Theory of the pseudogap in the elementary excitation spectrum of the normal phase of bilayer cuprates

Solutions of the integral equations for the pseudogap in the elementary excitation spectrum of current carriers in bilayer cuprates are found. In the general case, the pseudogap possesses s + id symmetry, where the s component is determined by the interaction of holes via the phonon field and the d component is due to the superexchange interaction of the copper spins and the Coulomb-repulsion screened holes. The s and d components exhibit different temperature dependences. This fact enabled us to explain the characteristic features of the temperature behavior of the normal-phase spin susceptibility of lightly doped cuprates, specifically, for the compound YBa₂Cu₄O₈ in the entire temperature interval T>T _c . The wave-number dependence of the pseudogap agrees with the photoemission data for Bi₂Sr₂CaCu₂O_8+y . Pis’ma Zh. éksp. Teor. Fiz. 66, No. 8, 533–538 (25 October 1997)     

Effects of a k⃗-dependent Hybridisation on the Fermi surface of an extended d–p Hubbard model

ABSTRACT

The topology of the Fermi surface of an extended d–p Hubbard model is investigated using Green's function technique in a n-pole approximation. The effects of the d–p hybridisation on the Fermi surface are the main focus in the present work. Nevertheless, the effects of doping, Coulomb interaction and hopping to second-nearest-neighbours on the Fermi surface, are also studied. Particularly, it is shown that the crossover from hole-like to electron-like Fermi surface (Lifshitz transition) is deeply affected by the d–p hybridisation. Moreover, the pseudogap present in the low doping regime is also affected by the hybridisation. The results show that both the doping and the hybridisation act in the sense of suppresses the pseudogap. Therefore, the systematic investigation of the Fermi surface topology, shows that not only the doping but also the hybridisation can be considered as a control parameter for both the pseudogap and the Lifshitz transition. Assuming that the hybridisation is sensitive to external pressure, the present results agree qualitatively with recent experimental data for the cuprate Nd-LSCO.     

Anomalous thermodynamics of the doped Mott-Hubbard insulators

The concentration dependence of the entropy of doped Mott-Hubbard insulators has been considered within the t-J model. It has been shown that a change in the type and statistics of charge carriers as compared to the Fermi gas leads to a radical change in the entropy s, in particular, to the giant growth of the entropy upon doping. The quantity ∂s/∂x ≈ k _B is approximately consistent with the experimental data for HTSC cuprates in the pseudogap phase.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

The Ginzburg-Landau expansion in the simple model of a superconductor with a pseudogap

We propose a simple model of the electron spectrum of a two-dimensional system with hot sections on the Fermi surface that significantly transforms the spectral density (pseudogap) in these sections. Using this model, we set up a Ginzburg-Landau expansion for s and d type Cooper pairing and analyze the effect of the pseudogap in the electron spectrum on the main properties of a superconductor. Zh. éksp. Teor. Fiz. 115, 632–648 (February 1999)     

EPR study of exchange interactions in the nonmagnetic Kondo system La1−x CexCu6

The EPR of paramagnetic impurities Gd³⁺ and Mn²⁺ was studied in nonmagnetic Kondo system La_1−x Ce_xCu₆ containing in the 1.6–200 K range. The exchange interaction parameters of gadolinium and manganese ions with conduction electrons, of cerium ions with conduction electrons and with one another, the Kondo temperature of cerium ions, and the temperature behavior of cerium-ion spin-fluctuation rate have been determined. A pseudogap in the density of states at the Fermi level has been detected in the CeCu₆ regular system, which is apparently due to s-f hybridization. This pseudogap can be destroyed by introducing an aluminum impurity, which induces strong conduction-electron scattering. It was also found that RKKY interaction among manganese ions in CeCu_6−y Mn_y is considerably stronger than it is in LaCu_6−y Mn_y, which implies enhancement of nonlocal spin susceptibility due to an f band contribution to conduction-electron states. Fiz. Tverd. Tela (St. Petersburg) 40, 593–599 (April 1998)     

Superconductivity in the presence of fermion condensation

Fermion condensation (FC) is studied within the density functional theory. FC can fulfill the role of a boundary, separating the region of strongly interacting electron liquid from the region of strongly correlated electron liquid. Consideration of the superconductivity in the presence of FC shows that, under certain circumstances, at temperatures above T _c the superconductivity vanishes and the superconducting gap smoothly transforms into a pseudogap. The pseudogap occupies only a part of the Fermi surface, and one that shrinks with increasing temperature and vanishes at T=T*, and the single-particle excitations of the gapped area of the Fermi surface have a width γ ∼(T-T _c ). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 491–496 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Origin of “Hot Spots” in the pseudogap regime of Nd1.85Ce0.15CuO4: An LDA + DMFT + Σk study

The material-specific electronic band structure of the electron-doped high- T _c cuprate Nd_1.85Ce_0.15CuO₄ (NCCO) is calculated in the pseudogap regime using the recently developed generalized LDA + DMFT + Σ _k scheme. The LDA/DFT (density-functional theory within local density approximation) provides model parameters (hopping integral values and local Coulomb interaction strength) for the one-band Hubbard model, which is solved by the DMFT (dynamical mean-field theory). To take pseudogap fluctuations into account, the LDA + DMFT is supplied with an “external” k-dependent self-energy Σ _k that describes interaction of correlated conducting electrons with nonlocal Heisenberg-like antiferromagnetic (AFM) spin fluctuations responsible for the pseudogap formation. Within this LDA + DMFT + Σ _k approach, we demonstrate the formation of pronounced hot spots on the Fermi surface (FS) map in NCCO, opposite to our recent calculations for Bi₂Sr₂CaCu₂O_{8 − δ} (Bi2212), which have produced a rather extended region of the FS “destruction.” There are several physical reasons for this fact: (i) the hot spots in NCCO are located closer to the Brillouin zone center; (ii) the correlation length ξ of AFM fluctuations is longer for NCCO; (iii) the pseudogap potential Δ is stronger than in Bi2212. Comparison of our theoretical data with recent bulk-sensitive high-energy angle-resolved photoemission (ARPES) data for NCCO provides good semiquantitative agreement. Based on that comparison, an alternative explanation of the van Hove singularity at −0.3 eV is proposed. Optical conductivity for both Bi2212 and NCCO is also calculated within the LDA + DMFT + Δ _k scheme and is compared with experimental results, demonstrating satisfactory agreement. The text was submitted by the authors in English.     

ARPES spectral functions and Fermi surface for La<Subscript>1.86</Subscript>Sr<Subscript>0.14</Subscript>CuO<Subscript>4</Subscript> compared with LDA + DMFT + Σ<Subscript>k</Subscript> calculations

The slightly underdoped high-temperature system La_1.86Sr_0.14CuO₄ (LSCO) is studied by means of high-energy high-resolution angular resolved photoemission spectroscopy (ARPES) and the combined LDA + DMFT + Σ _k computational scheme. The corresponding one-band Hubbard model is solved via dynamical mean field theory (DMFT), and the model parameters needed are obtained from first principles in the local density approximation (LDA). An “external” k-dependent self-energy Σ _k describes the interaction of correlated electrons with antiferromagnetic (AFM) pseudogap fluctuations. Experimental and theoretical data clearly show a “destruction” of the LSCO Fermi surface in the vicinity of the (π, 0) point and formation of “Fermi arcs” in the nodal directions. ARPES energy distribution curves as well as momentum distribution curves demonstrate a deviation of the quasiparticle band from the Fermi level around the (π, 0) point. The same behavior of spectral functions follows from theoretical calculations suggesting the AFM origin of the pseudogap state.     

Pseudogap phase formation in the crossover from Bose-Einstein condensation to BCS superconductivity

A phase diagram for a 2D metal with variable carrier density has been derived. It consists of a normal phase, where the order parameter is absent: a so-called “abnormal normal” phase where this parameter is also absent but the mean number of composite bosons (bound pairs) exceeds the mean number of free fermions; a pseudogap phase where the absolute value of the order parameter gradually increases but its phase is a random value, and finally a superconducting (here Berezinskii-Kosterlitz-Thouless) phase. The characteristic transition temperatures between these phases are found. The chemical potential and paramagnetic susceptibility behavior as functions of the fermion density and the temperature are also studied. An attempt is made to qualitatively compare the resulting phase diagram with the features of underdoped high-T _c superconducting compounds above their critical temperature. Zh. éksp. Teor. Fiz. 115, 1243–1262 (April 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor     

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.     

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. The text was submitted by the authors in English.     

The vortex-like excitations detected by Nernst signals in high-Tc superconductors

The nature of the pseudogap state and its relation to the d-wave superconductivity in high-T _c superconductors is still an open issue. The vortex-like excitations detected by the Nernst effect measurements exist in a certain temperature range above superconducting transition temperature T _c, which strongly support that the pseudogap phase is characterized by finite pairing amplitude with strong phase fluctuations and imply that the phase transition at T _c is driven by the loss of long-range phase coherence. We first briefly introduce the electronic phase diagram and pseudogap state of high-T _c superconductors, and then review the results of Nernst effect for different high-T _c superconductors. Related theoretical models are also discussed.     

Ageing of the avalanche angle in immersed granular matter

We have studied the temperature dependent resistivity ρ( T ) of La_2-xSr_xCuO₄ epitaxial thin films in the doping range 0.045 ⩽ x ⩽ 0.25 in pulsed magnetic fields up to 50 T. The zero-field resistivity ρ( T ) of these samples in the pseudogap regime, can be scaled onto one single universal curve in a broad temperature range by using a linear transformation of both temperature and resistivity. The high field data ρ( T ) reveal a metal to insulator transition (MIT) at low temperatures, well into the overdoped regime. For samples having k _F l < 1, with k_F the Fermi wave vector and l the mean free path, this low temperature insulating behavior of the resistivity is described by the variable range hopping conductivity (VRH). For samples with k _F l > 1, the divergence follows ρ( T ) ∼ ln (1/ T ) or a power law, depending upon the Sr-content. We further found that the residual conductivity at the minimum in ρ( T ), appearing due to the MIT, follows a linear behavior with respect to the Sr-content. It is argued that the unusual MIT in compounds with k _F l > 1, is most probably associated with the pseudogap and the behavior of charge stripes at low temperatures. Received 4 January 2002 / Received in final form 7 May 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: liesbet.weckhuysen@fys.kuleuven.ac.be     

Impurity effect on superconducting gap and pseudogap

Co substituted Bi2212 samples of Bi_2.1Sr_1.9Ca(Cu_1−xCo_x)O_8+δ (x = 0, 0.01, 0.02, 0.04, 0.06, and Tc = 85,71,52,35 K) were prepared, and their electronic density states were characterized by a low temperature STM. The experimental results revealed that superconducting gap-like features were rapidly destroyed, while pseudogap-like features were enhanced with increasing impurities, suggesting that the origin of the pseudogap is different from that of a superconducting gap. We suggested a two phase-like model to explain the behavior of a gap map and a gap distribution function. On the other hand, spatial gap and pseudogap inhomogeneity persisted in all Co concentrations. This indicates that the origin of inhomogeneity is not related to in-plane disorder or impurities.     

Polaron effects on superexchange interaction: Isotope shifts of T N , T c , and T* in layered copper oxides

A compact expression has been obtained for the superexchange coupling of magnetic ions via intermediate anions with regard to polaron effects on both magnetic ions and intermediate anions. This expression is used to analyze the main features of the behavior of isotope shifts for temperatures of three types in layered cuprates: the Neel temperatures (T _N ), critical temperatures of transitions to a superconducting state (T _c ), and characteristic temperatures of the pseudogap state of normal phases (T*).     

Photoinduced color centers creation in superionic crystals RbAg 4 I 5

Abstract

A new phenomenon of a reversible photoinduced coloration caused by light irradiation is discovered and investigated in superionic RbAg ₄ I ₅ crystals. The reversible photoinduced absorption is found to be a result of irradiation by light with wavelengths in the region from 420 nm to 450 nm. The proposed mechanism of the discovered effect is associated with ambipolar diffusion of screened by mobile ions optically excited electronic carriers. The processes of color centers creation in superionic crystals RbAg ₄ I ₅ due to additive coloring in iodine vapours, ionic implantation and γ-ray irradiation are considered.     

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     

Tunneling investigations of single crystals of the single-layer cuprate Bi2Sr2CuOz in high magnetic fields

The coexistence of a superconducting gap and a normal-state gap (pseudogap) is observed in tunneling experiments with high-quality single crystals of the single-layer cuprate Bi₂Sr₂CuO_z. At temperatures T< T _c the normal-state gap, whose width is close to that of the super-conducting gap, does not vanish in magnetic fields H>H _c2. The large smearing of the gap structure in the tunneling spectra and the high conductance of tunnel junctions at zero bias voltage are due to the strong angular dependence of the superconducting-and normal-state gaps. The results of the investigations are in good agreement with recently published angle-resolved photoemission data. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 217–222 (10 August 1998)