Optical conductivity in a simple model of a pseudogap state of a two-dimensional system

Calculations of the optical conductivity are performed in a simple model of the electronic spectrum of a two-dimensional system with “hot regions” on the Fermi surface. The model leads to a strong restructuring of the spectral density (pseudogap) in these regions. It is shown that this model makes it possible to reproduce qualitatively the basic features of the optical measurements in the pseudogap state of high-temperature superconducting cuprates. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 6, 447–452 (25 March 1999)     

Superconductivity in a simple model of the pseudogap state

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 T _c over the entire sample. At temperatures T > T _c 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 > T _c however, in this sense the temperature T = T _c itself is no different in any way. These anomalies show qualitative agreement with various experiments using underdoped high-temperature superconducting cuprates.     

Unified model of pseudogap features of conductivity in HTSCs

The pseudogap phenomenon in underdoped and optimally oxygen-doped high-temperature superconductors (HTSCs) of the Y₁Ba₂Cu₃O_x system is explained from a unified point of view within the model of negative U centers. It is shown that the pseudogap features of conductivity are not related directly to the superconductivity but arise due to the existence of statistical interaction of negative U centers with valence-band holes. Specifically due to this interaction, the hole density in the valence band does not remain constant. It differently changes with temperature for different mutual positions of the Fermi level and the valence band top. These differences lead to different temperature dependences of conductivity for underdoped and optimally doped samples.     

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     

Crossover from a pseudogap state to a superconducting state

This paper deduces that the particular electronic structure of cuprate superconductors confines Cooper pairs to be first formed in the antinodal region which is far from the Fermi surface,and these pairs are incoherent and result in the pseudogap state.With the change of doping or temperature,some pairs are formed in the nodal region which locates the Fermi surface,and these pairs are coherent and lead to superconductivity.Thus the coexistence of the pseudogap and the superconducting gap is explained when the two kinds of gaps are not all on the Fermi surface.It also shows that the symmetry of the pseudogap and the superconducting gap are determined by the electronic structure,and non-s wave symmetry gap favours the high-temperature superconductivity.Why the high-temperature superconductivity occurs in the metal region near the Mott metal-insulator transition is also explained.     

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.     

Quantum dot in the pseudogap Kondo state

We investigate the transport properties of a (small) quantum dot connected to Fermi liquid leads with a power-law density of states (DOS). Such a system, if experimentally realizable, will have interesting physical properties including: (i) non-saturating Coulomb blockade peak widths; (ii) a non-unitary Kondo peak symmetrically placed between Coulomb blockade peaks; (iii) an absence of conductance away from particle-hole symmetry at sufficiently low temperatures; and (iv) evidence of a quantum critical point as a function of dot-lead hopping. These properties are compared and contrasted with one dimensional Luttinger systems exhibiting a power-law “tunneling-DOS”.     

Electronic state in the 2D Hubbard model

Electronic state of the 2D Hubbard model near the half-filling is analyzed by use of the composite operator method. Doping and temperature dependence of density of states show similar behaviors obtained in numerical simulation. The weight of the upper and lower Hubbard bands at the half filling are not evenly distributed in the Brillouin zone, keeping roughly the original band distribution. With hole doping the lower Hubbard band spreads in the whole zone.     

Theory of the pseudogap formation in 2D attracting fermion systems

The two-dimensional fermion system with the indirect Einstein phonon-exchange attraction and additional local four-fermion interaction is considered. It is shown that as a result of the attraction between fermions, the normal phase of such a system is divided into two regions. In one of them, called the pseudogap region, the absolute value of the order parameter exists as essentially nonzero value, but its phase is a random quantity. It is important that in the case of attraction due to the phonons, this abnormal region appears at rather low carrier concentrations, i.e., it decreases appreciably with increasing doping. The relevance of the results obtained for high-temperature superconductors is speculated. Zh. éksp. Teor. Fiz. 114, 605–618 (August 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

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 ξ_corr. It is shown that the superconducting gap averaged over such fluctuations differs from zero in a wide temperature range above the temperature T _c 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>T _c, superconductivity apparently exists in individual regions (drops). These effects become weaker with decreasing correlation length ξ_corr; in particular, the range of existence for drops becomes narrower and vanishes as ξ_corr → 0, but for finite values of ξ_corr, complete self-averaging does not take place.     

Optical conductivity in the t − J model

Frequency dependent conductivity σ(ω) is calculated for the t ? J model by applying the memory function technique in terms of the Hubbard operators. The relaxation rate due to electron scattering on spin and charge dynamical fluctuations is calculated and a generalized Drude law for σ(ω) is obtained. For a model with an incoherent spectrum for one-hole excitations we obtain a universal form for frequency dependence of relaxation rate and conductivity in terms of the scaling function γ(ω/kT). The relaxation rate for the t ? J model is quite different from that one for the conventional Hubbard model in the strong coupling limit where it vanishes due to an exact cancellation of the intraband scattering and virtual interband transitions.     

Resonance state in the 2D attractive Hubbard model

The systematic change of a resonance state with high momenta is studied with increasing particle density in the 2D attractive Hubbard model. Within the conserving self-consistent T-matrix approximation, we present the spectral functions for the one and two particle Green's functions as well as the self-energy. In the small density limit, the resonant state becomes stable and the result from the self-consistent calculations shows a good agreement with that from a simple analytical calculation. As particle density is increased, the resonance state acquires a short lifetime due to the increasing decay into two free particles.     

Spectral density and density of states in a superconductor in an exactly solvable model of a pseudogap state

A simple, exactly solvable model of a pseudogap state induced by fluctuations of dielectric short-range order is used to study the peculiarities of the electronic spectral density and density of states of a superconductor in the model of the Fermi surface with hot patches. The problem is considered for arbitrary values of the short-range order correlation length ξ_corr. It is shown that the absence of self-averaging of the superconducting order parameter over the random field of dielectric fluctuations causes the spectral density and density of states to change significantly. The superconducting character of these quantities persists in a wide temperature range above the temperature T _c of the superconducting transition, which is uniform over the whole sample.     

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)     

Single-hole state in half-filled 2D Hubbard model

Summary We have investigated the ground state of a single hole in the half-filled Hubbard model on a 2D square lattice using the coupled-cluster method. In particular we obtained an analytical expression of the hole energy dispersion function ɛ(k) which is consistent with earlier studies on thet-J model in the strong-coupling limit. An appreciable discrepancy on the hole energy bandwidth is, however, observed between the Hubbard model and thet-J model. We believe that this discrepancy is due to the absence of the three-site interaction term in thet-J model.