Antinodal Region Research Articles

Energy gaps in Bi2Sr2CaCu2O8+δ cuprate superconductors

The relationship between the cuprate pseudogap (Δp) and superconducting gap (Δs) remains an unsolved mystery. Here, we present a temperature- and doping-dependent tunneling study of submicron Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions, which provides a clear evidence that Δs closes at a temperature Tc0 well above the superconducting transition temperature Tc but far below the pseudogap opening temperature T*. We show that the superconducting pairing first occurs predominantly on a limited Fermi surface near the node below Tc0, accompanied by a Fermi arc due to the lifetime effects of quasiparticles and Cooper pairs. The arc length has a linear temperature dependence, and as temperature decreases below Tc it reduces to zero while pairing spreads to the antinodal region of the pseudogap leading to a d-wave superconducting gap on the entire Fermi surface at lower temperatures.

Pseudogap, Superconducting Gap, and Fermi Arc in High-TcCuprates Revealed by Angle-Resolved Photoemission Spectroscopy

We present an overview of angle-resolved photoemission spectroscopy (ARPES) studies of high-temperature cuprate superconductors aiming at elucidating the relationship between the superconductivity, the pseudogap, and the Fermi arc. ARPES studies of underdoped samples show a momentum dependence of the energy gap below Tc which deviates from a simple d-wave form, suggesting the coexistence of multiple energy scales in the superconducting state. Hence, two distinct energy scales have been introduced, namely, the gap near the node (characterized by Delta_0) and in the anti-nodal region (characterized by Delta^*). Dichotomy between them has been demonstrated from the material, doping, and temperature dependence of the energy gap. While Delta^* at the same doping level is approximately material independent, Delta_0 shows a strong material dependence tracking the magnitude of Tc,max. The anti-nodal gap does not close at Tc in contrast to the gap near the node which follows something closer to a BCS-like temperature dependence. An effective superconducting gap Delta_sc defined at the end point of the Fermi arc is found to be proportional to Tc's in various materials.

Occurrence of Fermi Pockets without Pseudogap Hypothesis and Clarification of the Energy Distribution Curves of Angle-Resolved Photoemission Spectroscopy in Underdoped Cuprate Superconductors

Central issues in the electronic structure of underdoped cuprate superconductors are to clarify the shape of the Fermi surfaces and the origin of the pseudogap. On the basis of the model proposed by Kamimura and Suwa, which bears important features originating from the interplay of Jahn-Teller physics and Mott physics, the feature of Fermi surfaces in underdoped cuprates is the presence of Fermi pockets constructed from doped holes under the coexistence of a metallic state and a local antiferromagnetic order. Below $T_{\rm c}$, the holes on Fermi pockets form Cooper pairs with d-wave symmetry in the nodal region. In the antinodal region, there are no Fermi surfaces. In this study we calculate the energy distribution curves (EDCs) of angle-resolved photoemission spectroscopy (ARPES) below $T_{\rm c}$. It is shown that the feature of ARPES profiles of underdoped cuprates consists of a coherent peak in the nodal region and real transitions of photoexcited electrons from occupied states below the Fermi level to a free-electron state above the vacuum level in the antinodal region, where the latter transitions form a broad hump. From this feature, the origin of the two distinct gaps observed by ARPES is elucidated without introducing the concept of the pseudogap. Finally, a remark is made on the phase diagram of underdoped cuprates.

Chemical potential oscillations from nodal Fermi surface pocket in the underdoped high-temperature superconductor YBa2Cu3O6+x

The electronic structure of the normal state of the underdoped cuprates has thus far remained mysterious, with neither the momentum space location nor the charge carrier type of constituent small Fermi surface pockets being resolved. Whereas quantum oscillations have been interpreted in terms of a nodal-antinodal Fermi surface including electrons at the antinodes, photoemission indicates a solely nodal density-of-states at the Fermi level. Here we examine both these possibilities using extended quantum oscillation measurements. Second harmonic quantum oscillations in underdoped YBa₂Cu₃O(₆+x) are shown to arise chiefly from oscillations in the chemical potential. We show from the relationship between the phase and amplitude of the second harmonic with that of the fundamental quantum oscillations that there exists a single carrier Fermi surface pocket, likely located at the nodal region of the Brillouin zone, with the observed multiple frequencies arising from warping, bilayer splitting and magnetic breakdown.

Momentum-space electronic structures and charge orders of the high-temperature superconductors Ca2−xNaxCuO2Cl2and Bi2Sr2CaCu2O8+δ

We study the electronic structure of Ca${}_{2\ensuremath{-}x}$Na${}_{x}$CuO${}_{2}$Cl${}_{2}$ and Bi${}_{2}$Sr${}_{2}$CaCu${}_{2}$O${}_{8+\ensuremath{\delta}}$ samples in a wide range of doping, using angle-resolved photoemission spectroscopy, with emphasis on the Fermi surface (FS) in the near antinodal region. The ``nesting wave vector,'' i.e., the wave vector that connects two nearly flat pieces of the FS in the antinodal region, reveals a universal monotonic decrease in magnitude as a function of doping. Comparing our results to the charge order recently observed by scanning tunneling spectroscopy (STS), we conclude that the FS nesting and the charge order pattern seen in STS do not have a direct relationship. Therefore, the charge order likely arises due to strong-correlation physics rather than FS nesting physics.

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.

Composite fermion theory for pseudogap phenomena and superconductivity in underdoped cuprate superconductors

We study pseudogap phenomena and Fermi-arc formation experimentally observed in typical two dimensional doped Mott insulators, namely, underdoped cuprate superconductors. To develop a physically unequivocal theory, we start from the slave-boson mean-field theory for the Hubbard model on a square lattice. Our crucial step is to further take into account the charge dynamics and fluctuations. The extra charge fluctuations seriously modify low-energy single-particle spectra of doped Mott insulators near the Fermi level: An electron added around an empty site (or a hole added around a doubly occupied site) constitutes composite fermion (cofermion), called holo-electron (or doublo-hole) at low energy in distinction from the normal quasiparticles. These unexplored composite fermions substantiate the extra charge fluctuation. We show that the quasiparticles hybridize with the holo-electrons and doublo-holes. The resultant hybridization gap is identified as the pseudogap observed in the underdoped region of the high-T_c cuprates. Because the Fermi level crosses the top (bottom) of the low-energy band formed just below (above) the hybridization gap in the hole-doped (electron-doped) case, it causes a Fermi-surface reconstruction, namely, a topological change in the Fermi surface forced by the penetration of zeros of the quasiparticle Green function. This reconstruction signals the emergence of a non-Fermi-liquid phase. The pseudogap, and the resultant formation of pocket or arc of the Fermi surface reproduce the experimental results for the cuprate superconductors in the underdoped region. The pairing channel opens not only between two quasiparticles but also between a quasiparticle and a cofermion. This pairing solves the puzzle of the dichotomy between the d-wave superconductivity and the precursors of the the insulating gap in the antinodal region.

Two pseudogaps with different energy scales at the antinode of the high-temperature Bi2Sr2CuO6superconductor using angle-resolved photoemission spectroscopy

We have performed high-resolution angle-resolved photoemission spectroscopy on single-layered cuprate Bi$_2$Sr$_2$CuO$_6$ to clarify the origin of the pseudogap. By using various photon energies, we have succeeded in directly observing two different pseudogaps with two different energy scales which coexist in the antinodal region: one reflects the $d_{x^2-y^2}$-wave pairing strength while the other has a larger energy scale suggesting an origin distinct from superconductivity. The observed two-pseudogap behavior provides a key to fully understand the pseudogap phenomena in cuprates.

Underdoped cuprates as fractionalized Fermi liquids: Transition to superconductivity

We model the underdoped cuprates using fermions moving in a background with local antiferromagnetic order. The antiferromagnetic order fluctuates in orientation, but not in magnitude, so that there is no long-range antiferromagnetism, but a 'topological' order survives. The normal state is described as a fractionalized Fermi liquid (FL*), with electron-like quasiparticles coupled to the fractionalized excitations of the fluctuating antiferromagnet. The electronic quasiparticles reside near pocket Fermi surfaces enclosing total area x (the dopant density), centered away from the magnetic Brillouin zone boundary. The violation of the conventional Luttinger theorem is linked to a 'species doubling' of these quasiparticles. We describe phenomenological theories of the pairing of these quasiparticles, and show that a large class of mean-field theories generically displays a nodal-anti-nodal `dichotomy': the interplay of local antiferromagnetism and pairing leads to a small gap near the nodes of the d-wave pairing along the Brillouin zone diagonals, and a large gap in the anti-nodal region.

Publisher's Note: Loss of antinodal coherence with a singled-wave superconducting gap leads to two energy scales for underdoped cuprate superconductors [Phys. Rev. B82, 144516 (2010)

Received 19 November 2010DOI:https://doi.org/10.1103/PhysRevB.82.189903©2010 American Physical Society

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.

Interplane charge dynamics in a valence-bond dynamical mean-field theory of cuprate superconductors

We present calculations of the interplane charge dynamics in the normal state of cuprate superconductors within the valence-bond dynamical mean-field theory. We show that by varying the hole doping, the c-axis optical conductivity and resistivity dramatically change character, going from metallic-like at large doping to insulating-like at low-doping. We establish a clear connection between the behavior of the c-axis optical and transport properties and the destruction of coherent quasiparticles as the pseudogap opens in the antinodal region of the Brillouin zone at low doping. We show that our results are in good agreement with spectroscopic and optical experiments.

Spin Polaron-Bipolaron Scenario of Three Gap-Like Energy Scales in Superconducting Cuprates

We argue that three gaps observed in underdoped cuprates can be attributed to the formation of antiferromagnetic spin polarons and bipolarons. Within the spin polaron scenario the antinodal pseudogap at he high energy scale originates from the change of the Fermi surface topology, induced by antiferromagnetic correlations. That change gives rise to the diminishing of the spectral weight at the antinodal region near the Brillouin zone boundary. We demonstrate that effect by analyzing effective models of doped antiferromagnets. The second type of pseudogap appearing at the intermediate energy scale originates from the phenomena which are precursory to superconductivity and predominantly concern the portion of the Fermi surface near the nodal region. In order to analyze the latter phenomenon we use the negative U Hubbard model, in which many details typical to spin polaron physics are neglected, but which contains the essential ingredient of it, that is the strong short range attraction. The lowest energy scale is related to the true superconducting gap which develops with doping, although both types of pseudogap diminish with doping. This behavior can be explained by the fact that the spin polaron band is empty in the undoped system and therefore the formation of the superconducting state in the system is forbidden. Due to a pedagogical character of this report, we present in the introduction a short overview of mostly recent experimental results which are related to the gap-pseudogap physics.

Pseudogap in underdoped cuprates and spin-density-wave fluctuations

We analyze fermionic spectral function in the spin-density-wave (SDW) phase of quasi-2D cuprates at small but finite T. We use a non-perturbative approach and sum up infinite series of thermal self-energy terms, keeping at each order nearly-divergent (T/J) |log epsilon| terms, where epsilon is a deviation from a pure two-dimensionality, and neglecting regular T/J corrections. We show that, as SDW order decreases, the spectral function in the antinodal region acquires peak/hump structure: the coherent peak position scales with SDW order parameter, while the incoherent hump remains roughly at the same scale as at T=0 when SDW order is the strongest. We identify the hump with the pseudogap observed in ARPES and argue that the presence of coherent excitations at low energies gives rise to magneto-oscillations in an applied field. We show that the same peak/hump structure appears in the density of states and in optical conductivity.

Crossover region between nodal and antinodal states at the Fermi level of optimally doped and overdopedBi2Sr1.6Nd0.4CuO6+δ

We have studied Bi$_{2}$Sr$_{1.6}$Nd$_{0.4}$CuO$_{6+\delta}$ using Angle Resolved Photoemission Spectroscopy in the optimal and overdoped regions of the phase diagram. We identify a narrow crossover region in the electronic structure between the nodal and antinodal regions associated with the deviation from a pure d-wave gap function, an abrupt increase of the quasiparticle lifetime, the formation of Fermi arcs above T$_c$, and a sudden shift of the bosonic mode energy from higher energy, $\sim${60meV}, near the nodal direction, to lower energy, $\sim${20meV}, near the antinodal direction. Our work underscores the importance of a unique crossover region in the momentum space near E$_F$ for the single layered cuprates, between the nodal and antinodal points, that is independent of the antiferromagnetic zone boundary.

Large pseudogap and nodal superconducting gap inBi2Sr2−xLaxCuO6+δandBi2Sr2CaCu2O8+δ: Scanning tunneling microscopy and spectroscopy

In the present work, scanning tunneling microscopy/spectroscopy (STM/STS) measurements were carried out on underdoped ${\text{Bi}}_{2}{\text{Sr}}_{2\ensuremath{-}x}{\text{La}}_{x}{\text{CuO}}_{6+\ensuremath{\delta}}$ and ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$ to clarify the origin of the pseudogap, in particular, the inhomogeneous large pseudogap. The nodal part of a $d$-wave pairing gap, which is under no influence of the inhomogeneous large pseudogap, was also examined by relating the homogeneous bottom part of the STS gap to a nodal $d$-wave gap in momentum space. We report that the inhomogeneous large pseudogap in the antinodal region links to a two-dimensional electronic charge order, and that the gap size of the nodal $d$-wave part ${\ensuremath{\Delta}}_{\text{sc}}$ scales with the superconducting critical temperature ${T}_{\text{c}}$ in the pseudogap regime.

Investigation of a CDDW Hamiltonian to Explore Possibility of Magneto-Quantum Oscillations in Electronic Specific Heat of Hole-Doped Cuprates

We investigate a chiral d-density wave (CDDW) mean field model Hamiltonian in the momentum space suitable for the hole-doped cuprates, such as YBCO, in the pseudogap phase to obtain the Fermi surface (FS) topologies, including the anisotropy parameter() and the elastic scattering by disorder potential (). For , with the chemical potential eV for 10% doping level and (where eV is the first neighbor hopping), at zero/non-zero magnetic field (), the FS on the first Brillouin zone is found to correspond to electron pockets around antinodal regions and barely visible patches around nodal regions. For , we find Pomeranchuk distortion of FS. We next relate our findings regarding FS to the magneto-quantum oscillations in the electronic specific heat. Since the nodal quasiparticle energy values for are found to be greater than for , the origin of the oscillations for nonzero corresponds to the Fermi pockets around antinodal regions. The oscillations are shown to take place in the weak disorder regime (eV) only.

Checkerboard superconducting order and antinodal Bogoliubov quasiparticle interference

Numerical study of momentum-dependent gap function is presented to make clear the origin of superconductivity in copper oxides. We claim that antinodal region with pronounced nesting feature of the Fermi contour gives rise to superconducting pairing with large momentum under screened Coulomb repulsion. Such a pairing results in both spatial checkerboard pattern of the superconducting state below Tc and a gapped state of incoherent pairs in a broad temperature range above Tc. We explain the momentum dependence of the coherent spectral weight detected in angle-resolved photoemission spectroscopy and predict antinodal Bogoliubov quasiparticle interference other than observed in the nodal region.

Enhancement of oxygen isotope effect due to out-of-plane disorder inBi2Sr2Ln0.4CuO6+δsuperconductors

The disorder dependence of the oxygen isotope effect in optimally doped ${\text{Bi}}_{2}{\text{Sr}}_{1.6}{\text{Ln}}_{0.4}{\text{CuO}}_{6+\ensuremath{\delta}}$ superconductors which is introduced into cation sites in the planes adjacent to ${\text{CuO}}_{2}$ planes is studied. The degree of out-of-plane disorder is controlled by substituting Ln ions with different ionic radii from La to Gd. This type of disorder does not explicitly alter the nodal electronic structure or the underlying Fermi surface but markedly enhances the oxygen isotope exponent at the superconducting transition temperature $({\ensuremath{\alpha}}_{{T}_{c}})$. The enhancement in ${\ensuremath{\alpha}}_{{T}_{c}}$ is well explained by the pair-breaking model, suggesting the growth of a pseudogap state around the antinodal region due to the out-of-plane disorder.

Model for the coexistence ofd-wave superconducting and charge-density-wave order parameters in high-temperature cuprate superconductors

A theory describing a phase, where $d$-wave superconductivity coexists with charge-density waves (CDWs), has been developed. Numerical calculations were carried out for a specific case of cuprates when the CDW gap emerges at the nested antinodal regions of the two-dimensional Fermi surface. Different symmetries of the order parameters leads to their involved interplay so that the CDW one $\ensuremath{\Sigma}(T)$ is predicted to become temperature re-entrant for certain ranges of model parameters. Here, $T$ is the temperature. At the same time, the superconducting energy gap $\ensuremath{\Delta}(T)$ deviates substantially from the canonical ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ form. The CDW influence on $\ensuremath{\Delta}(T)$ is different from that on the critical temperature ${T}_{c}$. Hence, the resulting values of $2\ensuremath{\Delta}(0)/{T}_{c}$ are shown to fall into the range $5\textdiv{}8$, which is well known for high-${T}_{c}$ oxides and has not been explained yet.