Spin structures and the nature of the pseudogap in cuprates

The spin and charge structures formed in a Hubbard model for a finite two-dimensional cluster have been studied in the mean field approximation. The self-consistent iterative procedure reduces an uncorrelated initial spin distribution into stable structures with characteristic spectral properties. It has been shown that the density of states of the system for any doping has a sharp minimum at the Fermi level, the pseudogap. This means that the pinning of the gap at the Fermi level is not an exclusive property of a superconducting state, but is also typical of a normal state of spin glasses.     

Charge order driven by Fermi-arc instability and its connection with pseudogap in cuprate superconductors

The recently discovered charge order is a generic feature of cuprate superconductors, however, its microscopic origin remains debated. Within the framework of the fermion-spin theory, the nature of charge order in the pseudogap phase and its evolution with doping are studied by taking into account the electron self-energy (then the pseudogap) effect. It is shown that the antinodal region of the electron Fermi surface is suppressed by the electron self-energy, and then the low-energy electron excitations occupy the disconnected Fermi arcs located around the nodal region. In particular, the charge order state is driven by the Fermi-arc instability, with a characteristic wave vector corresponding to the hot spots of the Fermi arcs rather than the antinodal nesting vector. Moreover, although the Fermi arc increases its length as a function of doping, the charge order wave vector reduces almost linearity with the increase of doping. The theory also indicates that the Fermi arc, charge order and pseudogap in cuprate superconductors are intimately related to each other, and all of them emanates from the electron self-energy due to the interaction between electrons by the exchange of spin excitations.     

Mott physics, sign structure, ground state wavefunction, and high-T c superconductivity

In this article I give a pedagogical illustration of why the essential problem of high-T _c superconductivity in the cuprates is about how an antiferromagnetically ordered state can be turned into a short-range state by doping. I will start with half-filling where the antiferromagnetic ground state is accurately described by the Liang-Doucot-Anderson (LDA) wavefunction. Here the effect of the Fermi statistics becomes completely irrelevant due to the no double occupancy constraint. Upon doping, the statistical signs reemerge, albeit much reduced as compared to the original Fermi statistical signs. By precisely incorporating this altered statistical sign structure at finite doping, the LDA ground state can be recast into a short-range antiferromagnetic state. Superconducting phase coherence arises after the spin correlations become short-ranged, and the superconducting phase transition is controlled by spin excitations. I will stress that the pseudogap phenomenon naturally emerges as a crossover between the antiferromagnetic and superconducting phases. As a characteristic of non Fermi liquid, the mutual statistical interaction between the spin and charge degrees of freedom will reach a maximum in a high-temperature ??strange metal phase?? of the doped Mott insulator.     

Reconstructed Fermi surface of underdoped Bi2Sr2CaCu2O(8+δ) cuprate superconductors

The Fermi surface topologies of underdoped samples of the high-T(c) superconductor Bi2Sr2CaCu2O(8+δ) have been measured with angle resolved photoemission. By examining thermally excited states above the Fermi level, we show that the observed Fermi surfaces in the pseudogap phase are actually components of fully enclosed hole pockets. The spectral weight of these pockets is vanishingly small at the magnetic zone boundary, creating the illusion of Fermi "arcs." The area of the pockets as measured in this study is consistent with the doping level, and hence carrier density, of the samples measured. Furthermore, the shape and area of the pockets is well reproduced by phenomenological models of the pseudogap phase as a spin liquid.     

Pseudogap formation in copper oxide superconductors with inclusion of spin and charge fluctuations

The influence of spin and charge fluctuations on the pseudogap formation in cuprate superconductors has been studied using the diagram technique for Hubbard operators. It has been shown that the joint inclusion of the spin and charge fluctuations leads to the formation of “shadow” bands with a strong modulation of the spectral intensity and to a decrease in the density of electronic states at the Fermi level.     

Magnitude of spin and charge density wave amplitudes in underdoped cuprates

Self-consistent calculation of spin (charge) density wave (S(C)DW) order parameters have been performed for bilayered cuprates on the basis of a singlet-correlated band model. Evolution of the Fermi surface in the strongly underdoped regime is described by a two-band approach. The smooth development of the pseudogap formation temperature from underdoped to overdoped states is explained and the Fourier amplitudes 〈s_q〉 (spin) and 〈e_q〉 (charge) modulations are calculated. We have found a maximum of the incommensurability for doping 0.09 ÷ 0.11 holes per copper site.     

Carrier-concentration dependence of the pseudogap ground state of superconducting Bi₂Sr(₂-x)La(x)CuO(₆+δ) revealed by ⁶³,⁶⁵Cu-nuclear magnetic resonance in very high magnetic fields

We report the results of the Knight shift by ?3,??Cu-NMR measurements on single-layered copper-oxide Bi?Sr(?-x)La(x)CuO(?+δ) conducted under very high magnetic fields up to 44 T. The magnetic field suppresses superconductivity completely, and the pseudogap ground state is revealed. The ?3Cu-NMR Knight shift shows that there remains a finite density of states at the Fermi level in the zero-temperature limit, which indicates that the pseudogap ground state is a metallic state with a finite volume of Fermi surface. The residual density of states in the pseudogap ground state decreases with decreasing doping (increasing x) but remains quite large even at the vicinity of the magnetically ordered phase of x ≥ 0.8, which suggests that the density of states plunges to zero upon approaching the Mott insulating 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)     

镓掺杂氧化锌和硫化锌电子结构差异的第一性原理

运用第一性原理进行了相关计算研究Ga掺杂的ZnO和ZnS的电子结构的差异. 结果表明,LDA和LDA+U计算的结果在定性上是一致的. 掺杂Ga以后,ZnO和ZnS的费米能级处均出现杂质态. 掺杂中的ZnO,杂质态在导带是离域的. 掺杂后的ZnS,虽然p态比较离域,但其s态在费米能级处却是局域的. 前线轨道的电荷密度分布也给出了相同的信息. 交换ZnO和ZnS的晶格结构,结果不变. 局域化的Ga-s态是导致掺杂ZnS电学性能差的原因.     

Magnetic domains and stripes in a spin-fermion model for cuprates

Monte Carlo simulations applied to a model of interacting fermions and classical spins show the existence of antiferromagnetic spin domains and charge stripes upon hole doping. The stripes have a filling of approximately 1/2 hole per site, and they separate spin domains with a pi phase shift among them. The observed stripes run either along the x or y axes. No particular boundary conditions or external fields are needed to stabilize these structures. When magnetic incommensurate peaks are observed at momentum pi(1,1-delta), charge incommensurate peaks appear at (0,2delta). The charge fluctuations responsible for the stripe formation also induce a pseudogap in the density of states.     

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.     

Coulomb pairing of like-charged particles with negative effective mass in high-temperature superconductors

Quasi-steady states of pairs of like-charged quasi-particles can be formed because the electronic structure of compounds exhibiting high-temperature superconductivity has various important characteristics: a quasi-two-dimensional electron spectrum, clearly defined nesting of constant-energy lines, and the presence of a logarithmic singularity of the density of states in the immediate vicinity of the Fermi level. Thus, a situation is achieved where, in an extensive region of the Brillouin zone adjacent to the Fermi level, the principal values of the tensor of the reciprocal effective masses have opposite signs and differ appreciably in absolute value. As a result, the nature of the Coulomb correlation interaction between charge carriers of the same sign (holes in p-cuprates) varies: effective attraction may predominate, leading to the formation of long-lived states of relative motion of quasi-particles which form a pair having a quasi-momentum approximately equal to twice the Fermi quasi-momentum typical of this direction (focused pairs). Assuming that the correlation interaction is short-range (screened Coulomb interaction attenuated by filling of states inside the Fermi contour), we determine the energies and envelope functions of the relative motion of a hole pair which correspond to the density-of-states maxima of the pairs attributable to these quasi-steady states. The dependence of these quantities on the polar angle in the plane of the conducting layer reflects the symmetry of the electronic structure of the compound in the normal state and is generally consistent with a mixture of states assigned to s and d types of orbital symmetry. The quasi-steady state as a function of the doping level of the system agrees qualitatively with the concentration dependence of the temperature for the appearance of a pseudogap observed in p-cuprates at below-optimum doping levels. An estimate of the pair concentration above which a gain in correlation energy occurs gives a value which corresponds to the onset of effective pair overlap (for which the characteristic spatial scale is a few or a few tens of interatomic distances).     

Pseudogaps in the 2D Hubbard Model

We study the pseudogaps in the spectra of the 2D Hubbard model using both finite-size and dynamical cluster approximation (DCA) quantum Monte Carlo calculations. At half-filling, a charge pseudogap, accompanied by non-Fermi-liquid behavior in the self-energy, is shown to persist in the thermodynamic limit. The DCA (finite-size) method systematically underestimates (overestimates) the width of the pseudogap. A spin pseudogap is not seen at half-filling. At finite doping, a divergent d-wave pair susceptibility is observed.     

Time reversal symmetry breaking in cuprates induced by the spiral spin order

We propose a new interpretation of the spontaneous time reversal symmetry breaking (TRSB) observed recently in a pseudogap state of cuprates (Kaminsky et al.). It is shown that the TRSB dichroism in an ARPES signal may be related to the local spin spiral structures in the system. It may be caused by a spin-orbit interaction and by spin polarization of electrons at various sections of the Fermi surface in the spiral state. The angular dependence of the dichroism signal is studied in a schematic KKR approximation. Tests are proposed to check the existence of the local spiral spin structure and to distinguish it from the TRSB state with microcurrents constructed by Varma.     

Simple theory of extremely overdoped HTS

We demonstrate the existence of a simple physical picture of superconductivity for extremely over-doped CuO₂ planes. It has all the characteristic features of HTS, such as a high superconducting transition temperature, the \(d_{x^2 - y^2 } \) symmetry of the order parameter, and the coexistence of a single-electron Fermi surface and a pseudogap in the normal state. The values of the pseudogap are calculated for different doping levels. Orbital paramagnetism of preformed pairs is predicted.     

The high temperature superconductivity in cuprates: physics of the pseudogap region

We discuss the physics of the high temperature superconductivity in hole doped copperoxide ceramics in the pseudogap region. Starting from an effective reduced Hamiltonianrelevant to the dynamics of holes injected into the copper oxide layers proposed in aprevious paper, we determine the superconductive condensate wavefunction. We show that thelow-lying elementary condensate excitations are analogous to the rotons in superfluid⁴He. We arguethat the rotons-like excitations account for the specific heat anomaly at the criticaltemperature. We discuss and compare with experimental observations the London penetrationlength, the Abrikosov vortices, the upper and lower critical magnetic fields, and thecritical current density. We give arguments to explain the origin of the Fermi arcs andFermi pockets. We investigate the nodal gap in the cuprate superconductors and discussboth the doping and temperature dependence of the nodal gap. We suggest that the nodal gapis responsible for the doping dependence of the so-called nodal Fermi velocity detected inangle resolved photoemission spectroscopy studies. We discuss the thermodynamics of thenodal quasielectron liquid and their role in the low temperature specific heat. We proposethat the ubiquitous presence of charge density wave in hole doped cuprate superconductorsin the pseudogap region originates from instabilities of the nodal quasielectrons drivenby the interaction with the planar CuO₂ lattice. We investigate the doping dependence of thecharge density wave gap and the competition between charge order and superconductivity. Wediscuss the effects of external magnetic fields on the charge density wave gap andelucidate the interplay between charge density wave and Abrikosov vortices. Finally, weexamine the physics underlying quantum oscillations in the pseudogap region.     

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.     

A model of the T-dependent pseudogap and its competition with superconductivity in copper oxides

Results for pseudogaps are obtained from a band model, where the stability of the gap depends on the amplitudes of vibrational displacements, or magnetic moments, and their coupling to electrons. A one-particle gap is favored by normal thermal excitations of phonons or spin waves. Another gap can be generated by spontaneous waves at lower temperature, if the electronic energy gain overcomes the elastic/magnetic energy needed for increased amplitudes of the oscillations. This state is characterized by charge or spin density waves. The pseudogap has many features in common with the superconducting gap, and the model lends support to the interpretation that the pseudogap is a precursor of, and competes with, superconducting pairing.     

Fermi-liquid ground state in the n-type Pr(0.91)LaCe(0.09)CuO(4-y) copper-oxide superconductor

We report nuclear magnetic resonance studies on the low-doped n-type copper-oxide Pr(0.91)LaCe(0.09)CuO(4-y) (T(c)=24 K) in the superconducting state and in the normal state uncovered by the application of a strong magnetic field. We find that when the superconductivity is removed the underlying ground state is the Fermi liquid state. This result is at variance with that inferred from previous thermal conductivity measurement and appears to contrast with that in p-type copper oxides with a similar doping level where high-T(c) superconductivity sets in within the pseudogap phase. The data in the superconducting state are consistent with the line-node gap model.