zheng-yu weng institute for advanced study tsinghua university, beijing
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Mott Physics, Sign Structure, and High- Tc Superconductivity. Zheng-Yu Weng Institute for Advanced Study Tsinghua University, Beijing. Newton Institute, Cambridge 2013.9.16. Outline . Introduction to basic experimental phenomenology of high - T c cuprates - PowerPoint PPT PresentationTRANSCRIPT
Zheng-Yu Weng
Institute for Advanced StudyTsinghua University, Beijing
Newton Institute, Cambridge 2013.9.16
Mott Physics, Sign Structure, and High-Tc 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
Mueller Bednorz
Discovery of high-Tc superconductors
1986
,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.
T. Nakano, et al. PRB49, 16000(1994)
F
Fermi liquid Heisenberg model
Uniform spin susceptibility
no indication of Pauli susc.J
Photoemission
Optical measurement
NMR 1/T1
Nernst effect
uniform susceptibility, resistivity
d-wave superconducting order
T
T0
0antiferromagnetic order
~ J/kB
strong SC fluctuations
strong AF correlations
lower pseudogap phase
Underdoped phase diagram
strange metal: maximal scattering
T*TN
Tv
Tc
QCP
Pseudogap:
New quantum stateof matter? A non-Fermi-liquid
0TTc
xFL
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
T
T0
x
~ J/kB
T*TN
Tv
Tc
QCPHalf-filling: Mott insulator x=0
Anderson, Science 1987
Cuprates = doped Mott Insulator
one-band large-U Hubbard model:
Mott Insulator/ antiferromagnet
Mott insulator doped Mott insulator
Heisenberg model t-J modelFF
F
F
hopping superexchange
A minimal model for doped Mott insulators: t-J model
1
iicc
Pure CuO2 plane
H = J Si · Sj
large J = 135 meV
quantum spin S =1/2
Half-filling: Low-energy physics is described by Heisenberg model
Ando et al, PRL 87, 017001 (2001) K. M. Shen et al, PRL 93, 267002 (2004)
ARPES result: A broad peak at x=0charge localizationat low doping
Sebastian, et al., Reports on progress in physics 75, 102501 (2012)
La-Bi2201Peng, et al., arXiv:1302.3017 (2013)
La-Sr-Cu-O
Doping the Mott Insulator/ antiferromagnet
Sebastian, et al., Reports on progress in physics 75, 102501 (2012)
charge localizationLa-Bi2201Peng, et al., arXiv:1302.3017 (2013)
La-Sr-Cu-O
Doping the Mott Insulator/ antiferromagnet
• If charge localization is intrinsic in a doped Mott insulator with AFLRO?
• If charge delocalization (superconductivity) arises by destroying the AFLRO?
• Is localization-delocalization the underlying driving force or the T=0 phase diagram of the underdoped cuprates?
Questions
Outline • Introduction to basic experimental phenomenology of high-
Tc cuprates and 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
Statistical sign structure for Fermion systems
Fermion signs
Landau Fermi Liquid
nodal hypersurface
Nodal hypersurface
Pauli hypersurface
Test particled=2
interacting fermions: fractal nodes F. Kruger and J. Zaanen, (2008)
(1) Fermi liquid: Fermion signs
(2) Off Diagonal Long Rang Order (ODLRO): compensating the Fermion signs Bose condensation
Cooper pairing in SC state CDW (“exciton” condensation) SDW (weak coupling) normal state: Fermi liquid
Antiferromagnetic order (strong coupling)
Complete disappearance of Fermion signs!
Phase string effect
D.N. Sheng, Y.C. Chen, ZYW, PRL (1996)
(3) Single-hole doped Heiserberg model:
＋ －
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
(4) Exact sign structure of the t-J model
+
-
+
+-
+
+ +
+
+
+
+
++-
- -
--
--
--
-+
For a given path c:
(-) (-)3
K. Wu, ZYW, J. Zaanen, PRB (2008)
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)
“smooth” paths good for mean-field treatment
singular quantum phase interference
• 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:
Outline • Introduction to basic experimental phenomenology of high-
Tc cuprates and high-Tc cuprates as doped Mott insulators /doped antiferromagnets
• Basic principles: Sign structure and Mott physics
• Nontrivial examples: (1) one-hole case (2) finite doping and global phase diagram (3) ground state wavefunction
• Summary and conclusion
DMRG numerical study
t-J ladder systems
Z. Zhu, H-C Jiang, Y. Qi, C.S. Tian, ZYW, Scientific Report 3, 2586 (2013 ）
Effect of phase string effect
σ
no phase string effect
Self-localization of the hole!
σ
Removing the phase string: A sign-free model
no phase string effect!
Momentum distribution
without phase string effect
Quasiparticle picture restored!
t’
t
localization-delocalization transition
-
-+
+
-
-
-
+ +
+
+
-
+
D.N. Sheng, et al. PRL (1996); ZYW, et al. PRB (2001)
Theoretical understading of self-localization of the one-hole in 2D
-
Holon localization at low doping: S.P. Kou, ZYW, PRL (2003) T.-P. Choy and Philip Phillips, PRL (2005) P. Ye and Q.R. Wang, Nucl. Phys. B (2013)
destructive quantum phase interferenceleads to self-localization
Outline • Introduction to basic experimental phenomenology of high-
Tc cuprates and high-Tc cuprates as doped Mott insulators /doped antiferromagnets
• Basic principles: Sign structure and Mott physics
• Nontrivial examples: (1) one-hole case (2) finite doping and global phase diagram (3) ground state wavefunction
• Summary and conclusion
Example II: Delocalization and superconductivity
-
-+
+
-
-
-
+ +
+
+
-
+
-
-
-
+
+
-
-
-
+ +
+
-
-
+
localization/AFLRO delocalization/SC spin liquid/RVB!
AF spin liquiddoping
SC localization
-
-
+
+
-
-
-
+ +
+
-
-
+
Non-BCS elementary excitation in SC state
-
-
+
+
-
-
+
+-
-
+
-
-
+
+ -+-
-
+
+
-
Superconducting transition
spin-roton
spinon-vortex
spinon confinement-deconfinement transition
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
Outline • Introduction to basic experimental phenomenology of high-
Tc cuprates and high-Tc cuprates as doped Mott insulators /doped antiferromagnets
• Basic principles: Sign structure and Mott physics
• Nontrivial examples: (1) one-hole case (2) finite doping and global phase diagram (3) ground state wavefunction
• Summary and conclusion
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
• 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
• Non-BCS-like ground state wavefunction
Summary and Conclusion
Thank you For your attention!
P. W. Anderson: Resonating valence bond (RVB) theory (1987) Slave-boson mean-field theory: Baskaran, Zou, Anderson (1988) Kotliar, Liu (1988) …
Gauge theory description: U(1) P.A. Lee, N. Nagaosa, A. Larkin, … SU(2) X.G. Wen, P. A. Lee, … Z2 Sentil, Fisher ……..
Variational wave function: Gros, Anderson, Lee, Randeria, Rice, Trivedi, Zhang; T.K. Lee; Tao Li, …
Fermionic RVB theories
Lee, Nagaosa, Wen, RMP (2006)Anderson, et al., J. Phys.: Condens. Mater (2004)
(5) Hubbard model on bipartite lattices: A general sign structure (Long Zhang & ZYW, 2013 )
Hilbert space: spinons holon (h) doublon (d)
Basic hopping processes in the Hubbard model
Partition function ： t
U J
++ -
+
++ - +
-+
-
（ - ）
half-filling:
Spin-charge separation
three-leg ladder: