Zheng-Yu Weng
IAS, Tsinghua University
Hefei, USTC ICTS --- 2013.11.29
Mott physics, sign structure, and high-temperature superconductivity
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
High-Tc superconductors
heavy fermion organic metal
cuprates iron pnictides
CDW
Are the cuprates any special besides high Tc?
charge localization
,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
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.
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
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
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:
Understanding of Mott physics
Statistical sign structure for Fermion systems
Fermion signs
Landau Fermi Liquid
( 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!
hopping superexchange
A minimal model for doped Mott insulators: t-J model
1
iicc
Phase string effect
D.N. Sheng, Y.C. Chen, ZYW, PRL (1996) ; K. Wu, ZYW, J, Zaanen, PRB (2008)
Single-hole doped Heiserberg model:
+ -
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)
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
+
-
+
+-
+
+ +
+
+
+
+
++-
- -
--
--
--
-+
For a given path c:
(-) (-)3
K. Wu, ZYW, J. Zaanen, PRB (2008)
σ
Removing the phase string: σt-J model
no phase string effect!
• 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
Consequences of the sign structure
T
T0
δAF SC FL ?
pseudogap
AF = long-range RVB
localization
“strange metal”
Global phase diagram
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); ……
Effect of phase string effect
σ
no phase string effect
Self-localization of the hole!
Momentum distribution
without phase string effect
Quasiparticle picture restored!
t’
t
localization-delocalization transition
T
T0
δAF SC FL
pseudogap
AF = long-range RVB
localization
“strange metal”
Global phase diagram
AF spin liquiddoping
SC localization
Delocalization and superconductivity
-
-+
+
-
-
-
+ +
+
+
-
+
-
-
-
+
+
-
-
-
+ +
+
-
-
+
localization/AFLRO delocalization/spin liquid
AF spin liquiddoping
SC localization
-
-
+
+
-
-
-
+ +
+
-
-
+
Non-BCS elementary excitation in SC state
-
-
+
+
-
-
+
+-
-
+
-
-
+
+ -+-
-
+
+
-
Superconducting transition
spin-roton
spinon-vortex
spinon confinement-deconfinement transition
Tc formula Mei and ZYW (2010)
Spin-rotons
J.W. Mei & ZYW, PRB (2010)
neutron
Raman A1g
164 K
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
T
T0
xAF SC non-FL
pseudogap
strange metal
(Curie-Weiss metal) uniform susceptibility
resistivity
T0
bosonic RVB
0
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
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
• 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
Thank you For your attention!
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
Electron fractionalization form