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High- T c superconductivity in doped antiferromagnets (II). Zheng-Yu Weng Institute for Advanced Study Tsinghua University, Beijing. KITPC AdSCFT /CM Nov. 5, 2010. Outline. Introduction: High- T c phenomenology Pseudogap phenomenon
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High-Tc superconductivity in doped antiferromagnets (II) Zheng-Yu Weng Institute for Advanced Study Tsinghua University, Beijing KITPC AdSCFT/CM Nov. 5, 2010
Outline • Introduction: High-Tc phenomenology Pseudogap phenomenon • High-Tccuprates as doped Mott insulators /doped antiferromagnets • Pseudogap state as an RVB state and the slave-boson approach • Reduced fermion signs in doped Mott insulator: emergent mutual Chern-Simons gauge fields • Conclusion
Cuprates = doped Mott Insulator T Anderson, Science 1987 ~ J/kB T0 TN T* Tv Half-filling: Mott insulator Tc x=0 QCP x
Mottness and intrinsic guage invariance Conservations of spin and charge separately: Spin-charge separation and emergent gauge fields in low-energy action !
Finite doping U(1) symmetry
d-wave Baskaran, Zou, Anderson (1988) Zhang,Gros, Rice, Shiba (1988) Kotliar, Liu (1988) … Slave-boson mean-field theory
Fermionic RVB theories basic wave function Gutzwiller projection 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, … Lee, Nagaosa, Wen, RMP (2006)
Pseudogap phase T ~ J/kB strange metal: incoherent Pseudogap: An RVB state? T0 upper pseudogap phase strong AF correlations TN lower pseudogap phase T* Tv strong SC fluctuations Tc x QCP antiferromagnetic order d-wave superconducting order
PLAN • Introduction: High-Tc phenomenology Pseudogap phenomenon • High-Tccuprates as doped Mott insulators /doped antiferromagnets • Pseudogap state as an RVB state and the slave-boson approach • Reduced fermion signs in doped Mott insulator: Pseudogap - intrinsic mutual Chern-Simons gauge fields • Conclusion
Absence of fermion signs at half-filling Mott insulator Heisenberg model Total disapperance of fermion signs!
T Ground state at half-filling doping X=0 Bosonic RVB wavefunction Liang, Doucot, Anderson, PRL (1988) A spin singlet pair
Reduced fermion signs in doped case: single hole case - + + + + - - + - - + + - - + loop c Singular Phase String Effect! Phase String Effect
Phase string captured by mutual Chern-Simons fields flux tube anyonsigns Wilczek: Anyons (1982) Chern-Simons gauge field Phase string signs Mutual Chern-Simons (semion) gauge field
Exact mapping between the phase string and a mutual Chern-Simons gauge field description - + - Z.Y. Weng, et al PRB (1997); PRL (1998)
t-J model in the phase string representation bosonic hopping superexchange RVB order parameter U(1)XU(1) gauge invariance
Phase string model - Effective theory spinon part holon part mutual duality/mutual Chern-Simons gauge structure
Effective Hamiltonian for the pseudogap phase t-J model: exact sign structure + bosonic RVB Phase string model Emergent new model/physics at mutual Chern-Simons Electron fractionalization
One-dimensional case (open BC) no sign problem! phase string spinon holon
1D case i Correct correlation functions Weng, et al. (1997)
Effective Hamiltonian for the pseudogap phase t-J model: exact sign structure + bosonic RVB Phase string model Emergent new model/physics at mutual Chern-Simons Electron fractionalization
Half-filling Schwinger boson representation RVB condensation T<T0 quantum fluctuations RVB pairing High-temperature series expansion
Upper pseudogap phase (UPP) at finite doping ZhengchengGu & ZYW, PRB (2005)
Spinchannel - continued ZhengchengGu & ZYW, PRB (2005) NMR spin relaxation rates YBa2Cu3O7-y
Chargechannel RVB disappears a lot of unpaired spins excited A. Sanander-Syro, et al. PRB (2004) Y.S. Lee et al. PRB 72, (2005) ZhengchengGu & ZYW (2007)
Pseudogap phase T ~ J/kB strange metal: incoherent T0 upper pseudogap phase strong AF correlations lower pseudogap phase TN T* strong SC fluctuations Tv Tc x QCP d-wave superconducting order
electromagnetic field Lower pseudogap phase (LPP) π -π Bose condensation Generalized Ginzburg-Landau equaion
B v -T Spinon vortices Nernst effect Xu et al., Nature (2000), Wang et al., PRB (2001). Xiaoliang Qi, ZYW (2006)
Mutual Duality π-flux π-flux duality spinon chargon
Spinchannel π WeiqiangChen & ZYW, PRB (2005) S=1 excitation 0 0.05 0.125 C. Stock, et al. PRB (2004) 0.2
Lower pseudogap phase (LPP) Z.C. Gu and Z. Y. Weng (2007)
Pseudogap phase T ~ J/kB strange metal: incoherent Pseudogap: Mutual Chern-Simons? T0 upper pseudogap phase strong AF correlations TN lower pseudogap phase T* Tv strong SC fluctuations Tc x QCP antiferromagnetic order d-wave superconducting order
Spinon confinement in SC The low-lying excitations are degenerate Spin-Rotons as paired spinon-vortices: S=1 S=0 Jiawei, ZYW (2009) Spin-Charge entanglement
Superconducting phase transition Tc formula
“resonant mode” in neutron scattering Raman scattering in A1g channel
Superconducting transition spinon confinement-deconfinement transition Spin-rotons new elementary excitations in SC phase
Predictions spinon-vortex magnetic vortex with free moment Zn impurity dissipationless conserved spin Hall effect
Zinc impurity single spinon Xiaoliang Qi and ZYW (2005)
Probing single spinon: S=1/2 at a magnetic vortex core single spinon-vortex Muthukumar & ZYW (2002) W. Halperin (2003)
Lattice gauge field theoryPeng Ye, C.S. Tian, X.L. Qi, and ZYW, arXiv1007.2507Supeng Kou, X.L. Qi and ZYW, PRB (2005)
Nonlocal order parameters probing confinement - deconfinement of holons spinons
Quantitative results of two limits: dual! antiferromagnetic phase superconducting phase holon confinement spinon confinement
Intermediate δ: Bose insulating phase non-analytic; signaling spinondeconfinement QCP spinondeconfinement holondeconfinement non-analytic; signaling holondeconfinement QCP
Straightforward application of composition rule: BI phase is indeed insulating! dual!
Sumary of the phase string approach T ~ J/kB strange metal: incoherent Electron fractionalization with emergent mutual Chern-Simons T0 TN T* Tv Tc x QCP antiferromagnetic order BI d-wave superconducting order Low-T instabilities
Charge-spin entanglement induced by phase string - + + + + - - + - + + + - - + + + + + + + + - + + + AFM state Nagaoka state an extreme case ignoring the superexchange energy + - - + + + RVB/Pseudogap - - + + - minimizing the total exchange and kinetic energy + - -
Sumary of the phase string approach T ~ J/kB strange metal: incoherent Electron fractionalization with emergent mutual Chern-Simons T0 TN T* Tv ? Tc QP coherence x QCP antiferromagnetic order d-wave superconducting order Low-T instabilities