Models of the Pseudogap State in Cuprates

We review a certain class of ("nearly") exactly solvable models of electronic spectrum of two-dimensional systems with fluctuations of short range order of "dielectric" (e.g. antiferromagnetic) or "superconducting" type, leading to the formation of anisotropic pseudogap state on certain parts of the Fermi surface. The models are based on recurrence procedure for one- and two-electron Green's functions which takes into account of all Feynman diagrams in perturbation series with the use of the approximate Ansatz for higher-order terms in this series. These models can be applied to calculation of spectral density, density of states and conductivity in the normal state, as well as to calculation of some properties of superconducting state.Comment: M2S-HTCS-VI Conference Paper, 4 pages, 4 figures, using Elsevier style espcrc2.st

Cooper pairs as low-energy excitations in the normal state

We discuss the normal state of a fermionic system in an idealized PSEUDOGAP REGIME, $k_B T_c < k_B T << |\Delta| << E_F$. Stable Cooper pairs induce a pseudogap of width $|\Delta|$ in the fermion energy spectrum. Near two dimensions, we find a Bose-like condensation temperature in this predominantly fermionic system.Comment: 2 pages, LaTeX, espcrc2.sty file included. An outline of a presentation at the Beijing conference M2S-HTSC-V. To be published in Physica

Models of the Pseudogap State of Two-Dimensional Systems

We analyze a number of ``nearly exactly'' solvable models of electronic spectrum of two-dimensional systems with well-developed fluctuations of short range order of ``dielectric'' (e.g. antiferromagnetic) or ``superconducting'' type, which lead to the formation of anisotropic pseudogap state on certain parts of the Fermi surface. We formulate a recurrence procedure to calculate one-electron Green's function which takes into account all Feynman diagrams in perturbation series and is based upon the approximate Ansatz for higher-order terms in this series. Detailed results for spectral densities and density of states are presented. We also discuss some important points concerning the justification of our Ansatz for higher-order contributions.Comment: 22 pages, 15 figures, RevTeX 3.0, Postscript figures attache

Optical Conductivity in a Simple Model of Pseudogap State in Two-Dimensional System

We present calculation of optical conductivity in a simple model of electronic spectrum of two-dimensional system with "hot patches" on the Fermi surface, leading to non Fermi-liquid renormalization of the spectral density (pseudogap) on these patches. It is shown that this model qualitatively reproduces basic anomalies of optical experiments in the pseudogap state of copper oxides.Comment: 12 pages, 6 figures, RevTeX 3.0, Postscript figures attache

Non - Fermi Liquid Behavior in Fluctuating Gap Model: From Pole to Zero of the Green's function

We analyze non - Fermi liquid (NFL) behavior of fluctuating gap model (FGM) of pseudogap behavior in both 1D and 2D. We discuss in detail quasiparticle renormalization (Z - factor), demonstrating a kind of "marginal" Fermi liquid or Luttinger liquid behavior and topological stability of the "bare" Fermi surface (Luttinger theorem). In 2D case we discuss effective picture of Fermi surface "destruction" both in "hot spots" model of dielectric (AFM, CDW) pseudogap fluctuations, as well as for qualitatively different case of superconducting d - wave fluctuations, reflecting NFL spectral density behavior and similar to that observed in ARPES experiments on copper oxides.Comment: 11 pages, 8 figure

Superconductivity in an Exactly Solvable Model of the Pseudogap State: Absence of Self Averaging

We analyze the anomalies of superconducting state within a simple exactly solvable model of the pseudogap state, induced by fluctuations of ``dielectric'' short range order, for the model of the Fermi surface with ``hot'' patches. The analysis is performed for the arbitrary values of the correlation length xi_{corr} of this short range order. It is shown that superconducting energy gap averaged over these fluctuations is non zero in a wide temperature range above T_c - the temperature of homogeneous superconducting transition. This follows from the absence of self averaging of the gap over the random field of fluctuations. For temperatures T>T_c superconductivity apparently appears in separate regions of space (``drops''). These effects become weaker for shorter correlation lengths xi_{corr} and the region of ``drops'' on the phase diagram becomes narrower and disappears for xi_{corr}-->0, however, for the finite values of xi_{corr} the complete self averaging is absent.Comment: 20 pages, 6 figures, RevTeX 3.0, submitted to JETP, minor misprints correcte

Optical conductivity of a quasi-one-dimensional system with fluctuating order

We describe a formally exact method to calculate the optical conductivity of a one-dimensional system with fluctuating order. For classical phase fluctuations we explicitly determine the optical conductivity by solving two coupled Fokker-Planck equations numerically. Our results differ considerably from perturbation theory and in contrast to Gaussian order parameter fluctuations show a strong dependence on the correlation length.Comment: 7 pages, 2 figure