A phenomenological theory of the anomalous pseudogap phase in underdoped cuprates

The theoretical description of the anomalous properties of the pseudogap phase in the underdoped region of the cuprate phase diagram lags behind the progress in spectroscopic and other experiments. A phenomenological ansatz, based on analogies to the approach to Mott localization at weak coupling in lower dimensional systems, has been proposed by Yang et al (2006 Phys. Rev. B 73 174501). This ansatz has had success in describing a range of experiments. The motivation underlying this ansatz is described and the comparisons with experiment are reviewed. Implications for a more microscopic theory are discussed together with the relation to theories that start directly from microscopic strongly coupled Hamiltonians.

[1]  N. Ong,et al.  Diamagnetism and Cooper pairing above T c in cuprates , 2009, 0906.1823.

[2]  Weakly correlated electrons on a square lattice: Renormalization-group theory , 2000 .

[3]  R. Birgeneau,et al.  Dynamic stripes and resonance in the superconducting and normal phases of YBa2Cu3O6.5 ortho-II superconductor , 2003, cond-mat/0308168.

[4]  D. R. Noakes,et al.  Spin-density-wave antiferromagnetism in chromium alloys , 1994 .

[5]  N. Ong,et al.  Nernst effect in high-Tc superconductors , 2005, cond-mat/0510470.

[6]  H. Alloul,et al.  Correlations between magnetic and superconducting properties of Zn-substituted YBa2Cu3O6+x. , 1991, Physical review letters.

[7]  J. Storey,et al.  Evidence of a precursor superconducting phase at temperatures as high as 180 K in RBa2Cu3O(7-δ) (R=Y, Gd, Eu) superconducting crystals from infrared spectroscopy. , 2011, Physical review letters.

[8]  Y. Kuramoto,et al.  Theory of Successive Magnetic Transitions with Tilting of Moments–Application to NpFeGa5– , 2008 .

[9]  W. Pickett.  Electronic structure of the high-temperature oxide superconductors , 1989 .

[10]  Destruction of the Fermi surface in underdoped high-Tc superconductors , 1997, Nature.

[11]  K. Hradil,et al.  Dispersion of the odd magnetic resonant mode in near-optimally doped Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} , 2007, cond-mat/0701052.

[12]  K. Hradil,et al.  Incommensurate magnetic order and dynamics induced by spinless impurities in YBa(2)Cu(3)O(6.6). , 2010, Physical review letters.

[13]  Warren,et al.  Cu spin dynamics and superconducting precursor effects in planes above Tc in YBa2Cu3O6.7. , 1989, Physical review letters.

[14]  Spinon-holon binding in t − J model , 2004, cond-mat/0408374.

[15]  B. Keimer,et al.  Electronic Liquid Crystal State in the High-Temperature Superconductor YBa2Cu3O6.45 , 2008, Science.

[16]  P. Anderson.  The Resonating Valence Bond State in La2CuO4 and Superconductivity , 1987, Science.

[17]  A. Georges,et al.  Nodal-antinodal dichotomy and the two gaps of a superconducting doped Mott insulator. , 2007, Physical review letters.

[18]  Yang,et al.  Universal correlations between Tc and ns/m (carrier density over effective mass) in high-Tc cuprate superconductors. , 1989, Physical review letters.

[19]  H. Alloul,et al.  89Y NMR evidence for a fermi-liquid behavior in YBa2Cu3O6+x. , 1989, Physical review letters.

[20]  J. Cooper,et al.  Effect of hole doping on the London penetration depth in Bi 2.15 Sr 1.85 CaCu 2 O 8+δ and Bi 2.1 Sr 1.9 Ca 0.85 Y 0.15 Cu 2 O 8+δ , 2009 .

[21]  T. Timusk,et al.  The pseudogap in high-temperature superconductors: an experimental survey , 1999, cond-mat/9905219.

[22]  Hidden order in the cuprates , 2000, cond-mat/0005443.

[23]  Y. Wan,et al.  Model for determining the pairing symmetry and relative sign of the energy gap of iron-arsenide superconductors using tunneling spectroscopy. , 2009, Physical review letters.

[24]  Ranninger,et al.  Superfluid Precursor Effects in a Model of Hybridized Bosons and Fermions. , 1995, Physical review letters.

[25]  K. Tanabe,et al.  Pseudo spin-gap spectrum in the monolayer HgBa2CuO4+δ , 1998 .

[26]  T. M. Rice,et al.  Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials , 1995, Science.

[27]  T. M. Rice,et al.  Breakdown of Landau theory in overdoped cuprates near the onset of superconductivity. , 2008, Physical review letters.

[28]  D. Pines,et al.  Universal behaviour and the two-component character of magnetically underdoped cuprate superconductors , 2008, 0903.1835.

[29]  S. Kawasaki,et al.  Carrier-concentration dependence of the pseudogap ground state of superconducting Bi₂Sr(₂-x)La(x)CuO(₆+δ) revealed by ⁶³,⁶⁵Cu-nuclear magnetic resonance in very high magnetic fields. , 2010, Physical review letters.

[30]  C. Gros,et al.  Gutzwiller–RVB theory of high-temperature superconductivity: Results from renormalized mean-field theory and variational Monte Carlo calculations , 2007, 0707.1020.

[31]  E. Abrahams.  THE EVOLUTION OF HIGH-TEMPERATURE SUPERCONDUCTIVITY: THEORY PERSPECTIVE , 2010 .

[32]  Fu-Chun Zhang,et al.  Quasiparticles in the pseudogap phase of underdoped cuprate , 2008, 0812.3045.

[33]  N. Hussey,et al.  Phenomenology of the normal state in-plane transport properties of high-Tc cuprates , 2008, 0804.2984.

[34]  C. C. Tsuei,et al.  Pairing symmetry in cuprate superconductors , 2000 .

[35]  J. Cooper,et al.  Evidence on the pseudogap and condensate from the electronic specific heat , 2001 .

[36]  K. Müller,et al.  Possible highTc superconductivity in the Ba−La−Cu−O system , 1986 .

[37]  Hayashi,et al.  NMR study of spin dynamics at planar oxygen and copper sites in YBa2Cu4O8. , 1994, Physical review. B, Condensed matter.

[38]  T. M. Rice,et al.  Breakdown of the Landau-Fermi liquid in two dimensions due to umklapp scattering , 2001 .

[39]  Warren,et al.  63Cu NMR shift and linewidth anomalies in the Tc=60 K phase of Y-Ba-Cu-O. , 1990, Physical review. B, Condensed matter.

[40]  M. Cazayous,et al.  Temperature dependence of the gap size near the brillouin-zone nodes of HgBa2CuO4+delta superconductors. , 2008, Physical review letters.

[41]  J. Carbotte,et al.  Effect of pseudogap formation on the penetration depth of underdoped high $T_c$ cuprates , 2009, 0909.3814.

[42]  D. Vollhardt.  Normal He 3 : an almost localized Fermi liquid , 1984 .

[43]  Metzner,et al.  d-wave superconductivity and pomeranchuk instability in the two-dimensional hubbard model , 2000, Physical review letters.

[44]  Weak magnetism and non-Fermi liquids near heavy-fermion critical points , 2003, cond-mat/0305193.

[45]  John A. Wilson,et al.  Elucidation of the origins of transport behaviour and quantum oscillations in high temperature superconducting cuprates , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[46]  T. M. Rice,et al.  Superconductivity generated by coupling to a cooperon in a two-dimensional array of four-leg Hubbard ladders , 2010, 1002.0548.

[47]  L. Balicas,et al.  Correlation between the superconducting transition temperature and anisotropic quasiparticle scattering in Tl2Ba2CuO6+delta. , 2007, Physical review letters.

[48]  J. Roos,et al.  Absence of orbital currents in superconducting YBa2Cu4O8 using a zeeman-perturbed nuclear-quadrupole-resonance technique. , 2011, Physical review letters.

[49]  V. J. Emery,et al.  Importance of phase fluctuations in superconductors with small superfluid density , 1995, Nature.

[50]  J. Carbotte,et al.  Effect of pseudogap formation on the superconducting gap in underdoped cuprates , 2010 .

[51]  M. R. Norman,et al.  The pseudogap: friend or foe of high T c ? , 2005 .

[52]  Emanuel Gull,et al.  Momentum-space anisotropy and pseudogaps: A comparative cluster dynamical mean-field analysis of the doping-driven metal-insulator transition in the two-dimensional Hubbard model , 2010, 1007.2592.

[53]  Tokyo,et al.  Fermi-surface reconstruction and two-carrier model for the Hall effect in YBa2Cu4O8 , 2009, 0912.0175.

[54]  Karyn Le Hur,et al.  Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices , 2008, 0812.1581.

[55]  Fu-Chun Zhang,et al.  Andreev and single-particle tunneling spectra of underdoped cuprate superconductors. , 2010, Physical Review Letters.

[56]  M. Gutzwiller.  Effect of Correlation on the Ferromagnetism of Transition Metals , 1963 .

[57]  Thermodynamic signature of a phase transition in the pseudogap phase of YBa2Cu3Ox high-TC superconductor , 2008, 0806.2128.

[58]  C. Dasgupta,et al.  Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates , 2010, 1007.3287.

[59]  Pines,et al.  Phenomenological model of nuclear relaxation in the normal state of YBa2Cu3O7. , 1990, Physical review. B, Condensed matter.

[60]  Lin Zhao,et al.  Coexistence of Fermi arcs and Fermi pockets in a high-Tc copper oxide superconductor , 2009, Nature.

[61]  Taylor Francis Online,et al.  Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond , 2006, cond-mat/0606771.

[62]  Yukio Tanaka,et al.  Tunnelling effects on surface bound states in unconventional superconductors , 2000 .

[63]  M. Randeria,et al.  Observation of a d -wave nodal liquid in highly underdoped Bi 2 Sr 2 CaCu 2 O 8+ δ , 2009, 0910.1648.

[64]  H. Alloul,et al.  Defects in correlated metals and superconductors , 2007, 0711.0877.

[65]  M. R. Norman,et al.  Phenomenology of the low-energy spectral function in high-T c superconductors , 1998 .

[66]  E. Dagotto.  Correlated electrons in high-temperature superconductors , 1993, cond-mat/9311013.

[67]  Zhang,et al.  Effective Hamiltonian for the superconducting Cu oxides. , 1988, Physical review. B, Condensed matter.

[68]  B. Keimer,et al.  Neutron scattering study of the magnetic phase diagram of underdoped YBa2Cu3O6+x , 2010, 1008.4298.

[69]  M. Imada,et al.  Doped high- T c cuprate superconductors elucidated in the light of zeros and poles of the electronic Green's function , 2010, 1004.2569.

[70]  From semiconductors to superconductors: a simple model for pseudogaps , 1999, cond-mat/9902273.

[71]  H. Alloul,et al.  Superconducting fluctuations, pseudogap and phase diagram in cuprates , 2010, 1006.3165.

[72]  T. Giamarchi,et al.  Orbital currents in extended Hubbard models of high-Tc cuprate superconductors. , 2008, Physical review letters.

[73]  Naoto Nagaosa,et al.  Doping a Mott insulator: Physics of high-temperature superconductivity , 2004, cond-mat/0410445.

[74]  J. Carbotte,et al.  Optical self-energy of superconducting Pb in the terahertz region , 2008, 0803.0974.

[75]  Lynn,et al.  Oxygen dependence of the crystal structure of HgBa2CuO4+ delta and its relation to superconductivity. , 1995, Physical review. B, Condensed matter.

[76]  H. Takagi,et al.  Switching of the gapped singlet spin-liquid state to an antiferromagnetically ordered state in Sr(Cu1-xZnx)2O3 , 1997 .

[77]  Shirane,et al.  Neutron-scattering study of magnetic fluctuations in Zn-substituted YBa2Cu3O6.6. , 1993, Physical review. B, Condensed matter.

[78]  A. Alexandrov,et al.  Condensation of charged bosons hybridised with fermions , 1997 .

[79]  S. Hayden,et al.  Anomalous Criticality in the Electrical Resistivity of La2–xSrxCuO4 , 2009, Science.

[80]  J. Carbotte,et al.  Specific heat across the superconducting dome in the cuprates , 2010, 1008.1257.

[81]  A. Pasupathy,et al.  Electronic Origin of the Inhomogeneous Pairing Interaction in the High-Tc Superconductor Bi2Sr2CaCu2O8+δ , 2008, Science.

[82]  J. Carbotte,et al.  High energy scales in the optical self-energy of the cuprate superconductors. , 2007, Physical Review Letters.

[83]  O. Jepsen,et al.  LDA energy bands, low-energy hamiltonians, t′, t″, t⊥ (k), and J⊥ , 1995 .

[84]  J. Carbotte,et al.  Signatures of Fermi Surface Reconstruction in Raman Spectra of Underdoped Cuprates , 2009, 0910.3577.

[85]  G. Gu,et al.  Emergence of preformed Cooper pairs from the doped Mott insulating state in Bi2Sr2CaCu2O8+δ , 2008, Nature.

[86]  Jhinhwan Lee,et al.  Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states , 2010, Nature.

[87]  Qing-feng Sun,et al.  Resonant Andreev reflection in a normal-metal-quantum- dot-superconductor system , 1999 .

[88]  H. Alloul,et al.  High-field studies of superconducting fluctuations in high-T c cuprates: Evidence for a small gap distinct from the large pseudogap , 2011, 1102.2804.

[89]  J. Carbotte,et al.  Specific heat of underdoped cuprates: Resonating valence bond description versus Fermi arcs , 2009 .

[90]  Inelastic light scattering from correlated electrons , 2006, cond-mat/0607554.

[91]  H. Fukuyama,et al.  The t–J model for the oxide high-Tc superconductors , 2008 .

[92]  Emanuel Gull,et al.  Momentum-selective metal-insulator transition in the two-dimensional Hubbard model: An 8-site dynamical cluster approximation study , 2009 .

[93]  S. Sachdev,et al.  The underdoped cuprates as fractionalized Fermi liquids: transition to superconductivity , 2010, 1010.4567.

[94]  A. Damascelli,et al.  Two gaps make a high-temperature superconductor? , 2007, 0706.4282.

[95]  Yang Qi,et al.  Effective Theory of Fermi Pockets in Fluctuating Antiferromagnets , 2009, 0912.0943.

[96]  B. Vignolle,et al.  Quantum oscillations in an overdoped high-Tc superconductor , 2008, Nature.

[97]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[98]  L. Balicas,et al.  A coherent three-dimensional Fermi surface in a high-transition-temperature superconductor , 2003, Nature.

[99]  H. Eisaki,et al.  How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+δ , 2008, Nature.

[100]  Rice,et al.  Thermodynamics of the gauge field theories of the t-J model. , 1992, Physical review. B, Condensed matter.

[101]  H. Mook,et al.  The structure of the high-energy spin excitations in a high-transition-temperature superconductor , 2004, Nature.

[102]  A. Damascelli,et al.  Structural origin of apparent Fermi surface pockets in angle-resolved photoemission of Bi₂Sr(2-x)La(x)CuO(6+δ). , 2010, Physical review letters.

[103]  T. Maier,et al.  Dynamics of the pairing interaction in the hubbard and t-J models of high-temperature superconductors. , 2008, Physical review letters.

[104]  I. Dzyaloshinskiǐ.  Some consequences of the Luttinger theorem: The Luttinger surfaces in non-Fermi liquids and Mott insulators , 2003 .

[105]  Effect of chemical inhomogeneity in bismuth-based copper oxide superconductors , 2003, cond-mat/0312570.

[106]  H. Takagi,et al.  Nodal Quasiparticles and Antinodal Charge Ordering in Ca2-xNaxCuO2Cl2 , 2005, Science.

[107]  Quantum Impurities in the Two-Dimensional Spin One-Half Heisenberg Antiferromagnet , 2002, Science.

[108]  P. Lee.  From high temperature superconductivity to quantum spin liquid: progress in strong correlation physics , 2007, 0708.2115.

[109]  R. V. Aguilar,et al.  Temporal correlations of superconductivity above the transition temperature in La 2−x Sr x CuO 4 probed by terahertz spectroscopy , 2011, 1110.2097.

[110]  M. Oshikawa,et al.  Topological approach to Luttinger's theorem and the fermi surface of a kondo lattice , 2000, Physical review letters.

[111]  J. Cooper,et al.  Superconducting and normal state energy gaps in Y0.8Ca0.2Ba2Cu3O7−δ from the electronic specific heat , 1997 .

[112]  Theory of underdoped cuprates. , 1995, Physical review letters.

[113]  William F. Brinkman,et al.  Application of Gutzwiller's Variational Method to the Metal-Insulator Transition , 1970 .

[114]  T. M. Rice,et al.  d-Mott phases in one and two dimensions. , 2003, Physical review letters.

[115]  P. Leung.  Low-energy states with different symmetries in the t − J model with two holes on a 32-site lattice , 2002, cond-mat/0201031.

[116]  T. Maier,et al.  Zinc impurities in d-wave superconductors. , 2002, Physical review letters.

[117]  X. Chaud,et al.  Magnetic order in the pseudogap phase of high-Tc superconductors. , 2005, Physical review letters.

[118]  E. Fradkin,et al.  Dynamical layer decoupling in a stripe-ordered high-T(c) superconductor. , 2007, Physical review letters.

[119]  S. Chakravarty.  Quantum oscillations and key theoretical issues in high temperature superconductors from the perspective of density waves , 2011 .

[120]  A. Pasupathy,et al.  Extending Universal Nodal Excitations Optimizes Superconductivity in Bi2Sr2CaCu2O8+δ , 2009, Science.

[121]  B. Vignolle,et al.  Dichotomy in the T-linear resistivity in hole-doped cuprates , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[122]  Lee,et al.  Gap energy and long-range order in the boson-fermion model of superconductivity. , 1989, Physical review. B, Condensed matter.

[123]  G. D. Gu,et al.  Quantum magnetic excitations from stripes in copper oxide superconductors , 2004, Nature.

[124]  M. Ferrero,et al.  Pseudogap opening and formation of Fermi arcs as an orbital-selective Mott transition in momentum space , 2009, 0903.2480.

[125]  J. Carbotte,et al.  Non-Bardeen-Cooper-Schrieffer behavior of optical properties across the phase diagram of cuprate superconductors , 2009 .

[126]  T. Kondo,et al.  Competition between the pseudogap and superconductivity in the high-Tc copper oxides , 2009, Nature.

[127]  J. Cooper,et al.  Electronic specific heat of YBa2Cu3O6+x from 1.8 to 300 K , 1994 .

[128]  Andreev–Saint-James reflections: A probe of cuprate superconductors , 2004, cond-mat/0409225.

[129]  G. Desgardin,et al.  Experimental evidence for strong electron-phonon coupling to selected phonon modes in point-contact spectroscopy of YBa2Cu3O7−δ , 1995 .

[130]  Collin,et al.  89Y NMR probe of Zn induced local moments in YBa2(Cu1-yZny)3O6+x. , 1994, Physical review letters.

[131]  H. Nishimura,et al.  Novel superconducting characteristics and unusual normal-state properties in iron-based pnictide superconductors: 57FeNMR and 75AsNQR/NMR studies in REFeAsO1−y (RE=La, Pr, Nd) and Ba0.6K0.4Fe2As2 , 2009, 0901.4607.

[132]  Canada.,et al.  Comprehensive numerical and analytical study of two holes doped into the two-dimensional t−J model , 1998, cond-mat/9806018.

[133]  Guy Deutscher,et al.  Coherence and single-particle excitations in the high-temperature superconductors , 1999, Nature.

[134]  H. Schulz,et al.  Weakly correlated electrons on a square lattice: A renormalization group theory , 1997, cond-mat/9703189.

[135]  T. M. Klapwijk,et al.  Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion , 1982 .