0.1 0.15δ
0
0.05
0.1
∆tot
/t∆
nor/t
∆sc
/t= ( ∆2tot
-∆2nor
)0.5
/t
∆sc
/t= Zanod
Σano/t
AntiNodalGAP
AntiNodalGAP
NodalGAP
NodalGAP
pseudoGAPTanaka et al. Science 314, 1910 (2006)
2 ENERGY GAPS !
PHOTOEMISSION EXP
From quasi-particle spectra we measure gaps!
![Page 43: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/43.jpg)
CONCLUSIONS◊ Used Cellular DMFT to study the strongly
correlated many body systems:H-Tc Superconductor materials
◊ 2D Hubbard Model, Nomal Statea “mottness” region at small doping: PG, arcs FS
◊ Anomalous d-wave SC state - notal/antinodal dichotomy- 2 energy-gaps!: PG+ superconducting gap
![Page 44: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/44.jpg)
Collaborstors:G. Kotliar*Tudor Stanescu~Massimo Capone^A. Georges+
O. Parcollet$
K. Haule*
* Rutgers University, NJ USA~ University of Maryland, College Park, Maryland, USA$ SPhT, CEA Saclay, Paris, France+ Ecole Polytechnique, Palaiseau, France^ University of Rome “La Sapienza” and INFM, Italy
![Page 45: Nodal/Anti-nodal Dichotomy and the Energy-Gaps of a doped Mott …corpes07/BEITRAEGE/civelli.pdf · 2007-05-30 · Microsoft PowerPoint - CORPES07.ppt Author: marcs Created Date:](https://reader034.vdocument.in/reader034/viewer/2022050523/5fa66bb855a6ff594c132030/html5/thumbnails/45.jpg)
SPECIAL THANKS TO:
P. NOZIÈRESE. KATS