Pair-density-wave pseudogap and superconducting states in cuprates

Bogoliubov quasiparticle interference and localized high-energy excitations observed in cuprates in nodal and antinodal regions of the momentum space, respectively, would lead to a conclusion that only the nodal region might give rise to superconductivity whereas the antinodal one might be associated with the pseudogap. We argue that both pseudogap and superconducting states arise exactly in the antinodal region with pronounced nesting feature of the Fermi contour as spatially inhomogeneous incoherent and coherent states of pairs with large momentum. The nodal region gives rise to conventional superconducting pairing with zero momentum which, together with the pairing with large momentum in the antinodal region, forms a biordered superconducting state in the whole of the Brillouin zone. This coherent state with complicated momentum dependence of the order parameter manifests itself as a pair-density wave that can exist without any driving insulating order. We believe that quasiparticle interference, other than observed in the nodal region, should be observable in the antinodal region as well.     

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.     

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.     

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.     

Thermodynamics and phase diagram of high temperature superconductors

Thermodynamic quantities are derived for superconducting and pseudogap regimes by taking into account both amplitude and phase fluctuations of the pairing field. In the normal (pseudogap) state of the underdoped cuprates, two domains have to be distinguished: near the superconducting region, phase correlations are important up to temperature T(phi). Above T(phi), the pseudogap region is determined only by amplitudes, and phases are uncorrelated. Our calculations show excellent quantitative agreement with specific heat and magnetic susceptibility experiments on cuprates. We find that the mean field temperature T0 has a similar doping dependence as the pseudogap temperature T(*), whereas the pseudogap energy scale is given by the average amplitude above T(c).     

Pseudogap state of two-dimensional Kondo lattice

The pseudogap behavior of spectral function A(k, ω) of charge carriers is considered in the weak doping regime for a 2D Kondo lattice with a strong spin-hole antiferromagnetic interaction. The scattering of carriers is described in terms of a local polaron according to the irreducible Green functions. The behavior of the carrier spectrum in the nodal and antinodal domains is considered. The resultant value of the pseudogap is in conformity with experimental data on photoemission with angular resolution.     

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.     

The short-range correlations of a doped Mott insulator

This paper presents numerical studies of the single hole model that address the interplay between the kinetic energy of itinerant electrons and the exchange energy of local moments as of interest to doped Mott insulators. Due to this interplay, two different spin correlations coexist around a mobile vacancy. These local correlations provide an effective two-band picture that explains the two-band structure observed in various theoretical and experimental studies, the doping dependence of the momentum space anisotropic pseudogap phenomena and the asymmetry between hole and electron doped cuprates.     

Mechanism of Pseudogap Detected by Electronic Raman Scattering： Phase Fluctuation or Hidden Order？

We study the electronic Raman scattering in the cuprates to distinguish the two possible scenarios of the pseudogap normal state. In one scenario, the pseudogap is assumed to be caused by phase fluctuations of the preformed Cooper pairs. We find that pair-breaking peaks appear in both the B1g and B2g Raman channels, and they axe smeared and tend to shift to the same energy with the increasing strength of phase fluctuations. Thus both channels reflect the same pairing energy scale, irrespectively of the doping level. In another scenario, the pseudogap is assumed to be caused by a hidden order that competes with the superconducting order. As an example, we assume that the hidden order is the d-density-wave （DDW） order. We find analytically and numerically that in the DDW normal state there is no Raman peak in the B2g channel in a tight-binding model up to the second nearest-neighbor hopping, while the Raman peak in the Big channel reflects the energy gap caused by the DDW order. This behavior is in agreement with experiments in the pseudogap normal state. To gain further insights, we also calculate the Raman spectra in the DDW＋SC state. We study the doping and temperature dependence of the peak energy in both channels and find a two-gap behavior, which is in agreement with recent Raman experiments. Therefore, our results shed light on the hidden order scenario for the pseudogap.     

Competition between antiferromagnetism and superconductivity in the electron-doped cuprates triggered by oxygen reduction

We have performed a systematic angle-resolved photoemission study of as-grown and oxygen-reduced Pr(2-x)CexCuO4 and Pr(1-x)LaCexCuO4 electron-doped cuprates. In contrast with the common belief, neither the band filling nor the band parameters are significantly affected by the oxygen reduction process. Instead, we show that the main electronic role of the reduction process is to remove an anisotropic leading edge gap around the Fermi surface. While the nodal leading edge gap is induced by long-range antiferomagnetic order, the origin of the antinodal one remains unclear.     

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.     

Study of Pseudogap in Underdoped Cuprate

A mean-field spin-density wave (SDW) analysis of pseudogap in the underdoped cuprates is proposed on the basis of the t-t^ˊ-U Hubbard model. It is surprised to find that a simple t^ˊ term will do the trick to introduce the momentum dependence of the energy gap which mimics the pseudogap near (π,0) point at least. It implies that the pseudogap structure near (π,0) is not sensitive to the long-range order and will survive leading to the pseudogap phenomenon in the underdoped metallic phase. On the other hand, in the long-range ordering antiferromagnetic region, the mean-field SDW theory holds and the pseudogap structure predicated by the theory should be observable experimentally. Then one prediction is that the pseudogap would smoothly extrapolate between itinerant antiferromagnetic phase and underdoped metallic phase.     

Gap and pseudogap evolution within the charge-ordering scenario for superconducting cuprates

We describe the spectral properties of underdoped cuprates as resulting from a momentum-dependent pseudogap in the normal-state spectrum. Such a model accounts, within a BCS approach, for the doping dependence of the critical temperature and for the two-parameter leading-edge shift observed in the cuprates. By introducing a phenomenological temperature dependence of the pseudogap, which finds a natural interpretation within the stripe quantum-critical-point scenario for high- superconductors, we reproduce also the bifurcation near optimum doping. Finally, we briefly discuss the different role of the gap and the pseudogap in determining the spectral and thermodynamical properties of the model at low temperatures. Received 17 February 2000     

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.     

Near doping-independent pocket area from an antinodal Fermi surface instability in underdoped high temperature superconductors

Fermi surface models applied to the underdoped cuprates predict the small pocket area to be strongly dependent on doping whereas quantum oscillations in YBa(2)Cu(3)O(6+x) find precisely the opposite to be true--seemingly at odds with the Luttinger volume. We show that such behavior can be explained by an incommensurate antinodal Fermi surface nesting-type instability--further explaining the doping-dependent superstructures seen in cuprates using scanning tunneling microscopy. We develop a Fermi surface reconstruction scheme involving orthogonal density waves in two dimensions and show that their incommensurate behavior requires momentum-dependent coupling. A cooperative modulation of the charge and bond strength is therefore suggested.     

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.     

Essence of Pseudogap and Oscillation in High-Temperature Cuprate Superconductor Junction of Pseudogap State

This paper gives methods to calculate the pairing temperature T*,at which a pseudogap is opened,and the superconducting temperature Tc,at which superconductivity appears,in the high-Tc cuprates,and demonstrates directly that at Tc ＜ T ＜ T* the pseudogap is the gap of Cooper pair without long-range phase coherence,and at T ＜ Tc there is long-range phase coherence between Cooper pairs.Based on the above clear physical picture on the pseudogap state and our mechanism for the ac Josephson effect,this paper proposes that there should be a novel oscillatory current in P-I-P junction,induced by a constant bias on the junction.Here,P represents the high-Tc curates in the pseudogap state,where Cooper pairs do not have long-range phase coherence,and I represents the thin insulating barrier.This paper conjectures that there is a possible high-temperature superconductivity in the heavily underdoped high-Tc cuprates.     

Interplay of externally doped and thermally activated holes in La(2-x)Sr(x)CuO4 and their impact on the pseudogap crossover

We presented the recent Hall effect data for a number of carriers in La(2-x)Sr(x)CuO4 as the sum of two components: the temperature independent term n0(x), which is due to external doping, and the thermally activated contribution. Their balance determines the crossover temperature T*(x) from the marginal Fermi liquid to pseudogap regime. The activation energy Delta(x) for thermally excited carriers equals the energy between the Fermi surface "arc" and the band bottom, as seen in angle-resolved photoemission spectroscopy experiments. Other implications for the (T, x)-phase diagram of cuprates are also discussed.