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Three Discoveries in Underdoped Cuprates

Three Discoveries in Underdoped Cuprates. Giant Nernst effect Z. A. Xu et al., Nature 406 , 486 (2000). “Electron Crystal” in STM M. Vershinin et al., Science 303 , 1995 (2004);. T. Hanaguri, C. Lupien et al., Nature 430 , 1001 (2004). “Thermal metal” in non-SC YBCO

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Three Discoveries in Underdoped Cuprates

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  1. Three Discoveries in Underdoped Cuprates Giant Nernst effect Z. A. Xu et al., Nature 406, 486 (2000) “Electron Crystal” in STM M. Vershinin et al., Science 303, 1995 (2004); T. Hanaguri, C. Lupien et al., Nature 430, 1001 (2004) “Thermal metal” in non-SC YBCO Sutherland et al., cond-mat/050124

  2. Pairing d-wave Pseudogap in Underdoped Cuprates • “Normal” state appears strange and non-Fermi liquid in nature. Strong correlations among its fermionic excitations are apparent. • In contrast, the superconducting state appears BCS-like. Its low energy fermionic excitations are protected by a large d-wave (pseudo)gap. ? dSC • Construct a theory in which a correlated d-wave superconductor • serves as a reference state and the basis for exploration of the • pseudogap. As x is reduced, quantum vortex-antivortex pairs are • progressively admixed into the ground state. Key questions: • How does such superconductor become “normal”? • What are the quantum ground states in natural proximity to • such superconductor? What is the “pseudogap” state? • iii) What is the low energy effective theory within the pseudogap • whose role parallels that of a Fermi liquid in conventional metals?

  3. QED3 Phase Diagram As doping decreases, the number of quantum vortex-antivortex pairs admixed into dSC ground state increases (ns << n0).

  4. Courtesy of N.P. Ong Nernst Effect in HTS Vortex fluctuations in the pseudogap state !! BiSrCaCuO Z. A. Xu et al., Nature 406, 486 (2000)

  5. HTS are Nodal d-wave Superconductors (Phase sensitive exps., ARPES, FT-STS, etc.) Tsuei & Kirtley, 1997 FT-STS measured D ARPES D(q), Mesot -PRL 83,840 (1999) FT-STS from Davis’ group, Nature 422, 520 (2003). Courtesy of J.C. Davis

  6. “Thermal Metal” in YBCO H = 0 p < pSC YBCO : non-superconducting state is a thermal metal LSCO : non-superconducting state is an insulator Sutherland et al., cond-mat/050124 (2005) Courtesy of M. Sutherland

  7. QED3 Phase Diagram As doping decreases, the number of quantum vortex-antivortex pairs admixed into dSC ground state increases (ns << n0). Quantum vortex-antivortex pairs unbind and ODLRO is destroyed (ns = 0). Still, BdG chiral symmetry of d-wave nodal qparticles remains, protecting gapless fermionic excitations !! Chiral symmetry  d-wave amplitude stiffness

  8. QED3 Phase Diagram As doping decreases, the number of quantum vortex-antivortex pairs admixed into dSC ground state increases (ns << n0). Quantum vortex-antivortex pairs unbind and ODLRO is destroyed (ns = 0). Still, BdG chiral symmetry of d-wave nodal qparticles remains protecting gapless fermionic excitations !! Chiral symmetry  d-wave amplitude stiffness BdG chiral symmetry is finally broken, nodal fermions are gapped   AF/SDW

  9. “Electron Crystal” in Underdoped CupratesM. Vershinin et al., Science 303, 1995 (2004); T. Hanaguri, C. Lupien et al., Nature 430, 1001 (2004) Underdoped Ca2-xNaxCuO2Cl2 x=0.08 (I), 0.10 (SC), 0.12 (SC) Courtesy of J.C. Davis

  10. Courtesy of A. Yazdani 150 pS 35 pS Pseudogap State K-Space 100K Modulation along the Cu-O bond direction 500Å x 200 Å Cu-O Vershinin et al.Science 303, 1995 (2004)

  11. “Electron Crystal” in HTS (Vershinin, et al., Hanaguri, Lupien, et al.) Hofstadter Butterfly and Cooper Pair Density-Wave in HTS Hofstadter “Butterfly” Spectrum Dual theory supplies the connection between two phenomena. It leads to Hofstadter “magic fractions” f = p/q for Cooper pair DW at special x: f = p/q = (1 – x)/2 !!

  12. Pseudogap: Charge Insulator, Spin Conductor charge current Charge current cancels: Jc = 0 . Charge center-of-mass is pinned to the lattice: Abrikosov-Hofstadter dual vortex solid. Spin current Js is finite. Pseudogap is a spin (semi) metal: Spinful BdG nodal fermions with long range gauge field correlations -- chiral QED3. e e spin current The system consists of electrons paired in spin singlets (Cooper pairs) + unpaired electrons (BdG nodal fermions). Both carry charge (2e vs. e) but only BdG nodal fermions carry spin. As Cooper pairs and nodal fermions screen each other charges, the spin remains “free”   Wiedemann-Franz law is violated !!

  13. Phase Diagram from Dual Theory of a d-wave Superconductor Antiferromagnet/SDW (Mott ins.) Pairing pseudogap (chiral QED3) dSC Nodal pair DW (chiral QED3) Supersolid Nodal Pair CDW is a charge insulator (Abrikosov-Hofstadter dual solid) but a spin conductor (chiral QED3)  thermal metal

  14. QED3 Phase Diagram

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