Demonstration of a Robust Pseudogap in a Three-Dimensional Correlated Electronic System

We outline a partial-fractions decomposition method for determining the one-particle spectral function and single-particle density of states of a correlated electronic system on a finite lattice in the non self-consistent T-matrix approximation to arbitrary numerical accuracy, and demonstrate the application of these ideas to the attractive Hubbard model. We then demonstrate the effectiveness of a finite-size scaling ansatz which allows for the extraction of quantities of interest in the thermodynamic limit from this method. In this approximation, in one or two dimensions, for any finite lattice or in the thermodynamic limit, a pseudogap is present and its energy diverges as T _c is approached from above; this is an unphysical manifestation of using an approximation that predicts a spurious phase transition in one or two dimensions. However, in three dimensions one expects the transition predicted by the approximation to represent a true continuous phase transition, and whether or not a pseudo gap exists in the thermodynamic limit in three dimensions remains an open question. We have applied our method to the attractive Hubbard model on a three-dimensional simple cubic lattice, and find, similar to previous work, that for intermediate coupling a prominent pseudogap is found in the single-particle density of states, and this gap persists over a large temperature range. In addition, we also show that for weak coupling (an on-site Hubbard energy equal to one quarter the bandwidth) a pseudogap is also present. The pseudogap energy at the transition temperature is almost a factor of three larger than the T = 0 BCS gap for intermediate coupling, whereas for weak coupling the pseudogap and T = 0 BCS gap energies are essentially equal. These results show that a pseudogap due to superconducting fluctuations occurs in three dimensions even in the weak-coupling limit.     

Superconductivity with Local, Short-Range Attraction

The approaches to short coherence length superconductors based on theconcepts of local electron pairing are discussed. The properties of systemswith intersite pairing, the nature of the BCS-Bose superconductivitycrossover as well as a two-component model of local pairs and fermions areanalyzed. The question of a pseudogap and a possible scenario of crossoversin high temperature superconductors are briefly examined.     

Two-Dimensional Pseudogap Effects of an Ultracold Fermi Gas in the BCS-BEC Crossover Region

We investigate pseudogap phenomena originating from pairing fluctuations in the BCS-BEC crossover regime of a two-dimensional Fermi gas in a harmonic trap. Including pairing fluctuations within a T-matrix theory and effects of a trap within the local density approximation, we calculate the local density of states (LDOS) at the superfluid phase transition temperature T _c. In the weak-coupling regime, we show that the pseudogap already appears in LDOS around the trap center. The spatial region where the pseudogap can be seen in LDOS becomes wider for a strong pairing interaction. We also discuss how the pseudogap affects the spectrum of the photoemission-type experiment developed by JILA group.     

Bipolaron Jahn–Teller Pairing and Charge Transport in Cuprates

Recently the mechanism for an intersite pairing was proposed for cuprates, where the coupling of two fold electronic degenerated levels to local lattice models at finite wave vector was introduced. The model is able to describe the stripe phase and offers a possible explanation of the pseudogap. Moreover, we argue that the single particle and pair conductivity may differ. For a better analysis on this issue, we compute the charge mobility arising from single particle using a variable range hopping model. The general trend is that the mobility has a crossover from 1/T temperature behavior at high temperature to a strong reduction of the mobility at low temperatures.     

Dielectricly Enhanced T c in Underdoped Cuprates

It is proposed to create a multilayer structure in which an underdoped copper-oxide high-temperature superconductor is sandwiched between high-dielectric-constant insulator layers such as ferro- or ferri-electrics, thereby reducing the Coulomb repulsion between the intrinsically present clusters or stripes in the CuO₂ layers of the pseudogap phase. This should lead to an increase in the size of such clusters, resulting in smaller distances between them and coherence at higher temperature, i.e., a higher T _c with a smaller pseudogap (T ^??T _c ).     

Superconductivity in Fe and As Based Compounds: A Bridge Between MgB<Subscript>2</Subscript> and Cuprates

By interpreting various experimental data for the new high temperature FeAs type superconductors in terms of lattice mediated multigap superconductivity, it is shown that these systems strongly resemble MgB₂, however, with the distinction that local polaronic lattice effects exist. This fact establishes a connection to cuprate high temperature superconductors where polaron formation is essential for the pseudogap phase and the unconventional isotope effects observed there. However, similarly to MgB₂ and in contrast to cuprates, the two superconducting gaps in the Fe-As based materials are isotropic s-wave gaps.     

Evidence for a Local Structural Change in La2CuO4.1 Across the Superconducting Transition

Polarized Cu—K edge XAFS (X-ray absorption fine structure) on La₂CuO_4.1 indicate that the radial distribution function of the copper in plane oxygen pairs is a two-site distribution, in agreement with the results found by Bianconi et al. for temperatures below the appearance of a pseudogap. Additionally we find evidence of a change in this distribution across the superconducting transition, suggesting coupling between the local lattice structure and the charged particles involved in the superconductivity.     

Evidence for a Local Structural Change in La2CuO4.1 Across the Superconducting Transition

Polarized Cu—K edge XAFS (X-ray absorption fine structure) on La₂CuO_4.1 indicate that the radial distribution function of the copper in plane oxygen pairs is a two-site distribution, in agreement with the results found by Bianconi et al. for temperatures below the appearance of a pseudogap. Additionally we find evidence of a change in this distribution across the superconducting transition, suggesting coupling between the local lattice structure and the charged particles involved in the superconductivity.     

Lattice Instability in High-Temperature Superconducting Cuprates: Polarons Probed by EXAFS

Lattice instability in the planar Cu–O bond in high-temperature superconducting cuprates is probed by the Cu K-edge extended X-ray absorption fine structure (EXAFS). Refined temperature-dependent polarized EXAFS data for high-quality La_1.85Sr_0.15CuO₄ (LSCO) single crystals grown by MBE and TSFZ methods are analyzed and compared with the transport properties. Temperature-dependent oxygen displacement shows a signature of bond splitting at T ^* and a sharp drop due to superconductivity coherence at T _c. Detailed analysis of the anomalous oxygen displacement demonstrates the Cu–O bond splitting, i.e., long and short bonds (ΔR≈0.12 Å), which is in good agreement with the recent cluster calculation. The results indicate that the origin of pseudogap is related to the formation of charged dynamical lattice distortions (polarons) that are coexistent with metallic (superconducting) domains.     

Bose–Einstein Condensation in the Pseudogap Phase of Cuprate Superconductors

We have identified the unscreened Fröhlich electron–phonon interaction (EPI) as the most essential for pairing in cuprate superconductors as now confirmed by isotope substitution, recent angle-resolved photoemission (ARPES), and some other experiments. Low-energy physics is that of mobile lattice polarons and bipolarons in the strong EPI regime. Many experimental observations have been predicted or explained in the framework of our “Coulomb–Fröhlich” model, which fully takes into account the long-range Coulomb repulsion and the Fröhlich EPI. They include pseudo-gaps, unusual isotope effects and upper critical fields, the normal state Nernst effect, diamagnetism, the Hall–Lorenz numbers, and a giant proximity effect (GPE). These experiments along with the parameter-free estimates of the Fermi energy and the critical temperature support a genuine Bose–Einstein condensation of real-space lattice bipolarons in the pseudogap phase of cuprates. On the contrary, the phase fluctuation (or vortex) scenario is incompatible with the insulating-like in-plane resistivity and the magnetic-field dependence of orbital magnetization in the resistive state of underdoped cuprates.     

Particle–Hole Asymmetry and the Pseudogap Phase of the High-<Emphasis Type="Italic">T</Emphasis><Subscript>C</Subscript> Superconductors

In the pseudogap phase of the copper oxide superconductors, a significant portion of the Fermi surface is still gapped at temperatures above the superconducting transition temperature T _C. Instead of a closed Fermi surface, the low-energy electronic excitations appear to form unconnected Fermi arcs separated by gapped regions. It is generally believed that the spectral function is particle–hole symmetric (at low energies) in both regions—with a peak at the Fermi level on the Fermi arcs and a local minimum at the Fermi level in the gapped regions. Here, using high resolution angle-resolved photoemission and new techniques of analysis, we show that on a sizable portion of the Fermi surface, the electronic structure in the immediate vicinity of the Fermi level is not particle–hole symmetric in the pseudogap phase. This is clear evidence that an alternative ground state competes with the superconductivity. The observations are also consistent with the possibility that the Fermi arcs are, in fact, the inner surface of the predicted Fermi pockets.     

Van Hove model of pseudogaps and stripes in the uederdoped cuprates

Recent photoemission and thermodynamic experiments on underdoped cuprates strikingly confirm the prediction that the pseudogap is driven by a splitting of the degeneracy of the Van Hove singularity. The doping dependence of the pseudogap can be understood in terms of a crossover from magnetic to charge-dominated behavior (including strong electron-phonon coupling). The crossover is accompanied by a nanoscale phase separation (striped phase), which is shown to be driven by Van Hove nesting.     

Possible Nature of Field-Induced Antiferromagnetic Ordering in SC Cuprates

In the present work, the results of recent neutron scattering, STM, and NMR experiments concerning the structure of the vortex core in resistive state of the cuprates are discussed. It is demonstrated that “field-induced” antiferromagnetic (SDW) ordering observed in the SC state is the same as “temperature-induced” one arising above T _c in the pseudogap (SDW) state. It is pointed out that in resistivity measurements, due to short mobile charge carrier relaxation time, a magnetic structure is sampled on much shorter time scale as compared with other techniques such as neutron scattering, Mossbauer effect, etc. It is noted that existing theoretical models mainly consider the SDW order only as competing to the SC one rather than stimulating the SC to appear at higher temperature.     

Scanning tunnelling microscopy imaging of symmetry-breaking structural distortion in the bismuth-based cuprate superconductors

A complicating factor in unravelling the theory of high-temperature (high-T(c)) superconductivity is the presence of a 'pseudogap' in the density of states, the origin of which has been debated since its discovery. Some believe the pseudogap is a broken symmetry state distinct from superconductivity, whereas others believe it arises from short-range correlations without symmetry breaking. A number of broken symmetries have been imaged and identified with the pseudogap state, but it remains crucial to disentangle any electronic symmetry breaking from the pre-existing structural symmetry of the crystal. We use scanning tunnelling microscopy to observe an orthorhombic structural distortion across the cuprate superconducting Bi(2)Sr(2)Ca(n-1)Cu(n)O(2n+4+x) (BSCCO) family tree, which breaks two-dimensional inversion symmetry in the surface BiO layer. Although this inversion-symmetry-breaking structure can impact electronic measurements, we show from its insensitivity to temperature, magnetic field and doping, that it cannot be the long-sought pseudogap state. To detect this picometre-scale variation in lattice structure, we have implemented a new algorithm that will serve as a powerful tool in the search for broken symmetry electronic states in cuprates, as well as in other materials.     

Nonequilibrium Carrier Dynamics Studied in Underdoped Bi2212 by Polarized Optical Pump-Probe Spectroscopy

We investigate nonequilibrium quasiparticle dynamics measured by ultrafast optical spectroscopy on underdoped Bi2212 crystals, which provide direct evidence that superconducting (SC) and pseudogap (PG) quasiparticles coexist below T _c . We verify that the ratio of signals from SC and PG quasiparticles depends on both excitation energy and polarization of the probe beam due to the anisotropy of the probe transition matrix elements and the interband transition probability. Based on this property, we successfully separate the SC or PG component and precisely evaluate the temperature dependence of them across T _c .     

Low-Energy Scales and Temperature-Dependent Photoemission of Heavy Fermions

We solve the S=1/2 Kondo lattice model within the dynamical mean field theory. Detailed predictions are made for the dependence of the lattice Kondo resonance and the conduction electron spectral density on temperature and band filling, n_c. Two low-energy scales are identified in the spectra: a renormalized hybridization pseudogap scale T*, which correlates with the single-ion Kondo scale, and a lattice Kondo scale T ₀ T*, which acts as the Fermi-liquid coherence scale. The lattice Kondo resonance is split into a main branch, which is pinned at the Fermi level, and whose width is set by T ₀ , and an upper branch at T*. The weight of the upper branch decreases rapidly away from n_c=1 and vanishes for n_c0.7 (however, the pseudogap in the conduction electron spectral density persists for all n_c). On increasing temperature, we find that the lattice Kondo resonance vanishes on a temperature scale of order 10T ₀ , the same scale over which the single-ion Kondo resonance vanishes in impurity model calculations. In contrast to impurity model calculations, however, we find that the position of the lattice Kondo resonance depends strongly on temperature. The results are used to make predictions on the temperature dependence of the low-energy photoemission spectrum of metallic heavy fermions and doped Kondo insulators. We compare our results for the photoemission spectra with available high-resolution measurements on YbInCu ₄ and YbAgCu ₄ . The loss in intensity with increasing temperature, and the asymmetric lineshape of the low-energy spectra are well accounted for by our simplified S=1/2 Kondo lattice model.     

Phase Fluctuations of s-Wave Superconductors on a Lattice

Based on an attractive U Hubbard model on a lattice with up to second neighbor hopping we derive an effective Hamiltonian for phase fluctuations. The superconducting gap is assumed to have s-wave symmetry. The effective Hamiltonian we finally arrive at is of the extended XY type. While it correctly reduces to a simple XY in the continuum limit, in the general case, it contains higher neighbor interaction in spin space. An important feature of our Hamiltonian is that it gives a much larger fluctuation region between the Berezinskii–Kosterlitz–Thouless transition temperature identified with T _c for superconducting and the mean field transition temperature identified with the pseudogap temperature.     

Enhancing T c by Oxygen Isotope Substitution in Cuprates

The phase diagram of doped cuprates is generic. For low dopings a pseudogap is present at temperatures above the superconducting phase. The pseudogap phase is heterogeneous containing superconducting clusters which become phase coherent at T _c (Müller in J. Phys. Cond. Matter 19:251002, 2007). Most recent propositions suggest to increase the cluster size and therefore to enhance T _c . In the present note it is recalled that over a decade ago a giant oxygen isotope effect in low doped LSCO was reported. Thus, if indeed increasing the cluster sizes becomes possible, enhancing T _c towards the onset of the pseudogap phase, then it may be even further enhanced by ¹⁶O to ¹⁸O substitution.     

Evidence for Polaron Formation in High-Temperature Superconducting Cuprates: Experiment and Theory

We provide compelling support for the key role played by polaron formation to the physics of cuprate superconductors, which is evidenced above the pseudogap temperature T ^*, is the origin of the pseudogap phase itself and persists in the superconducting phase. Experimental and theoretical results are compared and show convincing agreement with each other.     

The Origin of the Pseudogap in Underdoped HTSC

Here, the origin of the pseudogap in HTSC is attributed to the modulated antiferromagnetic (AFM) phase, whose preliminary version has been sketched recently by the present author (in J. Super. Nov. Mag. 22:517, 2009). Starting from the t-J Hamiltonian, I show that the formal failure of the perturbation theory leads to a transformation to the pseudogap phase. This phase is characterized by the aggregation of the holes into rows and columns, which in turn results in two internal fields. The first is the modulated AFM field, whose main evidence comes from Neutron scattering experiments. The second internal field is made up by the checkerboard charge density waves that have been observed by scanning tunneling measurements. The present paper deals mainly with the internal field of the first type, and discusses the second type only tentatively. Formalism is derived that yields the ground state, the internal field, the Hamiltonian, and the propagators of the condensed phase. Our results resolve the presumably inherent self-contradictory concept of pseudogap. It is shown that the excitation energy spectrum is gapless despite the order parameter that is inherent to the condensed system. In addition, it is shown qualitatively that our model predicts “Fermi surface” that is in agreement with the experiment.