Pseudogap-state superconductivity in a “hot-point” model: Gor’kov equations

The specific features of the superconducting state (with s and d pairing) are considered in terms of a pseudogap state caused by short-range order fluctuations of the “dielectric” type, namely, antiferromagnetic (spin density wave) or charge density wave fluctuations, in a model of the Fermi surface with “hot points.” A set of recurrent Gor’kov equations is derived with inclusion of all Feynman diagrams of a perturbation expansion in the interaction between an electron and short-range order fluctuations causing strong scattering near hot points. The influence of nonmagnetic impurities on superconductivity in such a pseudogap state is analyzed. The critical temperature for the superconducting transition is determined, and the effect of the effective pseudogap width, correlation length of short-range-order fluctuations, and impurity scattering frequency on the temperature dependence of the energy gap is investigated.     

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.     

Superconductivity in the pseudogap state induced by short-order fluctuations

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 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.     

Disorder and pseudogap in strongly correlated systems: Phase diagram in the DMFT + Σ approach

The influence of disorder and pseudogap fluctuations on the Mott insulator-metal transition in strongly correlated systems has been studied in the framework of the generalized dynamic mean field theory (DMFT + Σ approach). Using the results of investigations of the density of states (DOS) and optical conductivity, a phase diagram (disorder-Hubbard interaction-temperature) is constructed for the paramagnetic Anderson-Hubbard model, which allows both the effects of strong electron correlations and the influence of strong disorder to be considered. Strong correlations are described using the DMFT, while a strong disorder is described using a generalized self-consistent theory of localization. The DOS and optical conductivity of the paramagnetic Hubbard model have been studied in a pseudogap state caused by antiferromagnetic spin (or charge) short-range order fluctuations with a finite correlation length, which have been modeled by a static Gaussian random field. The effect of a pseudogap on the Mott insulator-metal transition has been studied. It is established that, in both cases, the static Gaussian random field (related to the disorder or pseudogap fluctuations) leads to suppression of the Mott transition, broadening of the coexistence region of the insulator and metal phases, and an increase in the critical temperature at which the coexistence region disappears.     

Pseudogap and spin fluctuations in the normal state of the electron-doped cuprates

We present reliable many-body calculations for the t-t(')-t(')-U Hubbard model that explain in detail the results of recent angle-resolved photoemission experiments on electron-doped high-temperature superconductors. The origin of the pseudogap is traced to two-dimensional antiferromagnetic spin fluctuations whose calculated temperature-dependent correlation length also agrees with recent neutron scattering measurements. We make specific predictions for photoemission, for neutron scattering, and for the phase diagram.     

Models of the pseudogap state of two-dimensional systems

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. Zh. éksp. Teor. Fiz. 115, 1765–1785 (May 1999)     

Electronic structure and possible pseudogap behavior in iron based superconductors

Starting from the simplified analytic model of electronic spectrum of iron-pnictogen (chalcogen) high-temperature superconductors close to the Fermi level, we discuss the influence of antiferromagneting (AFM) scattering both for stoichiometric case and the region of possible short-range order AFM fluctuations in doped compounds. Qualitative picture of the evolution of electronic spectrum and Fermi surfaces (FS) for different dopings is presented, with the aim of comparison with existing and future ARPES experiments. Both electron and hole dopings are considered and possible pseudogap behavior connected with partial FS “destruction” is demonstrated, explaining some recent experiments.     

Electron spectrum in high-temperature cuprate superconductors

A microscopic theory for the electron spectrum of the CuO₂ plane within an effective p-d Hubbard model is proposed. The Dyson equation for the single-electron Green’s function in terms of the Hubbard operators is derived and solved self-consistently for the self-energy evaluated in the noncrossing approximation. Electron scattering on spin fluctuations induced by the kinematic interaction is described by a dynamical spin susceptibility with a continuous spectrum. The doping and temperature dependence of electron dispersions, spectral functions, the Fermi surface, and the coupling constant λ are studied in the hole-doped case. At low doping, an arc-type Fermi surface and a pseudogap in the spectral function close to the Brillouin zone boundary are observed. The text was submitted by the authors in English.     

Pseudogap behavior in Bi<Subscript>2</Subscript>Ca<Subscript>2</Subscript>SrCu<Subscript>2</Subscript>O<Subscript>8</Subscript>: Results of the generalized dynamical mean-field approach

Pseudogap phenomena are observed for the normal underdoped phase of different high-T _c cuprates. Among others, the Bi₂Sr₂CaCu₂O_{8 − δ} (Bi2212) compound is one of the most studied experimentally. To describe the pseudogap regime in Bi2212, we use a novel generalized ab initio LDA + DMFT + Σ_k hybrid scheme. This scheme is based on the strategy of one of the most powerful computational tools for real correlated materials: the local density approximation (LDA) + dynamical mean-field theory (DMFT). Conventional LDA + DMFT equations are here supplied with an additional (momentum-dependent) self-energy Σ_k in the spirit of our recently proposed DMFT + Σ_k approach taking into account pseudogap fluctuations. In the present model, Σ_k describes nonlocal correlations induced by short-range collective Heisenberg-like antiferromagnetic spin fluctuations. The effective single-impurity problem of the DMFT is solved by the numerical renormalization group (NRG) method. Material-specific model parameters for the effective x ² − y ² orbital of Cu-3d shell of the Bi2212 compound, e.g., the values of intra-and interlayer hopping integrals between different Cu sites, the local Coulomb interaction U, and the pseudogap potential Δ were obtained within the LDA and LDA + DMFT schemes. Here, we report on the theoretical LDA + DMFT + Σ_k quasiparticle band dispersion and damping, Fermi surface renormalization, momentum anisotropy of (quasi)static scattering, densities of states, spectral densities, and angular-resolved photoemission (ARPES) spectra, taking into account pseudogap and bilayer splitting effects for normal (slightly) underdoped Bi2212 (δ = 0.15). We show that LDA + DMFT + Σ_k successfully describes strong (pseudogap) scattering close to Brillouin zone boundaries. Our calculated LDA + DMFT + Σ_k Fermi surfaces and ARPES spectra in the presence of pseudogap fluctuations are almost insensitive to the bilayer splitting strength. However, our LDA-calculated value of bilayer splitting is rather small to describe the experimentally observed peak-dip-hump structure. The results obtained are in good semiquantitative agreement with various recent ARPES experiments. The article was submitted by the authors in English.     

Mechanism of Pseudogap Detected by Electronic Raman Scattering： Phase Fluctuation or Hidden Order？

We study the electronic Raman scattering in the cuprates to distinguish the two possible scenarios of the pseudogap normal state. In one scenario, the pseudogap is assumed to be caused by phase fluctuations of the preformed Cooper pairs. We find that pair-breaking peaks appear in both the B1g and B2g Raman channels, and they axe smeared and tend to shift to the same energy with the increasing strength of phase fluctuations. Thus both channels reflect the same pairing energy scale, irrespectively of the doping level. In another scenario, the pseudogap is assumed to be caused by a hidden order that competes with the superconducting order. As an example, we assume that the hidden order is the d-density-wave （DDW） order. We find analytically and numerically that in the DDW normal state there is no Raman peak in the B2g channel in a tight-binding model up to the second nearest-neighbor hopping, while the Raman peak in the Big channel reflects the energy gap caused by the DDW order. This behavior is in agreement with experiments in the pseudogap normal state. To gain further insights, we also calculate the Raman spectra in the DDW＋SC state. We study the doping and temperature dependence of the peak energy in both channels and find a two-gap behavior, which is in agreement with recent Raman experiments. Therefore, our results shed light on the hidden order scenario for the pseudogap.     

Reconstruction of the Fermi surface in the pseudogap state of cuprates

Reconstruction of the Fermi surface of high-temperature superconducting cuprates in the pseudogap state is analyzed within a nearly exactly solvable model of the pseudogap state, induced by short-range order fluctuations of the antiferromagnetic (AFM), spin-density wave (SDW), or a similar charge-density wave (CDW) order parameter, competing with the superconductivity. We explicitly demonstrate the evolution from “Fermi arcs” (on the “large” Fermi surface) observed in the ARPES experiments at relatively high temperatures (when both the amplitude and phase of the density waves fluctuate randomly) towards the formation of typical “small” electron and hole “pockets,” which are apparently observed in the de Haas-van Alphen and Hall resistance oscillation experiments at low temperatures (when only the phase of the density waves fluctuate and the correlation length of the short-range order is large enough). A qualitative criterion for the quantum oscillations in high magnetic fields to be observable in the pseudogap state is formulated in terms of the cyclotron frequency, the correlation length of fluctuations, and the Fermi velocity. The text was submitted by the authors in English.     

Commensurate spin dynamics in the superconducting state of an electron-doped cuprate superconductor

We report neutron scattering studies on two single crystal samples of the electron-doped (n-type) superconducting (SC) cuprate Nd2-xCexCuO4 (x=0.15) with T(c)=18 and 25 K. Unlike the hole-doped (p-type) SC cuprates, where incommensurate magnetic fluctuations commonly exist, the n-type cuprate shows commensurate magnetic fluctuations at the tetragonal (1/2 1/2 0) reciprocal points both in the SC and in the normal state. A spin gap opens up when the n-type cuprate becomes SC, as in the optimally doped p-type La2-xSrxCuO4. The gap energy, however, increases gradually up to about 4 meV as T decreases from T(c) to 2 K, which contrasts with the spin pseudogap behavior with a T-independent gap energy in the SC state of p-type cuprates.     

Influence of the Pseudogap on the Inelastic Neutron Scattering Spectra of the Underdoped Lanthanum Cuprate

The influence of pseudogap on the inelastic neutron scattering spectra of the underdoped lanthanum cuprate is studied on the basis of the model which incorporates both the superconducting state and pseudogap state.It is found that the striking effects of the influence of the pseudogap on the incommensurability of the spin excitation spectrum are that in the superconducting state the pseudogap makes the intensity of the incommensurate peak increase,in the normal state the pseudogap not only makes the intensity of the incommensurate peak increase,but also sharpens the incommensurate peak and increases incommensurability.     

Sources of 1/F noise in gallium arsenide IMPATT diodes

The quasistatic approximation is used to analyze 1/F noise in IMPATT diodes in the static and dynamic (self-oscillating) modes. Sources of 1/F noise are defined in accordance with the fluctuator model: allowance is made for fluctuations of the charge of traps and fluctuations of the electron drift velocity caused by their scattering by traps and metastable neutral centers. It is shown that the fluctuations of the voltage across the diode and the fluctuations of the oscillation frequency are mainly determined by the fluctuations of the trap charge, while the fluctuations of the oscillation amplitude are determined by scattering by neutral centers. A method is developed to determine the intensity of noise sources using the results of measurements of the fluctuations in the static and dynamic modes of IMPATT diodes and a method of checking the model as a whole is checked. Experimental results are presented and these show satisfactory agreement with the calculations. Zh. Tekh. Fiz. 67, 65–70 (August 1997)     

Thermodynamics and phase diagram of high temperature superconductors

Thermodynamic quantities are derived for superconducting and pseudogap regimes by taking into account both amplitude and phase fluctuations of the pairing field. In the normal (pseudogap) state of the underdoped cuprates, two domains have to be distinguished: near the superconducting region, phase correlations are important up to temperature T(phi). Above T(phi), the pseudogap region is determined only by amplitudes, and phases are uncorrelated. Our calculations show excellent quantitative agreement with specific heat and magnetic susceptibility experiments on cuprates. We find that the mean field temperature T0 has a similar doping dependence as the pseudogap temperature T(*), whereas the pseudogap energy scale is given by the average amplitude above T(c).     

Nernst coefficient and magnetoresistance in high-T(c) superconductors: the role of superconducting fluctuations

In high-T(c) cuprates, the Nernst coefficient (nu) as well as the magnetoresistance (Deltarho/rho) increases drastically below the pseudogap temperature, T(*), which attracts much attention as a key phenomenon in the pseudogap region. We study these transport phenomena in terms of the fluctuation-exchange+T-matrix approximation. In this present theory, the d-wave superconducting (SC) fluctuations, which are mediated by antiferromagnetic (AF) correlations, become dominant below T(*). We especially investigate the vertex corrections both for the charge current and the heat one to keep the conservation laws. As a result, the mysterious behaviors of nu and Deltarho/rho are naturally explained as the reflection of the enhancement of the SC fluctuation, without assuming thermally excited vortices. The present result suggests that the pseudogap phenomena are well described in terms of the Fermi liquid with AF and SC fluctuations.     

Exactly solvable toy model for the pseudogap state

We present an exactly solvable toy model which describes the emergence of a pseudogap in an electronic system due to a fluctuating off-diagonal order parameter. In one dimension our model reduces to the fluctuating gap model (FGM) with a gap that is constrained to be of the form , where A and Q are random variables. The FGM was introduced by Lee, Rice and Anderson [Phys. Rev. Lett. 31, 462 (1973)] to study fluctuation effects in Peierls chains. We show that their perturbative results for the average density of states are exact for our toy model if we assume a Lorentzian probability distribution for Q and ignore amplitude fluctuations. More generally, choosing the probability distributions of A and Q such that the average of vanishes and its covariance is , we study the combined effect of phase and amplitude fluctuations on the low-energy properties of Peierls chains. We explicitly calculate the average density of states, the localization length, the average single-particle Green's function, and the real part of the average conductivity. In our model phase fluctuations generate delocalized states at the Fermi energy, which give rise to a finite Drude peak in the conductivity. We also find that the interplay between phase and amplitude fluctuations leads to a weak logarithmic singularity in the single-particle spectral function at the bare quasi-particle energies. In higher dimensions our model might be relevant to describe the pseudogap state in the underdoped cuprate superconductors. Received 15 March 2000     

Exact results for the crossover from Gaussian to non-Gaussian order parameter fluctuations in quasi-one-dimensional electronic systems

The physics of quasi-one-dimensional Peierls systems is dominated by order parameter fluctuations. We present an algorithm which allows us for the first time to exactly calculate physical properties of the electrons gas coupled to classical order parameter fluctuations. The whole range from the Gaussian regime dominated by amplitude fluctuations to the non-Gaussian regime dominated by phase fluctuations is accessible. Our results provide insight into the "pseudogap" phenomenon occurring in underdoped high- T(c) superconductors, quasi-one-dimensional organic conductors, and liquid metals.