Zheng -Yu Weng IAS, Tsinghua University
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Transcript of Zheng -Yu Weng IAS, Tsinghua University
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Zheng-Yu Weng
IAS, Tsinghua University
Hefei, USTC ICTS --- 2013.11.29
Mott physics, sign structure, and high-temperature superconductivity
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Outline
• Introduction to basic experimental phenomenology of high-Tc cuprates
• High-Tc cuprates as doped Mott insulators /doped antiferromagnets
• Basic principles: Mott physics and sign structure
• Nontrivial examples: (1) one-hole case (2) finite doping and global phase diagram (3) ground state wavefunction
• Summary and conclusion
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High-Tc superconductors
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heavy fermion organic metal
cuprates iron pnictides
CDW
Are the cuprates any special besides high Tc?
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charge localization
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,kkZ
Pauli susceptibility
Korringa behavior
Landau paradigm
ARPES
Sommerfeld constantFermi degenerate temperature
/F F BT E k
Fermi sea
F
typical Fermi liquid behavior:FTT
TTconstTC
s
v
1/1.
KeVEF 000,101~
Fermi surface of copper
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La2-xSrxCuO4 Spin susceptibility (T. Nakano, et al. (1994))
Specific heat (Loram et al. 2001)
NMR spin-lattice relaxation rate (T. Imai et al. (1993))
Pauli susceptibility
Korringa behavior
Sommerfeld constant
Fermi liquid behavior:
TTconstTC
s
v
1/1.
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d-wave superconducting order
T
T0
0AFM
~ J/kB
strong SC fluctuations
strong AF correlations
Cuprate phase diagram
T*TN
Tv
Tc
QCP xFL?
Strange metal: maximal scattering
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Mott insulator doped Mott insulator
Heisenberg model t-J model
FF
F
F
Anderson, Science 1987
Cuprates = doped Mott Insulator
one-band large-U Hubbard model
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Anderson’s RVB theory
RVBˆ BCSGP
i
iiG nnP 1ˆGutzwiller projection
Half-filling:Mott-RVB insulator
doping:Superconductor
Science, 235, 1196 (1987)
d-wave and pseudogap:
Zhang, Gross, Rice, Shiba (1988)Kotliar, Liu (1988) ……
Anderson, et al., J. Phys.: Condens. Mater (2004)
Review:
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Understanding of Mott physics
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Statistical sign structure for Fermion systems
Fermion signs
Landau Fermi Liquid
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( 1 ) Fermi liquid: Fermion signs
( 2 ) Bose condensation:
Off Diagonal Long Rang Order (ODLRO) compensating the Fermion signs Cooper pairing in SC state CDW (“exciton” condensation) SDW (weak coupling) normal state: Fermi liquid
Antiferromagnetic order (strong coupling)
Complete disappearance of Fermion signs!
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hopping superexchange
A minimal model for doped Mott insulators: t-J model
1
iicc
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Phase string effect
D.N. Sheng, Y.C. Chen, ZYW, PRL (1996) ; K. Wu, ZYW, J, Zaanen, PRB (2008)
Single-hole doped Heiserberg model:
+ -
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C. N. Yang (1974) , Wu and Yang (1975)
A
BNonintegrable phase factor:
Emergent gauge force in doped Mott insulators!
“An intrinsic and complete description of electromagnetism”“Gauge symmetry dictates the form of the fundamental forces in nature”
Mutual Chern-Simons gauge theory ZYW et al (1997) (1998)
Kou, Qi, ZYW PRB (2005); Ye, Tian, Qi, ZYW, PRL (2011); Nucl. Phys. B (2012)
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at arbitrary doping, dimensions, temperature
Wu, Weng, Zaanen, PRB (2008)
= total steps of hole hoppings
)(CM = total number of spin exchange processes
)(CMh
)(CMQ = total number of opposite spin encounters
Exact sign structure of the t-J model
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+
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- -
--
--
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-+
For a given path c:
(-) (-)3
K. Wu, ZYW, J. Zaanen, PRB (2008)
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σ
Removing the phase string: σt-J model
no phase string effect!
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• Mott physics = phase string sign structure replacing the Fermion signs
• Strong correlations = charge and spin are long-range entangled
• Sign structure + restricted Hilbert space = unique fractionalization
New guiding principles:
“smooth” paths good for mean-field treatment
singular quantum phase interference
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Consequences of the sign structure
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T
T0
δAF SC FL ?
pseudogap
AF = long-range RVB
localization
“strange metal”
Global phase diagram
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DMRG numerical study
t-J ladder systems
Z. Zhu, H-C Jiang, Y. Qi, C.S. Tian, ZYW, Scientific Report 3, 2586 (2013 );Z. Zhu, et al. (2013); ……
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Effect of phase string effect
σ
no phase string effect
Self-localization of the hole!
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Momentum distribution
without phase string effect
Quasiparticle picture restored!
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t’
t
localization-delocalization transition
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T
T0
δAF SC FL
pseudogap
AF = long-range RVB
localization
“strange metal”
Global phase diagram
AF spin liquiddoping
SC localization
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Delocalization and superconductivity
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localization/AFLRO delocalization/spin liquid
AF spin liquiddoping
SC localization
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Non-BCS elementary excitation in SC state
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Superconducting transition
spin-roton
spinon-vortex
spinon confinement-deconfinement transition
Tc formula Mei and ZYW (2010)
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Spin-rotons
J.W. Mei & ZYW, PRB (2010)
neutron
Raman A1g
164 K
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T
T0
δAF SC FL
pseudogap
AF = long-range RVB
localization
“strange metal”
Global phase diagram
charge-spin long-range entanglement by phase string effect
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T
T0
xAF SC non-FL
pseudogap
strange metal
(Curie-Weiss metal) uniform susceptibility
resistivity
T0
bosonic RVB
0
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Example III : “Parent” ground state
1 2( , ,..., )
| |h d
h
h d
l jh h N
hd l j
z zl l l
z z
jdlh iu
ZYW, New J. Phys. (2011)
1 2( , ,..., ) constanthh Nl l l
short-ranged
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T
T0
δAF SC FL*
pseudogap
AF = long-range RVB
localization
“strange metal”
Global phase diagram
charge-spin long-range entanglement by phase string effect
1 2( , ,..., )
| |h d
h
h d
l jh h N
hd l j
z zl l l
z z
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• Cuprates are doped Mott insulators with strong Coulomb interaction
• New organizing principles of Mott physics: An altered fermion sign structure due to large-U
• Consequences:
(1) Intrinsic charge localization in a lightly doped antiferromagnet (2) Charge delocalization (superconductivity) arises by destroying the AFLRO (3) Localization-delocalization is the underlying driving force for the T=0 phase diagram of the underdoped cuprates
(4) Non-BCS-like ground state wavefunction
Summary
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Thank you For your attention!
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Example III : “Parent” ground state
1 2( , ,..., )
| |h d
h
h d
l jh h N
hd l j
z zl l l
z z
jdlh iu
1 2( , ,..., ) constanthh Nl l l
Superconducting state:
emergent (ghost) spin liquid
AFM state:
ZYW, New J. Phys. (2011)
short-ranged
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Electron fractionalization form