Persistence of strong electron coupling to a narrow boson spectrum in overdoped Bi2Sr2CaCu2O(8+delta) tunneling data

A d-wave, Eliashberg analysis of break-junction and STM tunneling spectra on Bi2Sr2CaCu2O(8+delta) (Bi2212) reveals that the spectral dip feature is directly linked to strong electronic coupling to a narrow boson spectrum, evidenced by a large peak in alpha2F(omega). The tunneling dip feature remains robust in the overdoped regime of Bi2212 with bulk T(c) values of 56 K-62 K. This is contrary to recent optical conductivity measurements of the self-energy that suggest the narrow boson spectrum disappears in overdoped Bi2212 and therefore cannot be essential for the pairing mechanism. The discrepancy is resolved by considering the way each technique probes the electron self-energy, in particular, the unique sensitivity of tunneling to the off-diagonal or pairing part of the self-energy.     

Superconductivity in the cuprates: Deduction of mechanism for d-wave pairing through analysis of ARPES

In the Eliashberg integral equations for d-wave superconductivity, two different functions (α²F)_n(ω, θ) and (α²F)_p,d(ω) determine, respectively, the “normal” self-energy and the “pairing” self-energy. ω is the frequency of fluctuations scattering the fermions whose momentum is near the Fermi-surface and makes an angle θ to a chosen axis. We present a quantitative analysis of the high-resolution laser based Angle Resolved Photoemission Spectroscopy (ARPES) data on a slightly under doped cuprate compound Bi2212 and use the Eliashberg equations to deduce the ω and θ dependence of (α²F)_n(ω, θ) for T just above T_c and below T_c. Besides its detailed ω dependence, we find the remarkable result that this function is nearly independent of θ between the (π; π)-direction and 25 degrees from it, except for the dependence of the cut-off energy on θ. Assuming that the same fluctuations determine both the normal and the pairing self-energy, we ask what theories give the function (α²F)_p,d(ω) required for the d-wave pairing instability at high temperatures as well as the deduced (α²F)_n(θ, ω). We show that the deduced (α²F)_n(θ, ω) can only be obtained from antiferromagnetic (AFM) fluctuations if their correlation length is smaller than a lattice constant. Using (α²F)_p,d(ω) consistent with such a correlation length and the symmetry of matrix-elements scattering fermions by AFM fluctuations, we calculate T_c and show that AFM fluctuations are excluded as the pairing mechanism for d-wave superconductivity in cuprates. We also consider the quantumcritical fluctuations derived microscopically as the fluctuations of the observed loop–current order discovered in the under-doped cuprates, and which lead to the marginal Fermi–liquid properties in the normal state. We show that their frequency dependence and the momentum dependence of their matrix-elements to scatter fermions are consistent with the θ and ω dependence of the deduced (α²F)_n(ω, θ). The pairing kernel (α²F)_p,d(ω) calculated using the experimental values in the Eliashberg equation gives d-wave instability at T_c comparable to the experiments.     

Energy scales and quasiparticle properties in an extended Hubbard model for HTC

By means of a strong-coupling approach, developed in previous works, we study the quasiparticle properties in an extended Hubbard model in presence of critical charge fluctuations near a stripe-quantum critical-point. We show that the quasiparticle dispersion has a kink along the diagonal Brillouin zone at the energy of the order 50 meV, for realistic values of the parameters. The energy and momentum distribution curves (EDC, MDC) along the diagonal are also analyzed. The results for the EDC derived quasiparticle width reveals an anomalous drop in the low-energy scattering rate at the same energy of the kink. This drop corresponds to a new energy scale in the system that reflects the interaction between the quasiparticles and the critical charge fluctuations. The results offer a possible interpretation of the ARPES and photoemission experiments on Bi2212.Received: 17 November 2003, Published online: 19 February 2004PACS: 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.10.Hf Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems     

Second order self-energy of the two-dimensional Hubbard model

The self-energy Σ(k; ω) of the 2D Hubbard model on the square lattice is calculated numerically in second order perturbation theory. In the limit of small frequencies the imaginary part of Σ(k; ω) is also obtained analytically. We find that at half filling ImΣ(k; ω) ～ ω for k on the Fermi surface, with a logarithmically divergent prefactor close to the corners k = (0,±π) and (±π,0) in agreement with the numerical results.     

Electron-phonon coupling on the surface of the topological insulator Bi2Se3 determined from surface-phonon dispersion measurements

In this Letter, we report measurements of the coupling between Dirac fermion quasiparticles (DFQs) and phonons on the (001) surface of the strong topological insulator Bi2Se3. While most contemporary investigations of this coupling have involved examining the temperature dependence of the DFQ self-energy via angle-resolved photoemission spectroscopy measurements, we employ inelastic helium-atom scattering to explore, for the first time, this coupling from the phonon perspective. Using a Hilbert transform, we are able to obtain the imaginary part of the phonon self-energy associated with a dispersive surface-phonon branch identified in our previous work [Phys. Rev. Lett. 107, 186102 (2011)] as having strong interactions with the DFQs. From this imaginary part of the self-energy we obtain a branch-specific electron-phonon coupling constant of 0.43, which is stronger than the values reported from the angle-resolved photoemission spectroscopy measurements.     

Comparative study of electron- and hole-doped high-Tc compounds in pseudogap regime: LDA+DMFT+Σk approach

Pseudogap regime for the prototype high-T_c compounds hole-doped Bi₂Sr₂CaCu₂O_8−x (Bi2212) and electron-doped Nd_2−xCe_xCuO₄ (NCCO) is described by means of novel generalized LDA+DMFT+Σ_k approach. Here, conventional dynamical mean-field theory (DMFT) equations are supplied with additional (momentum dependent) self-energy Σ_k. In the present case, Σ_k describes nonlocal dynamical correlations induced by short-ranged collective Heisenberg-like antiferromagnetic spin fluctuations. Material-specific model parameters of two neighboring CuO₂ layers of Bi2212 and single CuO₂ layer of NCCO were obtained within local density approximation (LDA) and constrained LDA method. We show that Fermi surface in presence of the pseudogap fluctuations have perfectly visible “hot-spots” for NCCO, while in Bi2212 there is just a rather broad region with strong antiferromagnetic scattering. Results obtained are in good agreement with recent ARPES and optical experiments.     

Evidence for a pseudogap in underdoped Bi{2}Sr_{2}CaCu{2}O{8+delta} and YBa2Cu3O6.50 from in-plane optical conductivity measurements

The real part of the in-plane optical self-energy data in underdoped Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} (Bi-2212) and ortho II YBa2Cu3O6.5 contains new and important information on the pseudogap. Using a theoretical model approach, a major new finding is that states lost below the pseudogap Delta_{pg} are accompanied by a pileup of states just above this energy. The pileup along with a sharp mode in the bosonic spectral function leads to an unusually rapid increase in the optical scattering rate as a function of frequency and a characteristically sloped peak in the real part of the optical self-energy. These features are not found in optimally doped and overdoped samples and represent the clearest signature so far in the in-plane optical conductivity of the opening of a pseudogap.     

Bosonic spectral density of epitaxial thin-film La1.83Sr0.17CuO4 superconductors from infrared conductivity measurements

We use optical spectroscopy to investigate the excitations responsible for the structure in the optical self-energy of thin epitaxial films of La(1.83)Sr(0.17)CuO(4). Using Eliashberg's formalism to invert the optical spectra we extract the electron-boson spectral function and find that at low temperature it has a two component structure closely matching the spin excitation spectrum recently measured by magnetic neutron scattering. We contrast the temperature evolution of the spectral density and the two-peak behavior in La(2-Sr(x)CuO(4) with another high temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+delta). The bosonic spectral functions of the two materials account for the low T(c) of LSCO as compared to Bi-2212.     

Self-consistent calculation of the optical potential and ground-state properties of nuclear matter

On the basis of the Green-function formalism, we performed a self-consistent calculation of the self-energy ∑(k, ω) of a particle interacting with the infinite nuclear medium. The function ∑(k, ω) was mapped out in the energy-momentum plane, and the single-particle energy ω(k), momentum distribution ?(k) and the “on-shell” part of the self-energy, ∑(k, ω(k)), were defined, from which all physical properties followed. In particular we investigated the ground-state properties of nuclear matter in two Λ-approximations of the T-matrix. In one, the intermediate two-particle propagator, Λ₀₀, represented free-particle propagation; in the other, called Λ₁₁, intermediate states included both interacting particles and holes. Pauli principle effects were included in both approximations. The second approximation was expected to be conserving because it included a large part of the rearrangement effects which, we found, contributed ～6 MeV per particle to the average energy and ～28 MeV to the singleparticle energy at zero momentum. The Hugenholtz-van Hove theorem was nearly satisfied, with only 1 MeV separating the chemical potential from the average energy. We also studied, in the Λ₀₀-approximation, the optical potential for the scattering of a particle by a large nucleus; it was directly related to the “on-shell” part of the self-energy. It was found that, below 100 MeV, the real part varied as (?90 + 0.584E) [MeV], and the imaginary part as (2.4 + 0.009 E) [MeV].     

Oxygen isotope effect in optimally doped Bi2Sr2CaCu2O8+δ studied by low-energy ARPES

Using angle-resolved photoemission spectroscopy (ARPES) with low-energy tunable photons, we studied the oxygen isotope effect in optimally doped Bi₂Sr₂CaCu₂O_8+δ (Bi2212). We found the oxygen isotope shift in the real part of the electron self-energies [ReΣ(ω)s] along the nodal direction derived not only from the momentum distribution curves (MDCs) but also from the energy distribution curves (EDCs). Present results indicate straightforwardly the coupling between the nodal electrons and the phonons.     

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.     

Anomalous Hall Effect in Spin-Polarized Two-Dimensional Hole Gas with Cubic-Rashbsa Spin-Orbit Interaction

Based on the Kubo formalism, the anomalous Hall effect in a magnetic two-dimensional hole gas with cubic-Rashba spin-orbit coupling is studied in the presence of δ-function scattering potential. When the weak, short-ranged disorder scattering is considered in the Born approximation, we find that the self-energy becomes diagonal in the helicity basis and its value is independent of the wave number, and the vertex correction to the anomalous Hall conductivity due to impurity scattering vanishes when both subbandsare occupied. That is to say, the anomalous Hall effect is not vanishing or influenced by the vertex correction for two-dimensional heavy-hole system, which is in sharp contrast to the case of linear-Rashba spin-orbit coupling in the electron band when the short-range disorder scattering is considered and the extrinsic mechanism as well as the effect of external electric field on the SO interaction are ignored.     

Electron-boson coupling and oxygen-isotope effect in the optical conductivity of high-Tc superconductors

We have investigated electron-boson coupling in the optical conductivity of high-T_c superconductors through the optical self-energy. The real part of the self-energy (ReΣ^op(ω)) of YBa₂Cu₃O_y (YBCO) shows a characteristic doping dependence. In the optimally doped YBCO, ReΣ^op(ω) has a single peak around 65 meV, which corresponds to the kink structure of the band dispersion. On the other hand, in the under-doped YBCO, the peak structure of ReΣ^op(ω) splits into two parts. To evaluate contribution from the phonons in electron-boson coupling, we have measured oxygen-isotope effects by substituting ¹⁶O→¹⁸O for the optimally doped and under-doped YBCO.     

(Bi,Pb)_2Sr_2CaCu_2O_y单晶的磁通钉扎研究

我们通过对重Pb掺杂的Bi-2212((Bi,Pb)-2212)单晶磁化性质的测量来研究磁通钉扎性能,发现样品中存在与温度有明显依赖关系的鱼尾效应,且此鱼尾效应不仅体现在磁滞洄线上,还体现在不同磁场下零场冷的M～T曲线的交叠上.同时我们采用非线性磁通蠕动模型,并考虑表面位垒和体钉扎的影响,运用数值模拟分析了样品的磁化性质,结果表明(Bi,Pb)-2212单晶的鱼尾效应源于重Pb掺杂导致样品各向异性的降低所引起的强的体钉扎效应,而高温的磁化性质主要取决于表面位垒的作用.     

Mechanisms of the pancake vortex and vortex line movement in the high Tc superconductors Bi2Sr2CaCu2O8+δand La1.93Sr0.07CuO4+δ

In the strict sense, it is not very clear why with magnetic field increasing, the normal-superconductive (NS) transition becomes broad for Bi2Sr2CaCu2O8+δ(Bi2212) while the NS transitions are almost parallel for La1.93Sr0.07CuO4+δ(La214). In this paper, R-T relations are measured by the six-probe method. We propose a moving mechanism of the pancake vortex and vortex line for Bi2212. The theoretical curves fit the experiment data well.     

Nodal-antinodal dichotomy and the two gaps of a superconducting doped Mott insulator

We study the superconducting state of the hole-doped two-dimensional Hubbard model using cellular dynamical mean-field theory, with the Lanczos method as impurity solver. In the underdoped regime, we find a natural decomposition of the one-particle (photoemission) energy gap into two components. The gap in the nodal regions, stemming from the anomalous self-energy, decreases with decreasing doping. The antinodal gap has an additional contribution from the normal component of the self-energy, inherited from the normal-state pseudogap, and it increases as the Mott insulating phase is approached.     

Kinks and waterfalls in the dispersion of ARPES features

In this paper we use a generic form for the Green function G(k, ω) in a correlated metal, already proven successful in describing ARPES line shapes [1]. The associated many body self-energy function has only a single pole. We now investigate, whether this generic model can be used all the way to the limit of strong correlations and, when applied to ARPES intensities, whether it is able to explain some of the ubiquitous dispersive crossover phenomena that have been attributed to dynamical, i.e.: ω-dependent effects. We argue that a quantitative interpretation of experimental data requires to calculate extrema not only in the momentum distribution curve but also in the energy distribution curve. In passing, we give a formula for the extrema in the latter distribution that is valid for the general G(k, ω) in a many body system. To our knowledge, this is a new formula, not found in the literature. The investigation of the generic model proceeds on two levels: on the one hand, we explore the rich variety of crossovers that can be predicted and linked to well defined features in the complex ω-plain. On the other hand, we show that the generic one-pole self-energy can be viewed as a projection on the low energy sector of a microscopic solution, belonging to a lattice model of interacting fermions. To obtain approximate microscopic solutions, we use our continued fraction method [2] and [3]. As an explicit example, we study the projection for the case of a hole doped Hubbard model in infinite dimension. A discussion section gives examples, how the generic model is able to cope with the ubiquity of the crossover phenomena, also in finite dimension and beyond the Hubbard model.     

Doping dependence of the coupling of electrons to bosonic modes in the single-layer high-temperature Bi2Sr2CuO6 superconductor

A recent highlight in the study of high-T(c) superconductors is the observation of band renormalization or self-energy effects on the quasiparticles. This is seen in the form of kinks in the quasiparticle dispersions as measured by photoemission and interpreted as signatures of collective bosonic modes coupling to the electrons. Here we compare for the first time the self-energies in an optimally doped and strongly overdoped, nonsuperconducting single-layer Bi-cuprate (Bi2Sr2CuO6). In addition to the appearance of a strong overall weakening, we also find that the weight of the self-energy in the overdoped system shifts to higher energies. We present evidence that this is related to a change in the coupling to c-axis phonons due to the rapid change of the c-axis screening in this doping range.     

Reconstruction of bands in metallic hydrogen

The generalized theory of normal properties of a metal for the case of the properties of the electronic band of electron–phonon systems with a variable electron density of states is used to study the normal phase of metallic hydrogen at a pressure of 500 GPa and a temperature of 200 K. We calculated the frequency dependence of the real ReΣ(ω) and imaginary ImΣ(ω) parts of the self-energy part of the electron Green’s function Σ(ω), as well as the electron density of states N(ε) of the stable phase of metallic hydrogen with the I41/amd symmetry at a pressure of 500 GPa, renormalized by the strong electron–phonon coupling. It is found that the electron conduction band of the I41/amd phase of metallic hydrogen undergoes insignificant reconstruction near the Fermi level because of the renormalization by the electron–phonon coupling.