Antinodal Gap Research Articles

Temperature dependence of quasiparticle interference in $d$-wave superconductors

We investigate the temperature dependence of quasiparticle interference in the high T_cTc-cuprates using an exact-diagonalization + Monte-Carlo based scheme to simulate the dd-wave superconducting order parameter. The quasiparticle interference patterns have features largely resulting from the scattering vectors of the octet model at lower temperature. Our findings suggest that the features of quasiparticle interference in the pseudogap region of the phase diagram are also dominated by the set of scattering vectors belonging to the octet model because of the persisting antinodal gap beyond the superconducting transition T_cTc. However, beyond a temperature when the antinodal gap becomes very small, a set of scattering vectors different from those belonging to the octet model are responsible for the quasiparticle interference patterns. With a rise in temperature, the patterns are increasingly broadened.

Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-T_{c} Superconductivity.

Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k_{B}T_{c}≈6.5 (where Δ is the pairing gap and T_{c} is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N_{0} and the height of the jump δγ(T_{c}) in the coefficient γ of the fermionic specific heat at T_{c} are strongly peaked. In the cuprates, δγ(T_{c}) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T_{c}) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T_{c}.

Hard antinodal gap revealed by quantum oscillations in the pseudogap regime of underdoped high-Tc superconductors

An understanding of the missing antinodal electronic excitations in the pseudogap state is essential for uncovering the physics of the underdoped cuprate high temperature superconductors. The majority of high temperature experiments performed thus far, however, have been unable to discern whether the antinodal states are rendered unobservable due to their damping, or whether they vanish due to their gapping. Here we distinguish between these two scenarios by using quantum oscillations to examine whether the small Fermi surface pocket, found to occupy only 2% of the Brillouin zone in the underdoped cuprates, exists in isolation against a majority of completely gapped density of states spanning the antinodes, or whether it is thermodynamically coupled to a background of ungapped antinodal states. We find that quantum oscillations associated with the small Fermi surface pocket exhibit a signature sawtooth waveform characteristic of an isolated two-dimensional Fermi surface pocket. This finding reveals that the antinodal states are destroyed by a hard gap that extends over the majority of the Brillouin zone, placing strong constraints on a drastic underlying origin of quasiparticle disappearance over almost the entire Brillouin zone in the pseudogap regime.

Intrinsic cluster-shaped density waves in cellular dynamical mean-field theory

It is well known that cellular dynamical mean-field theory (CDMFT) leads to the artificial breaking of translation invariance. In spite of this, it is one of the most successful methods to treat strongly correlated electrons systems. Here, we investigate in more detail how this broken translation invariance manifests itself. This allows us to disentangle artificial broken translation invariance effects from the genuine strongly correlated effects captured by CDMFT. We report artificial density waves taking the shape of the cluster---cluster density waves---in all our zero temperature CDMFT solutions, including pair density waves in the superconducting state. We discuss the limitations of periodization regarding this phenomenon, and we present mean-field density-wave models that reproduce CDMFT results at low energy in the superconducting state. We then discuss how these artificial density waves help the agreement of CDMFT with high temperature superconducting cuprates regarding the low-energy spectrum, in particular for subgap structures observed in tunneling microscopy. We relate these subgap structures to nodal and antinodal gaps in our results, similar to those observed in photoemission experiments. This fortuitous agreement suggests that spatial inhomogeneity may be a key ingredient to explain some features of the low-energy underdoped spectrum of cuprates with strongly correlated methods. This work deepens our understanding of CDMFT and clearly identifies signatures of broken translation invariance in the presence of strong correlations.

Single origin of the nodal and antinodal gaps in cuprates

Recent angle-resolved photoemission electron spectroscopy (ARPES) experiments demonstrate that the momentum dependence of the spectral gap in underdoped cuprates does not follow a pure d-wave form (Anzai H. et al., Nat. Commun., 4 (2013) 1815). This deviation is highly controversial. It has often been interpretated as a proof of the non-superconducting origin of the antinodal gap in the underdoped regime. In this paper, we show that the measured angular dependence of the spectral gap can be explained by the basic nature of pairs in high-Tc cuprates. Hole pairs, or pairons, form as a result of the local antiferromagnetic environment on the scale , the magnetic coherence length. The spatial extension of the pairon wave function beyond first nearest neighbours gives rise to the anomalous angular dependence of the gap, in quantitative agreement with experiments. This simple interpretation strongly indicates the common origin of the nodal and antinodal gaps.

Pairing Symmetry, Nodal and Antinodal Superconducting Gap in $$\text {La}_{2-x}\text {Sr}_x\text {CuO}_{4}$$: A Doping Scenario

Using the many-body quantum dynamics and Dyson’s equation formalism, the phonon Green’s function has been developed via a Hamiltonian that includes the contribution of harmonic electron and phonon field and their interaction, phonon field anharmonicities and defects. The renormalized electron–phonon dispersion is obtained using the modified form of Born–Mayer–Huggins potential (MBMHP) and phonon Green’s function for a representative high-temperature superconductor (HTS) $$\text {La}_{2-x}\text {Sr}_x\text {CuO}_4$$. The in-plane gap analysis has produced a v-shaped gap that confesses the anisotropy of the superconducting gap (SG). The nodal gap, antinodal gap and SG exhibit increment with decreasing doping with the vanishing of the nodal gap at $$x=0.104$$. A dominated $$d_{x^2-y^2}$$ pairing symmetry is observed along with a small component of s or $$d_{xy}$$ pairing state in the underdoped regime. The variation in the nodal gap, antinodal gap and SG shows monotonic increment with decreasing doping. It is found that doping has a nonlinear effect on $$d_{x^2-y^2}$$ pairing symmetry. The impact of antiferromagnetic (AF) spin fluctuations has been incorporated in the SG equation and on the pairing symmetry.

Quantitative Comparison between Electronic Raman Scattering and Angle-Resolved Photoemission Spectra in Bi2Sr2CaCu2O8+δ Superconductors: Doping Dependence of Nodal and Antinodal Superconducting Gaps

Both electronic Raman scattering (ERS) and angle-resolved photoemission spectra (ARPES) revealed two energy scales for the gap in different momentum spaces in the cuprates. However, the interpretations were different, and the gap values were also different in two experiments. In order to clarify the origin of these discrepancies, we directly compared ERS and ARPES by calculating ERS from the experimental data of ARPES through the Kubo formula. The calculated ERS spectra were in good agreement with the experimental results except for the B$_{1g}$ peak energies. The doping-dependent B$_{2g}$ peak energy was well reproduced from a doping-independent d-wave gap deduced from ARPES, by assuming a particular spectral weight distribution along the Fermi surface. The B$_{1g}$ peak energies could not be reproduced by the ARPES data. The difference between B$_{1g}$ ERS and antinodal ARPES became larger with underdoping, which implies that the effect of the pseudogap is different in these two techniques.

Double pair breaking peak in Raman scattering spectra of the triple-layer cuprate Bi2Sr2Ca2Cu3O10+z

We report the Raman scattering measurements on the triple layer Bi2Sr2Ca2Cu3O10 (Bi2223) crystals of four different doping levels from slightly overdoped to strongly underdoped regimes. We observed a double pair-breaking peak in the antinodal B1g configuration that we attribute to the two antinodal gaps opening on the outer and inner CuO2-plane (OP and IP) band, respectively. The doping dependence of the pair-breaking peak energy was investigated. Considering the difference in doping level between the IP and OP, all the B1g pair-breaking peak energies for OP and IP were found to align on a single line as a function of doping, which is consistent with the previous results on the double and mono-layer cuprates. Within our experimental accuracy the IP and OP peaks start to appear almost at the same temperature. These findings suggest some sort of interaction between the layers. The observed gap energy is very large, not scaling with Tc.

Intertwining Topological Order and Broken Symmetry in a Theory of Fluctuating Spin-Density Waves.

The pseudogap metal phase of the hole-doped cuprate superconductors has two seemingly unrelated characteristics: a gap in the electronic spectrum in the "antinodal" region of the square lattice Brillouin zone and discrete broken symmetries. We present a SU(2) gauge theory of quantum fluctuations of magnetically ordered states which appear in a classical theory of square lattice antiferromagnets, in a spin-density wave mean field theory of the square lattice Hubbard model, and in a CP^{1} theory of spinons. This theory leads to metals with an antinodal gap and topological order which intertwines with the observed broken symmetries.

Electron scattering, charge order, and pseudogap physics inLa1.6−xNd0.4SrxCuO4: An angle-resolved photoemission spectroscopy study

We report an angle-resolved photoemission study of the charge stripe ordered La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ system. A comparative and quantitative line shape analysis is presented as the system evolves from the overdoped regime into the charge ordered phase. On the overdoped side ($x=0.20$), a normal state anti-nodal spectral gap opens upon cooling below ~ 80 K. In this process spectral weight is preserved but redistributed to larger energies. A correlation between this spectral gap and electron scattering is found. A different lineshape is observed in the antinodal region of charge ordered Nd-LSCO $x=1/8$. Significant low-energy spectral weight appears to be lost. These observations are discussed in terms of spectral weight redistribution and gapping %of spectral weight originating from charge stripe ordering.

STM spectroscopy on deuterated κ-(ET-d[3,3])2Cu[N(Cn)2]Br

We performed the STM Spectroscopy (STS) measurement on organic superconductor deuterated κ-(ET-d[3,3])2Cu[N(CN)2]Br to clarify the mechanism of superconductivity. The mechanism of superconductivity in κ-ET2X is predicted as the spin fluctuation mechanism where the gap symmetry changes from dx2−y2 to dxy with increasing the electron correlation. In previous STS measurements, we found that d[2,2]-Br, d[0,0]-Br and Cu(NCS)2 were d-wave superconductors and the symmetry was described by the dx2−y2. The electron correlation of these salts is still weak in the frame of the spin fluctuation model. So, we investigated the d[3,3]-Br which located at stronger electron correlation region than the previously studied salts by the STS. We also investigated the STS on the cut lateral surfaces by the focused ion beam (FIB) method to measure the in-plane anisotropy of superconducting gap in more detail as well as the as-grown surfaces. It was found from the result that d[3,3]-Br was d-wave superconductor and the gap symmetry was dx2−y2 as well as the previously studied ET salts. Therefore, d[3,3]-Br is also still weak in spite of stronger electron correlation than other ET salts. On the other hand, we also observed the two-type superconducting gaps which are the nodal and anti-nodal type gaps at the same angle surface. This suggests the coexistence of dx2−y2 and dxy. It may be the evidence of the change from dx2−y2 to dxy caused by the locally stronger electron correlation around the anti-ferromagnetic insulating region.

Linking dynamic and thermodynamic properties of cuprates: An angle-resolved photoemission study of (CaxLa1−x)(Ba1.75−xLa0.25+x)Cu3Oy(x=0.1and 0.4)

We report angle-resolved photoemission spectroscopy (ARPES) on two families of high temperature superconductors (Ca$_{x}$La$_{1-x}$)(Ba$_{1.75-x}$ La $% _{0.25+x}$)Cu$_{3}$O$_{y}$ with $x=0.1$ ($T_{c}^{max}=56$ K) and $x=0.4$ ($% T_{c}^{max}=82$ K). The Fermi surface (FS) is found to be independent of $x$ or $y$, and its size indicates extreme sample-surface overdoping. This universal FS allowes the comparison of dynamical properties between superconductors of similar structure and identical doping, but different $% T_{c}^{max}$. We find that the high-energy ($\left\vert E\right\vert >50$% meV) nodal velocity in the $x=0.4$ family is higher than in the $x=0.1$ family. The implied correlation between $T_{c}^{max}$ and the hopping rate $% t $ supports the notion of kinetic energy driven superconductivity in the cuprates. We also find that the antinodal gap is higher for the $x=0.4$ family.

Band structure effects on the superconductivity in Hubbard models

We study the influence of the band structure on the symmetry and superconducting transition temperature in the (solvable) weak-coupling limit of the repulsive Hubbard model. Among other results we find that (1) as a function of increasing nematicity, starting from the square-lattice (zero nematicity) limit where a nodal $d$-wave state is strongly preferred, there is a smooth evolution to the quasi-1D limit, where a striking near-degeneracy is found between a $p$-wave- and a $d$-wave-type paired states with accidental nodes on the quasi-one-dimensional Fermi surfaces---a situation that may be relevant to the Bechgaard salts. (2) In a bilayer system, we find a phase transition as a function of increasing bilayer coupling from a $d$-wave to an ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave state reminiscent of the iron-based superconductors. (3) When an antinodal gap is produced by charge-density-wave order, not only is the pairing scale reduced, but the symmetry of the pairs switches from ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ to ${d}_{xy}$; in the context of the cuprates, this suggests that were the pseudogap entirely due to a competing CDW order, this would likely cause a corresponding symmetry change of the superconducting order (which is not seen in experiment).

Relation between the nodal and antinodal gap and critical temperature in superconducting Bi2212

An energy gap is, in principle, a dominant parameter in superconductivity. However, this view has been challenged for the case of high-Tc cuprates, because anisotropic evolution of a d-wave-like superconducting gap with underdoping has been difficult to formulate along with a critical temperature Tc. Here we show that a nodal-gap energy 2ΔN closely follows 8.5 kBTc with underdoping and is also proportional to the product of an antinodal gap energy Δ* and a square-root superfluid density √Ps for Bi2Sr2CaCu2O8+δ, using low-energy synchrotron-radiation angle-resolved photoemission. The quantitative relations imply that the distinction between the nodal and antinodal gaps stems from the separation of the condensation and formation of electron pairs, and that the nodal-gap suppression represents the substantial phase incoherence inherent in a strong-coupling superconducting state. These simple gap-based formulae reasonably describe a crucial part of the unconventional mechanism governing Tc.

Spin-Density-Wave Gap with Dirac Nodes and Two-Magnon Raman Scattering in BaFe2As2

Raman selection rules for electronic and magnetic excitations in BaFe 2 As 2 were theoretically investigated and applied them to the separate detection of the nodal and anti-nodal gap excitations at the spin density wave (SDW) transition and the separate detection of the nearest and the next nearest neighbor exchange interaction energies. Raman spectra are composed of magnetic excitations with gradually decreasing intensity toward far above the SDW transition temperature ( T SDW ) and electronic excitations induced by the Brillouin zone folding below T SDW . The SDW gap has Dirac nodes, because many orbitals participate in the electronic states near the Fermi energy. Using a two-orbital band model the electronic excitations near the Dirac node and the anti-node are found to have different symmetries. Applying the symmetry difference to Raman scattering the nodal and anti-nodal electronic excitations are separately obtained. The low-energy spectra from the anti-nodal region have critical fluctuation just above T SDW and change into the gap structure by the first order transition at T SDW , while those from the nodal region gradually change into the SDW state. Magnetic excitations are observed as a very broad peak in all polarization configurations. The selection rule for two-magnon scattering from the stripe spin structure was obtained. Applying it to the two-magnon Raman spectra it is found that the magnetic exchange interaction energies are not presented by the short-range superexchange model, but the second derivative of the total energy of the stripe spin structure with respect to the moment directions. The selection rule and the peak energy are expressed by the two-magnon scattering process in an insulator, but the large spectral weight above twice the maximum spin wave energy is difficult to explain by the decayed spin wave. It may be explained by the electronic scattering of itinerant carriers with the magnetic self-energy in the localized spin picture or the particle–hole excitation model in the itinerant spin picture. The magnetic scattering spectra are compared to the insulating and metallic cuprate superconductors whose spins are believed to be localized.

Effect of out-of-plane disorder on superconducting gap anisotropy in Bi2+xSr2−xCaCu2O8+δas seen via Raman spectroscopy

We report a systematic study of the variation of electronic Raman spectra as a function of disorder for Bi${}_{2+x}$Sr${}_{2\ensuremath{-}x}$CaCu${}_{2}$O${}_{8+\ensuremath{\delta}}$ with different Bi:Sr nonstoichiometry. We have observed that, with increasing disorder, the suppression of the superconducting gap is observed only in the nodal region, while there is no change in the antinodal gap. This dichotomy of the response to disorder in the nodal and the antinodal gap can be interpreted as evidence for different origins of these two gaps.

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.

Disorder-Induced Change of Gap Anisotropy in Bi2+xSr2-xCaCu2O8+δStudied by Raman Spectroscopy

We report electronic Raman scattering measurements on out-of-plane disordered Bi 2+ x Sr 2- x CaCu 2 O 8+δ . With increasing out-of-plane disorder, the critical temperature T c is significantly suppressed, but suppression of the superconducting gap energy is observed only in the nodal region. Our experimental finding advocate the two-gap scenario that the origins of the nodal and the antinodal gap are different.

Interpreting quantum oscillation experiments on underdopedYBa2Cu3O6+x

On the basis of negative transport coefficients, it has been argued that the quantum oscillations observed in underdoped YBa(2)Cu(3)O(6+x) in high magnetic fields must be due to antinodal electron pockets. We point out a counter example in which electron-like transport in a hole-doped cuprate is associated with Fermi-arc states. We also present evidence that the antinodal gap in YBa(2)Cu(3)O(6+x) is robust to modest applied magnetic fields. We suggest that these observations should be taken into account when interpreting the results of the quantum oscillation experiments.

Effects of out-of-plane disorder on the nodal quasiparticle and superconducting gap in single-layerBi2Sr1.6L0.4CuO6+δ(L=La,Nd,Gd)

How out-of-plane disorder affects the electronic structure has been investigated for the single-layer cuprates Bi$_2$Sr$_{1.6}$$Ln$$_{0.4}$CuO$_{6+\delta}$ ($Ln$ = La, Nd, Gd) by angle-resolved photoemission spectroscopy. We have observed that, with increasing disorder, while the Fermi surface shape and band dispersions are not affected, the quasi-particle width increases, the anti-nodal gap is enhanced and the superconducting gap in the nodal region is depressed. The results indicate that the superconductivity is significantly depressed by out-of-plane disorder through the enhancement of the anti-nodal gap and the depression of the superconducting gap in the nodal region.