Nodal superconductivity and antinodal pseudogap in cuprate superconductors

According to recent experimental findings the leading pairing resides in the nodal (FS arcs) momentum region of hole doped cuprates. The pseudogap is an antinodal feature. A corresponding multiband model of the electronic background evolving with doping serves the usually presented phase diagram. The pairing is due by the pair-transfer between overlapping nodal defect (polaron) band and the itinerant band. A bare gap vanishing with extended doping between the antinodal defect subband and the itinerant band top leads to the formation of the pseudogap as a perturbative band-structure effect. The calculated behaviour of two superconducting gaps and of the pseudogap on the whole doping scale is in qualitative agreement with the observations. Arguments to include cuprates into the class of multiband-multigap superconductors are given by these results.     

Extinction of quasiparticle scattering interference in cuprate superconductors

The quasiparticle scattering interference phenomenon characterized by the peaks in the local density of states is studied within the kinetic energy driven superconducting mechanism in the presence of a single impurity. By calculation of the Fourier transformed ratio of the local density of states at opposite energy, it is shown that the quasiparticle scattering interference phenomenon can be described qualitatively by a single impurity in the kinetic energy driven homogeneous d-wave superconducting state. The amplitude of the peak increases with increasing energy at the low energy, and reaches a maximum at the intermediate energy, then diminishes to zero at the high energy. The theory also predicts that with increasing doping, the position of the peak along the nodal direction moves towards to the center of the Brillouin zone, while the position of the peak along the antinodal direction is shifted to large momentum region.     

Fermi-arc superconductivity, pseudogap and charge order in Bi2Sr2CaCu2O8+δ

We report STM/STS observations on the 4a×4a charge order in the pseudogap (PG) and superconducting (SC) states of Bi₂Sr₂CaCu₂O_8+δ, and suggest that the charge order is associated with incoherent quasiparticle or pair states around the antinodal fermi surface (FS), which are also responsible for the PG, and it can coexist with the superconductivity caused by the pairing of coherent quasiparticles on the nodal fermi arc. We also suggest that the nanometer-scale gap inhomogeneity in the SC state, reported previously [Pan, et al., Nature 413 (2001) 282; Mommo, et al., J. Phys. Soc. Jpn. 74 (2005) 2400; Hashimoto, et al., Phys. Rev. B74 (2006) 064508] arises from that in the PG state, which occurs around the antinodal FS.     

Quasiparticle scattering interference in the renormalized Hubbard model

In this paper, we study the quasiparticle scattering interference phenomenon in the presence of a single impurity within the renormalized Hubbard model. By calculating the energy and momentum dependence of the Fourier-transformed local density of states in the full Brillouin zone, we can qualitatively describe the main features of the quasiparticle scattering interference phenomenon in cuprate superconductors using a single point-like impurity. In particular, we show that with increasing energy, the position of the peak along the nodal ([0, 0] → [π, π]) direction moves steadily to a large momentum region, while the position of the peak along the antinodal ([0, 0] → [π, 0]) direction moves toward the center of the Brillouin zone.     

Doubly ordered superconducting state in a doped antiferromagnet

In a weakly doped quasi-two-dimensional antiferromagnet with a Fermi contour in the form of small pockets, the Coulomb repulsion gives rise to a doubly ordered superconducting state of coexisting condensates with a large pair momentum and a zero one. The pairing with the large momentum determines the superconducting transition temperature, below which the order with zero momentum coexists as an induced order until the temperature corresponding to the initiation of the phonon pairing mechanism is reached. The superconductivity-induced orbital current density wave eliminates the pairing-repulsion-caused zero points from the two-gap quasiparticle spectrum and leads to a deviation of the relative phase of the superconducting order parameter components from π.     

Phenomenological description of the two energy scales in underdoped cuprate superconductors

Raman and angle-resolved photoemission spectroscopy experiments have demonstrated that in superconducting underdoped cuprates nodal and antinodal regions are characterized by two energy scales instead of the one expected in BCS theory. The nodal scale decreases with underdoping while the antinodal one increases. Contrary to the behavior expected for an increasing energy scale, the antinodal Raman intensity decreases with decreasing doping. Using the Yang-Rice-Zhang model, we show that these features are a consequence of the nonconventional nature of the superconducting state in which superconductivity and pseudogap correlations are both present and compete for the phase space.     

Tetracritical point and staggered vortex currents in superconducting state

A phase diagram reflecting the main features of the typical phase diagram of cuprate superconductors has been studied within the framework of the Ginzburg-Landau phenomenology in the vicinity of a tetracritical point, which appears as a result of the competition of the superconducting and insulating pairing channels. The superconducting pairing under repulsive interaction corresponds to a two-component order parameter, whose relative phase is related to the orbital antiferromagnetic insulating ordering. Under weak doping, the insulating order coexists with the superconductivity at temperatures below the superconducting phase transition temperature and is manifested as a weak pseudogap above this temperature. A part of the pseudogap region adjacent to the superconducting state corresponds to developed fluctuations of the order parameter in the form of quasi-stationary states of noncoherent superconducting pairs and can be interpreted as a strong pseudogap. As the doping level is increased, the system exhibits a phase transition from the region of coexistence of the superconductivity and the orbital antiferromagnetism to the usual superconducting state. In this state, a region of developed fluctuations of the order parameter in the form of quasi-stationary states of uncorrelated orbital circular currents exists near the phase transition line.     

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.     

Quasiparticle scattering interference in electron-doped cuprate superconductors

By considering the nonmonotonic d-wave gap effect, the energy and momentum dependence of quasiparticle scattering interference is studied in the presence of a single impurity. It is shown that the pattern of the quasiparticle scattering peaks in the full Brillouin zone of electron-doped cuprate superconductors is very different from that in the hole-doped case described by the Octet model. This difference is the result of the nonmonotonic d-wave superconducting gap in the electron-doped case. As the energy increases, the position of the local peaks in the Brillouin zone moves rapidly. In particular, the characteristic peaks of the electron-doped cuprate superconductors appear between the antinodal and nodal directions, unlike in the hole-doped case.     

Evidence for two energy scales in the superconducting state of optimally doped (Bi,Pb)2(Sr,La)2CuO6+delta

We use angle-resolved photoemission spectroscopy to investigate the energy gap(s) in (Bi,Pb)2(Sr,La)2CuO6+delta. We find that the spectral gap has two components in the superconducting state: a superconducting gap and pseudogap. Differences in their momentum and temperature dependence suggest that they represent two separate energy scales. Spectra near the node reveal a sharp peak with a small gap below T(c) that closes at T(c). Near the antinode, spectra are broad with a large energy gap of approximately 40 meV above and below T(c). The latter spectral shape and gap magnitude are almost constant across T(c), indicating that the pseudogap state coexists with the superconducting state below T(c), and it dominates spectra around the antinode. We speculate that the pseudogap state competes with the superconductivity by diminishing spectral weight in antinodal regions, where the superconducting gap is largest.     

Electronic structure of strongly correlated d-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.     

Nematic order of spin structures of clusters in the hubbard model

The possibility of interpreting the normal pseudogap state of cuprates as a result of the formation of spin and charge structures is investigated for solutions of the Hubbard model of a finite 2D cluster based on the mean field method. The iterative self-consistency procedure reduces the initial uncorrelated spin distributions to stable structures. The Fourier components of the charge and spin distributions in such structures have peaks for characteristic incommensurate quasi-momenta depending on the doping. It is shown that for any doping, the density of states of the system has a sharp minimum (pseudogap) at the Fermi level. This emergence of the gap just at the Fermi level is a property typical of not only the superconducting state, but also the normal state of spin glasses. The characteristics of the Fermi surface averaged over the implemented structures and the properties of quasiparticles in the nodal and antinodal regions of the quasi-momentum are considered.     

The influence of out-of-plane disorder on the formation of pseudogap and Fermi arc in Bi2Sr2−xRxCuOy (R=La and Eu)

We found that the length of the Fermi arc decreases with increasing out-of-plane disorder by performing angle resolved photoemission spectroscopy (ARPES) measurements in the superconducting state of optimally doped R=La and Eu samples of Bi₂Sr_2−xR_xCuO_y. Since out-of-plane disorder stabilizes the antinodal pseudogap as was shown in our previous study of the normal state, the present results indicate that this antinodal pseudogap persists into the superconducting state and decreases the Fermi arc length. We think that the shrinkage of the Fermi arc reduces the superfluid density, which explains the large suppression of the superconducting transition temperature when out-of-plane disorder is increased.     

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.     

Dichotomy between nodal and antinodal quasiparticles in underdoped (La2-xSrx)CuO4 superconductors

High resolution angle-resolved photoemission measurements on an underdoped (La(2-x)Srx)CuO4 system show that, at energies below 70 meV, the quasiparticle peak is well defined around the (pi/2,pi/2) nodal region and disappears rather abruptly when the momentum is changed from the nodal point to the (pi,0) antinodal point along the underlying "Fermi surface." It indicates that there is an extra low energy scattering mechanism acting upon the antinodal quasiparticles. We propose that this mechanism is the scattering of quasiparticles across the nearly parallel segments of the Fermi surface near the antinodes.     

The “pair” Fermi contour and high-temperature superconductivity

Superconducting pairing of holes with a large (on the order of doubled Fermi) total pair momentum and small relative motion momenta is considered taking into account the quasi-two-dimensional electronic structure of high-T _c cuprates with clearly defined nesting of the Fermi contour situated in an extended neighborhood of the saddle point of the electronic dispersion law (the momentum space region with a hyperbolic metric) and the arising of a spatially inhomogeneous (stripe) structure as a result of the redistribution of current carriers (holes) that restores regions with antiferromagnetic ordering. The superconducting energy gap and condensation energy were determined, and their dependences on the doping level were qualitatively studied. The energy gap was shown to exist in some hole concentration region limited on both sides. The superconducting state with a positive condensation energy appears in a narrower range of doping within this region. The reason for the arising of the superconducting state at a repulsive screened Coulomb interaction between holes is largely the redistribution of hole pairs in the momentum space related to the special features of the hyperbolic metric, which is responsible for the formation of the “pair” Fermi contour, and the renormalization of the kinetic energy of holes when the chemical potential changes because of the condensation of pairs. Hole pairs of the type under consideration exist not only in the condensate but also in the form of quasi-stationary states with very weak decay at temperatures substantially exceeding the superconducting transition temperature. The pseudogap region of the phase diagram of high-T _c cuprates is related to such states. The pairing mechanism under consideration allows not only the principal characteristics of the phase diagram but also key experimental data on high-T _c cuprate materials to be qualitatively explained.     

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.     

Probing the unconventional superconducting state of LiFeAs by quasiparticle interference

A crucial step in revealing the nature of unconventional superconductivity is to investigate the symmetry of the superconducting order parameter. Scanning tunneling spectroscopy has proven a powerful technique to probe this symmetry by measuring the quasiparticle interference (QPI) which sensitively depends on the superconducting pairing mechanism. A particularly well-suited material to apply this technique is the stoichiometric superconductor LiFeAs as it features clean, charge neutral cleaved surfaces without surface states and a relatively high T(c)～18 K. Our data reveal that in LiFeAs the quasiparticle scattering is governed by a van Hove singularity at the center of the Brillouin zone which is in stark contrast to other pnictide superconductors where nesting is crucial for both scattering and s(±) superconductivity. Indeed, within a minimal model and using the most elementary order parameters, calculations of the QPI suggest a dominating role of the holelike bands for the quasiparticle scattering. Our theoretical findings do not support the elementary singlet pairing symmetries s(++), s(±), and d wave. This brings to mind that the superconducting pairing mechanism in LiFeAs is based on an unusual pairing symmetry such as an elementary p wave (which provides optimal agreement between the experimental data and QPI simulations) or a more complex order parameter (e.g., s+id wave symmetry).     

Anomalous momentum dependence of the superconducting coherence peak and its relation to the pseudogap of La1.85Sr0.15CuO4

We performed high-resolution angle-resolved photoemission spectroscopy on La1.85Sr0.15CuO4 to study the nature of the single-particle excitation gap. We found that there is a well-defined superconducting coherence peak in the off-nodal region while it is strongly suppressed around the antinode. The momentum dependence of the single-particle excitation gap shows a striking deviation from the dx-y2--wave symmetry with anomalous enhancement around the antinode in both the superconducting and the pseudogap state. The observed close correlation between the superconducting coherence peak and the pseudogap suggests a substantial contribution of the pseudogap to the anomalous behavior of the gap in the superconducting state.     

Non-Fermi-liquid behavior and d-wave superconductivity near the charge-density-wave quantum critical point

A scenario is presented, in which the presence of a quantum critical point due to formation of incommensurate charge density waves accounts for the basic features of the high temperature superconducting cuprates, both in the normal and in the superconducting states. Specifically, the singular interaction arising close to this charge-driven quantum critical point gives rise to the non-Fermi liquid behavior universally found at optimal doping. This interaction is also responsible for d-wave Cooper pair formation with a superconducting critical temperature strongly dependent on doping in the overdoped region and with a plateau in the optimally doped region. In the underdoped region a temperature dependent pairing potential favors local pair formation without superconducting coherence, with a peculiar temperature dependence of the pseudogap and a non-trivial relation between the pairing temperature and the gap itself. This last property is in good qualitative agreement with so far unexplained features of the experiments.