Nodal Fermi Velocity Research Articles

Universal Fermi velocity in highly compressed hydride superconductors

The Fermi velocity vF is one of the primary characteristics of any conductor, including any superconductor. For conductors at ambient pressure, several experimental techniques have been developed to measure vF, and, for instance, Zhou et al. [Nature 423, 398 (2003)] reported that high-Tc cuprates exhibited a universal nodal Fermi velocity vF,univ=2.7±0.5×105 m/s. However, there have been no measurements of vF in highly compressed near-room-temperature superconductors (NRTS), owing to experimental challenges. Here, to answer the question of the existence of a universal Fermi velocity in NRTS materials, we analyze the full inventory of data on the ground-state upper critical field Bc2(0) for these materials and find that this class of superconductors exhibits a universal Fermi velocity vF,univ=1/1.3×2Δ0/kBTc×105 m/s, where Δ(0) is the ground-state amplitude of the energy gap. The ratio 2Δ0/kBTc varies within a narrow range 3.2≤2Δ0/kBTc≤5, and so vF,univ in NRTS materials lies in the range 2.5 × 105 m/s ≤ vF,univ ≤ 3.8 × 105 m/s, which is similar to the range of values found for the high-Tc cuprate counterparts of these materials.

Superconductivity in the three-band model of cuprates: nodal direction characteristics and influence of intersite interactions

The three-band Emery model is applied to study the selected principal features of the d-wave superconducting phase in the copper-based compounds. The electron–electron correlations are taken into account by the use of the diagrammatic expansion of the Guztwiller wave function (DE-GWF method). The nodal Fermi velocity, Fermi momentum, and effective mass are all determined in the paired state and show relatively good agreement with the available experimental data, as well as with the corresponding single-band calculations. Additionally, the influence of the next-nearest neighbor oxygen–oxygen hopping and intersite Coulomb repulsion terms on the superconducting phase is analyzed.

Universal properties of high-temperature superconductors from real-space pairing: Role of correlated hopping and intersite Coulomb interaction within the t−J−U model

We study the effect of the correlated hopping term and the intersite Coulomb interaction term on principal features of the $d$-$wave$ superconducting (SC) state, in both the electron and hole doped regimes within the t-J-U model. In our analysis we use the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF) which allows us to go beyond the renormalized mean field theory (RMFT). We show that the correlated hopping term enhances the pairing at the electron-doped side of the phase diagram. Moreover, the so-called non-BCS regime (which manifests itself by the negative kinetic energy gain at the transition to the SC phase) is narrowed down with the increasing magnitude of the correlated hopping $\sim K$. Also, the doping dependences of the nodal Fermi velocity and Fermi momentum, as well as the average number of double occupancies, are analyzed with reference to the experimental data for selected values of the parameter $K$. For the sake of completeness, the influence of the intersite Coulomb repulsion on the obtained results is provided. Additionally, selected results concerning the Hubbard-model case are also presented. A complete model with all two-site interactions is briefly discussed in the Appendix for reference.

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

We discuss the physics of the high temperature superconductivity in hole doped copper oxide ceramics in the pseudogap region. Starting from an effective reduced Hamiltonian relevant to the dynamics of holes injected into the copper oxide layers proposed in a previous paper, we determine the superconductive condensate wavefunction. We show that the low-lying elementary condensate excitations are analogous to the rotons in superfluid $^4He$. We argue that the rotons-like excitations account for the specific heat anomaly at the critical temperature. We discuss and compare with experimental observations the London penetration length, the Abrikosov vortices, the upper and lower critical magnetic fields, and the critical current density. We give arguments to explain the origin of the Fermi arcs and Fermi pockets. We investigate the nodal gap in the cuprate superconductors and discuss both the doping and temperature dependence of the nodal gap. We suggest that the nodal gap is responsible for the doping dependence of the so-called nodal Fermi velocity detected in angle resolved photoemission spectroscopy studies. We discuss the thermodynamics of the nodal quasielectron liquid and their role in the low temperature specific heat. We propose that the ubiquitous presence of charge density wave in hole doped cuprate superconductors in the pseudogap region originates from instabilities of the nodal quasielectrons driven by the interaction with the planar $CuO_2$ lattice. We investigate the doping dependence of the charge density wave gap and the competition between charge order and superconductivity. We discuss the effects of external magnetic fields on the charge density wave gap and elucidate the interplay between charge density wave and Abrikosov vortices. Finally, we examine the physics underlying quantum oscillations in the pseudogap region.

High-temperature superconductivity in the two-dimensional t–J model: Gutzwiller wavefunction solution

A systematic diagrammatic expansion for Gutzwiller wavefunctions (DE-GWFs) proposed very recently is used for the description of the superconducting (SC) ground state in the two-dimensional square-lattice t–J model with the hopping electron amplitudes t (and ) between nearest (and next-nearest) neighbors. For the example of the SC state analysis we provide a detailed comparison of the methodʼs results with those of other approaches. Namely, (i) the truncated DE-GWF method reproduces the variational Monte Carlo (VMC) results and (ii) in the lowest (zeroth) order of the expansion the method can reproduce the analytical results of the standard Gutzwiller approximation (GA), as well as of the recently proposed ‘grand-canonical Gutzwiller approximation’ (called either GCGA or SGA). We obtain important features of the SC state. First, the SC gap at the Fermi surface resembles a wave only for optimally and overdoped systems, being diminished in the antinodal regions for the underdoped case in a qualitative agreement with experiment. Corrections to the gap structure are shown to arise from the longer range of the real-space pairing. Second, the nodal Fermi velocity is almost constant as a function of doping and agrees semi-quantitatively with experimental results. Third, we compare the doping dependence of the gap magnitude with experimental data. Fourth, we analyze the k-space properties of the model: Fermi surface topology and effective dispersion. The DE-GWF method opens up new perspectives for studying strongly correlated systems, as it (i) works in the thermodynamic limit, (ii) is comparable in accuracy to VMC, and (iii) has numerical complexity comparable to that of the GA (i.e., it provides the results much faster than the VMC approach).

Superconductivity in the two-dimensional Hubbard model: Gutzwiller wave function solution

A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) is formulated and used for the description of superconducting (SC) ground state in the two-dimensional Hubbard model with electron-transfer amplitudes t (and t') between nearest (and next-nearest) neighbors. The method is numerically very efficient and allows for a detailed analysis of the phase diagram as a function of all relevant parameters (U, \delta, t') and a determination of the kinetic-energy driven pairing region. SC states appear only for substantial interactions, U/t > 3, and for not too large hole doping, \delta < 0.32 for t' = 0.25 t; this upper critical doping value agrees well with experiment for the cuprate high-temperature superconductors. We also obtain other important features of the SC state: (i) the SC gap at the Fermi surface resembles $d_{x^2-y^2}$-wave only around the optimal doping and the corrections to this state are shown to arise from the longer range of the pairing; (ii) the nodal Fermi velocity is almost constant as a function of doping and agrees quantitatively with the experimental results; (iii) the SC transition is driven by the kinetic-energy lowering for low doping and strong interactions.

Universal intrinsic doping behavior of in-plane dc conductivity for hole-doped high-temperature cuprate superconductors

Understanding the normal state transport properties in hole-doped high-temperature cuprate superconductors (HTCSs) is a challenging task which has been widely believed to be one of the key steps toward revealing the pairing mechanism of high-temperature superconductivity. Here, we present a true intrinsic and universal doping dependence of in-plane dc conductivity for all underdoped HTCSs. The doping dependence of in-plane dc conductivity normalized to that at optimal doping can be represented by a simple exponential formula. The doping behavior of the square of the nodal Fermi velocity derived by the high-resolution laser-based angle-resolved photoemission spectroscopy in the superconducting state follows reasonably well the universal intrinsic doping behavior. Our findings suggest a commonality of the low-energy quasiparticles both in the normal and superconducting states that place a true universal and stringent constraint on the mechanism of high-temperature superconductivity for HTCSs.

Doping-Dependent Nodal Fermi Velocity of the High-Temperature SuperconductorBi2Sr2CaCu2O8+δRevealed Using High-Resolution Angle-Resolved Photoemission Spectroscopy

The improved resolution of laser-based angle-resolved photoemission spectroscopy (ARPES) allows reliable access to fine structures in the spectrum. We present a systematic, doping-dependent study of a recently discovered low-energy kink in the nodal dispersion of Bi2Sr2CaCu2O(8+δ) (Bi-2212), which demonstrates the ubiquity and robustness of this kink in underdoped Bi-2212. The renormalization of the nodal velocity due to this kink becomes stronger with underdoping, revealing that the nodal Fermi velocity is nonuniversal, in contrast with assumed phenomenology. This is used together with laser ARPES measurements of the gap velocity (v2) to resolve discrepancies with thermal conductivity measurements.

A model of a 2d non-Fermi liquid with SO(5) symmetry, AF order and a d-wave SC gap

Demanding a consistent quantum field theory description of spin- particles near a circular Fermi surface in 2d leads to a unique fermionic theory with relevant quartic interactions which has an emergent Lorentz symmetry and automatically has an Sp(4) = SO(5) internal symmetry. The interacting theory has a low-energy interacting fixed point and is thus a non-Landau/Fermi liquid. Anti-ferromagnetic (AF) and superconducting (SC) order parameters are bilinears in the fields and form the five-dimensional vector representation of SO(5). An AF phase occurs at low doping which terminates in a first-order transition. We incorporate momentum-dependent scattering of Cooper pairs near the Fermi surface to 1-loop and derive a new kind of SC gap equation beyond mean field with a d-wave gap solution. Taking into account the renormalization group (RG) scaling properties near the low-energy fixed point, we calculate the complete phase diagram as a function of doping, which shows some universal geometric features. The d-wave SC dome terminates on the over-doped side at the fixed point of the RG, which is a quantum critical point. Optimal doping is estimated to occur just below 3/2π2. The critical temperature for SC at optimal doping is set mainly by the universal nodal Fermi velocity and lattice spacing, and is estimated to average around 140 K for LSCO. The pseudogap energy scale is identified with the RG scale of the coupling.

Strong-coupling theory of the universal linear temperature dependence of the nodal Fermi velocity in layered cuprates

We explain the recently observed linear temperature dependence of the nodal Fermi velocity vFT in nearly optimally doped cuprates. We argue that it originates from electron-electron interaction and it is a fundamental property of an arbitrary two-dimensional 2D Fermi liquid. We consider a spin-fermion model with input parameters extracted from the data, and we show that the T term is about 30% at 300 K, in agreement with the data. We show that the sub-leading term in vFT is a regular and small T 2 correction. We also show that at a2 kF quantum-critical point, temperature corrections to the dispersion are singular. DOI: 10.1103/PhysRevB.78.060509

Doping-dependent evolution of low-energy excitations and quantum phase transitions within an effective model for high-Tc copper oxides

In this paper a mean-field theory for the spin-liquid paramagnetic non-superconducting phase of the p- and n-type high-Tc cuprates is developed. This theory applied to the effective t-t'-t′′-J* model with the ab initio calculated parameters and with the three-site correlated hoppings. The static spin-spin and kinematic correlation functions beyond Hubbard-I approximation are calculated self-consistently. The evolution of the Fermi surface and band dispersion is obtained for the wide range of doping concentrations x. For p-type systems the three different types of behavior are found and the transitions between these types are accompanied by the changes in the Fermi surface topology. Thus a quantum phase transitions take place at x = 0.15 and at x = 0.23.Due to the different Fermi surface topology we found for n-type cuprates only one quantum critical concentration, x = 0.2. The calculated doping dependence of the nodal Fermi velocity and the effective mass are in good agreement with the experimental data.

LDA + GTB (generalized tight-binding) method for the electronic structure calculations of strongly correlated electron systems: Application for the band structure calculations of p-type cuprates

Mean-field theory of the non-superconducting phase of the high- T c cuprates is formulated within the effective t– t′– t″– J model with three-site correlated hoppings. This model with the ab initio calculated parameters results from the LDA + GTB method. The static spin and kinematical correlation functions beyond Hubbard I approximation are calculated self-consistently taking into account hoppings to the first, the second, and the third neighboring sites, as well as the three-site correlated hoppings. The obtained Fermi surface evolves from hole-pockets at low-doping to large hole-type Fermi surface at higher doping concentrations. Calculated doping dependence of the nodal Fermi velocity, the effective mass and the chemical potential shift are in good agreement with experimental data.

Electronic Structure of Strongly Correlatedd-Wave Superconductors

We study the electronic structure of a strongly correlated d-wave superconducting state. Combining a renormalized mean field theory with direct calculation of matrix elements, we obtain explicit analytical results for the nodal Fermi velocity upsilon(F), the Fermi wave vector k(F), and the momentum distribution n(k) as a function of hole doping in a Gutzwiller projected d-wave superconductor. We calculate the energy dispersion E(k) and spectral weight of the Gutzwiller-Bogoliubov quasiparticles and find that the spectral weight associated with the quasiparticle excitation at the antinodal point shows a nonmonotonic behavior as a function of doping. Results are compared to angle resolved photoemission spectroscopy of the high-temperature superconductors.

Role of Strong Correlation in the Recent Angle-Resolved Photoemission Spectroscopy Experiments on Cuprate Superconductors

Motivated by recent photoemission experiments on cuprates, the low-lying excitations of a strongly correlated superconducting state are studied numerically. It is observed that along the nodal direction these low-lying one-particle excitations show a linear momentum dependence for a wide range of excitation energies and, thus, they do not present a kinklike structure. The nodal Fermi velocity v(F), as well as other observables, are systematically evaluated directly from the calculated dispersions, and they are found to compare well with experiments. It is argued that the parameter dependence of v(F) is quantitatively explained by a simple picture of a renormalized Fermi velocity.

On the break in the single-particle energy dispersions and the ‘universal’ nodal Fermi velocity in the high-temperature copper oxide superconductors

Recent data from angle-resolved photoemission experiments published by Zhou et al. [Nature, 423, 398 (2003)] concerning a number of hole-doped copper-oxide-based high-temperature superconductors reveal that in the nodal directions of the underlying square Brillouin zones (i.e. the directions along which the d-wave superconducting gap is vanishing) the Fermi velocities for some finite range of k inside the Fermi sea and away from the nodal Fermi wave vector k F are to within an experimental uncertainty of approximately 20% the same both in all the compounds investigated and over a wide range of doping concentrations and that, in line with earlier experimental observations, at some characteristic wave vector k ☆ away from k F ( typically amounts to approximately 5% of ) the Fermi velocities undergo a sudden change, with this change (roughly speaking, an increase for ) being the greatest (smallest) in the case of underdoped (overdoped) compounds. We demonstrate that these observations establish four essential facts: firstly, the ground-state momentum distribution function must be discontinuous at k = k ☆; with and denoting the measured velocities close to and , we obtain in which is the ‘Fermi’ velocity corresponding to the case in which (for two-body interaction potentials of shorter range than the Coulomb potential, whereby ); secondly, the single-particle spectral function must at k = k ☆ possess a coherent contribution corresponding to a well-defined quasiparticle excitation at an energy of approximately 70 meV below the Fermi energy; thirdly, the amount of discontinuity in at the nodal Fermi points must be small and ideally vanishing; fourthly, the long range of the two-body Coulomb potential is of vital importance for realization of a certain aspect of the observed behaviour in the Fermi velocities (specifi- cally) in the underdoped regime. The condition conforms with the observation through an earlier angle-resolved photoemission experiment by Valla et al. [Science, 285, 2110 (1999)], on the optimally doped compound Bi2Sr2CaCu2O8 + δ, which shows that the imaginary part of the self-energy along the nodal directions of the Brillouin zone and in the vicinity of the nodal Fermi points satisfies the scaling behaviour characteristic of marginal Fermi-liquid metallic states, for which is indeed vanishing. We present arguments advocating the viewpoint that the observed ‘kink’ in the measured energy dispersions cannot be a direct consequence of electron-phonon interaction, although a finite may possibly arise from this interaction. In other words, even though possibly vital, the role played by phonons in bringing about the latter ‘kink’ must be indirect. Our approach further provides a consistent interpretation of the observed sudden decrease in the width of the so-called ‘momentum distribution curve’ on ‖k| increasing above .