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