E. Z. Kuchinskii

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 Greens 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.We analyze several almost exactly solvable models of the electronic spectrum of two-dimensional systems with well-developed short-range-order dielectric (e.g., antiferromagnetic) or superconducting fluctuations that give rise to an anisotropic pseudogap state in certain segments of the Fermi surface. We develop a recurrence procedure for calculating the one-electron Green’s function that is equivalent to summing all Feynman diagrams. The procedure is based on an approximate ansatz for higher order terms in the perturbation series. We do detailed calculations of the spectral densities and the one-electron density of states. Finally, we analyze the limits of the adopted approximations and some important points concerning the substantiation of these approximations.

Non-Fermi-liquid behavior in the fluctuating gap model: From the pole to a zero of the Green’s function

We analyze the non-Fermi-liquid (NFL) behavior of the fluctuating gap model (FGM) of pseudogap behavior in both one and two dimensions. A detailed discussion of quasiparticle renormalization (Z-factor) is given, demonstrating a kind of marginal Fermi-liquid or Luttinger-liquid behavior and topological stability of the bare Fermi surface (the Luttinger theorem). In the two-dimensional case, we discuss the effective picture of the Fermi surface destruction both in the hot spot model of dielectric (AFM, CDW) pseudogap fluctuations and for the qualitatively different case of superconducting d-wave fluctuations, reflecting the NFL spectral density behavior and similar to that observed in ARPES experiments on copper oxides.

Combinatorial analysis of Feynman diagrams in problems with a Gaussian random field

We construct an algorithm for calculating the generating function for the number of skeleton graphs of the irreducible self-energy and vertex parts in the diagram technique for problems with a Gaussian random field. The exact recursion relation, defining the number of graphs in any order of perturbation theory, and the asymptotics in the high-order limit are found. The results obtained are applied to an analysis of the problem of an electron in a Gaussian random field with a white-noise correlator. A closed integral equation for the one-electron Green’s function, the kernel of which is determined by the generating function, can be constructed in the approximation of equal skeleton graphs for the self-energy part in a given order of perturbation theory. An analysis shows that the approximation considered gives a qualitatively correct description of the tail of the state density in the region of negative energies and, probably, is fully applicable in the most interesting region of strong scattering near the edge of the original band where the asymptotics of the Green’s function and the state density can be determined in the limit of infinitely strong scattering.The algorithm to calculate the generating function for the number of skeleton diagrams for the irreducible self-energy and vertex parts is derived for the problems with Gaussian random fields. We find an exact recurrence relation determining the number of diagrams for any given order of perturbation theory, as well as its asymptotics for the large order limit. These results are applied to the analysis of the problem of an electron in the Gaussian random field with the white-noise correlation function. Assuming the equality of all skeleton diagrams for the self-energy part in the given order of perturbation theory, we construct the closed integral equation for the one-particle Greens function, with its kernel defined by the previously introduced generating function. Our analysis demonstrate that this approximation gives the qualitatively correct form of the localized states tail in the density of states in the region of negative energies and is apparently quite satisfactory in the most interesting region of strong scattering close to the former band-edge, 1 where we can derive the asymptotics of the Greens function and density of states in the limit of very strong scattering.

Superconductivity in the pseudogap state in the hot spot model: The influence of impurities and the phase diagram

We analyze the peculiarities of the superconducting state (s- and d-wave paring) in the model of the pseudogap state induced by Heisenberg antiferromagnetic short-range order spin fluctuations. The model is based on the pattern of strong scattering near hot spots at the Fermi surface. The analysis is based on the microscopic derivation of the Ginzburg-Landau expansion with the inclusion of all Feynman diagrams of perturbation theory for the interaction of an electron with short-range order fluctuations and in the ladder approximation for the scattering by normal (nonmagnetic) impurities. We determine the dependence of the critical superconducting transition temperature and other superconductor characteristics on the pseudogap parameters and the degree of impurity scattering. We show that the characteristic shape of the phase diagram for high-temperature superconductors can be explained in terms of the model under consideration.We analyze the anomalies of superconducting state in the model of pseudogap state induced by fluctuations of short - range order ofdielectric(AFM(SDW) or CDW) type, and based on the scenario ofhot spotsformation on the Fermi surface, with the account of all Feynman graphs for electron interaction with pseudogap fluctuations, leading to strong scattering around thehot spots. We determine the dependence of superconducting critical temperature T_c on the effective width of the pseudogap, correlation length of short - range order and concentration of nonmagnetic impurities. We also discuss possible connection of these results with the general form of the phase diagram of superconducting cuprates.

Superconductivity in the pseudogap state in the hot-spot model: Ginzburg-Landau expansion

Peculiarities of the superconducting state (s and d pairing) are considered in the model of the pseudogap state induced by short-range order fluctuations of the dielectric (AFM (SDW) or CDW) type, which is based on the model of the Fermi surface with “hot spots.” A microscopic derivation of the Ginzburg-Landau expansion is given with allowance for all Feynman diagrams in perturbation theory in the electron interaction with short-range order fluctuations responsible for strong scattering in the vicinity of hot spots. The superconducting transition temperature is determined as a function of the effective pseudogap width and the correlation length of short-range order fluctuations. Similar dependences are derived for the main parameters of a superconductor in the vicinity of the superconducting transition temperature. It is shown, in particular, that the specific heat jump at the transition point is considerably suppressed upon a transition to the pseudogap region on the phase diagram.We analyze properties of superconducting state (for both s-wave and d-wave pairing), appearing on thebackgroundof the pseudogap state, induced by fluctuations ofdielectric(AFM(SDW) or CDW) short -- range order in the model of the Fermi surface withhot spots. We present microscopic derivation of Ginzburg - Landau expansion, taking into account all Feynman diagrams of perturbation theory over electron interaction with this short - range order fluctuations, leading to strong electronic scattering in the vicinity ofhot spots. We determine the dependence of superconducting critical temperature on the effective width of the pseudogap and on correlation length of short - range order fluctuations. We also find similar dependences of the main characteristics of such superconductor close to transition temperature. It is shown particularly, that specific heat discontinuity at the transition temperature is significantly decreased in the pseudogap region of the phase diagram.

Superconductivity in a toy model of the pseudogap state

Abstract We analyze superconducting pairing ( s and d -wave) in a simple exactly solvable model of the pseudogap state induced by fluctuations of short—range order (e.g. antiferromagnetic), based on the model Fermi—surface with “hot”—patches. The average superconducting gap is found to be non zero in the temperature range above the mean-field T c , where superconductivity persists apparently in separated “drops” due to fluctuations. We also calculate the spectral density and the density of states demonstrating that superconducting anomalies there also show up in the region of T > T c , while at T c itself there are no special features due to superconducting transition in a sample as a whole.

Superconductivity in a simple model of the pseudogap state

We analyze superconducting state (both s and d - wave) in a simple exactly solvable model of pseudogap state, induced by short - range order fluctuations (e.g. antiferromagnetic), which is based upon model Fermi - surface withhot patches. It is shown that superconducting energy gap averaged over these fluctuations is non zero even for the temperatures larger than mean - field T_c of superconducting transition in a sample as a whole. For temperatures T>T_c superconductivity apparently exists within separate regions (drops). We study the spectral density and the density of states and demonstrate that superconductivity signals itself in these already for T>T_c, while at T_c itself nothing special happens from this point of view. These anomalies are in qualitative agreement with a number experiments on underdoped cuprates.An analysis is made of characteristics of the superconducting state (s-and d-pairing) using a simple, exactly solvable model of the pseudogap state produced by fluctuations of the short-range order (such as antiferromagnetic) based on a Fermi surface model with “hot” sections. It is shown that the superconducting gap averaged over these fluctuations is nonzero at temperatures higher than the mean-field superconducting transition temperature Tc over the entire sample. At temperatures T > Tc superconductivity evidently exists in isolated sections (“ drops”). Studies are made of the spectral density and the density of states in which superconducting characteristics exist in the range T > Tc however, in this sense the temperature T = Tc itself is no different in any way. These anomalies show qualitative agreement with various experiments using underdoped high-temperature superconducting cuprates.

Superconductivity in the pseudogap state induced by short-order fluctuations

We analyze the anomalies of superconducting state (s and d-wave pairing) in a simple model of pseudogap state, induced by fluctuations of short - range order (e.g. antiferromagnetic), based on the model Fermi surface withhot patches. We derive a system of recursion relations for Gorkovs equations which take into account all diagrams of perturbation theory for electron interaction with fluctuations of short-range order. Then we find superconducting transition temperature and gap behavior for different values of the pseudogap width and correlation lengths of short-range order fluctuations. In a similar approximation we derive the Ginzburg-Landau expansion and study the main physical characteristics of a superconductor close to the transition temperature, both as functions of the pseudogap width and correlation length of fluctuations. Results obtained are in qualitative agreement with a number of experiments on underdoped HTSC-cuprates.Peculiarities of the superconducting state (s and d pairing) are considered in a simple model of the pseudogap state caused by short-range fluctuations (e.g., of the antiferromagnetic type), which is based on the model of a Fermi surface with “hot” regions. A system of Gor’kov recurrence equations is constructed taking into account all diagrams in perturbation theory in the electron interaction with short-range fluctuations. The superconducting transition temperature is determined, and the temperature variation of the energy gap depending on the pseudogap width and the correlation length of short-range fluctuations is analyzed. In a similar approximation, a microscopic derivation of the Ginzburg-Landau expansion is carried out, and the behavior of the main physical parameters of the superconductor near the transition temperature is studied depending on the pseudogap width as well as the correlation length of the fluctuations. The obtained results are in qualitative agreement with a number of experiments with underdoped HTSC cuprates.

Superconductivity in the exactly solvable model of pseudogap state: The absence of self-averaging

The features of the superconducting state are studied in the simple exactly solvable model of the pseudogap state induced by fluctuations of the short-range “dielectric” order in the model of the Fermi surface with “hot” spots. The analysis is carried out for arbitrary short-range correlation lengths ξcorr. It is shown that the superconducting gap averaged over such fluctuations differs from zero in a wide temperature range above the temperature Tc of the uniform superconducting transition in the entire sample, which is a consequence of non-self-averaging of the superconducting order parameter over the random fluctuation field. In the temperature range T>Tc, superconductivity apparently exists in individual regions (drops). These effects become weaker with decreasing correlation length ξcorr; in particular, the range of existence for drops becomes narrower and vanishes as ξcorr → 0, but for finite values of ξcorr, complete self-averaging does not take place.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.

Suppression of superconductivity close to the metal-insulator transition in strongly disordered systems

By means of the self-consistent theory proposed earlier for a metal-insulator transition in strongly disordered systems, which takes into account interelectron interaction effects, the effects of the suppression of the superconducting-transition temperature Tc, caused by the formation of a Coulomb pseudo-gap in the density of states, are studied in a wide interval of disorder values—from a weakly disordered metal to an Anderson insulator. It is shown that the proposed theory gives a satisfactory description of the experimental data for a number of systems that have been studied.