Nodal Direction Research Articles

Role of the upper branch of the hour-glass magnetic spectrum in the formation of the main kink in the electronic dispersion of high-Tccuprate superconductors

We investigate the electronic dispersion of the high-T$_{\mathrm{c}}$ cuprate superconductors using the fully self-consistent version of the phenomenological model, where charge planar quasiparticles are coupled to spin fluctuations. The inputs we use ---the underlying (bare) band structure and the spin susceptibility $\chi$--- are extracted from fits of angle resolved photoemission and inelastic neutron scattering data of underdoped YBa$_{2}$Cu$_{3}$O$_{6.6}$ by T. Dahm and coworkers (T. Dahm et al., Nat. Phys. 5, 217 (2009)). Our main results are: (i) We have confirmed the finding by T. Dahm and coworkers that the main nodal kink is, for the present values of the input parameters, determined by the upper branch of the hour-glass of $\chi$. We demonstrate that the properties of the kink depend qualitatively on the strength of the charge-spin coupling. (ii) The effect of the resonance mode of $\chi$ on the electronic dispersion strongly depends on its kurtosis in the quasimomentum space. A low (high) kurtosis implies a negligible (considerable) effect of the mode on the dispersion in the near-nodal region. (iii) The energy of the kink decreases as a function of the angle $\theta$ between the Fermi surface cut and the nodal direction, in qualitative agreement with recent experimental observations. We clarify the trend and make a specific prediction concerning the angular dependence of the kink energy in underdoped YBa$_{2}$Cu$_{3}$O$_{6.6}$.

Resonant inelastic x-ray scattering study of the spin and charge excitations in the overdoped superconductorLa1.77Sr0.23CuO4

We present a resonant inelastic x-ray scattering (RIXS) study of spin and charge excitations in overdoped La1.77Sr0.23CuO4 along two high-symmetry directions. The line shape of these excitations is analyzed and they are shown to be highly overdamped. Their spectral weight and damping are found to be strongly momentum dependent. Qualitative agreement between these observations and a calculated RPA susceptibility is obtained for this overdoped compound, implying that a significant contribution to the RIXS signal stems from a continuum of charge excitations. Furthermore, this suggests that the spin-excitations in the overdoped regime can be captured qualitatively by an itinerant picture. Our calculations also predict a new low-energy spin excitation branch to exist along the nodal direction near the zone center. With the energy resolution of the present experiment, this branch is not resolvable but we show that next generation of high-resolution spectrometers will be able to test this prediction.

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.

Dynamical vertex approximation for the two-dimensional Hubbard model

Recently, diagrammatic extensions of dynamical mean field theory (DMFT) have been proposed for including short- and long-range correlations beyond DMFT on an equal footing. We employ one of these, the dynamical vertex approximation (DΓA), and study the two-dimensional Hubbard model on a square lattice. We define two transition lines in the phase diagram which correspond, respectively, to the opening of the gap in the nodal direction and throughout the Fermi surface. Our self-energy data show that the evolution between the two regimes occurs in a gradual way (crossover) and also that at low enough temperatures the whole Fermi surface is always gapped. Furthermore, we present a comparison of our DΓA calculations at a parameter set where data obtained by other techniques are available.

Tunneling Spectroscopy in Organic Superconductor κ-(BEDT-TTF-d[3,3])2Cu[N(CN)2]Br

We performed tunneling spectroscopy (STS) measurement in an organic superconductor, partially deuterated κ-(BEDT-TTF-d[3,3])2Cu[N(CN)2]Br. We carried out angle-resolved STS on cut lateral surfaces by the focused ion beam (FIB) method as well as as-grown single-crystal surfaces. It was found that the d[3,3]-Br salt is a strong-coupling d-wave superconductor and that the nodal direction is at an angle of π/4 from the a*-axis, corresponding to the \(d_{x^{2} - y^{2}}\) symmetry in the bulk superconducting phase. It is understood that the electron correlation in the d[3,3]-Br salt is not strong enough on the basis of the spin fluctuation mechanism. On the other hand, we also observed two types of superconducting gap. This suggests the coexistence of the \(d_{x^{2} - y^{2}}\) and dxy symmetries. This indicates a change in the symmetry from \(d_{x^{2} - y^{2}}\) in the bulk superconducting phase to dxy around the insulating region with increasing electron correlation.

Nodal bilayer-splitting controlled by spin-orbit interactions in underdoped high-Tc cuprates.

The highest superconducting transition temperatures in the cuprates are achieved in bilayer and trilayer systems, highlighting the importance of interlayer interactions for high Tc. It has been argued that interlayer hybridization vanishes along the nodal directions by way of a specific pattern of orbital overlap. Recent quantum oscillation measurements in bilayer cuprates have provided evidence for a residual bilayer-splitting at the nodes that is sufficiently small to enable magnetic breakdown tunneling at the nodes. Here we show that several key features of the experimental data can be understood in terms of weak spin-orbit interactions naturally present in bilayer systems, whose primary effect is to cause the magnetic breakdown to be accompanied by a spin flip. These features can now be understood to include the equidistant set of three quantum oscillation frequencies, the asymmetry of the quantum oscillation amplitudes in c-axis transport compared to ab-plane transport, and the anomalous magnetic field angle dependence of the amplitude of the side frequencies suggestive of small effective g-factors. We suggest that spin-orbit interactions in bilayer systems can further affect the structure of the nodal quasiparticle spectrum in the superconducting phase. PACS numbers: 71.45.Lr, 71.20.Ps, 71.18.+y

Symmetry of charge order in cuprates.

Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of strongly correlated states of matter. The recent discovery of charge order in various cuprate families has fuelled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-T(c) superconductors. Here, we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi2Sr(2-x)La(x)CuO(6+δ) (Bi2201) and YBa2Cu3O(6+y) (YBCO). We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum structure of charge order. We also resolve the intra-unit-cell symmetry of the charge-ordered state, which is revealed to be best represented by a bond order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights into the origin and microscopic description of charge order in cuprates, and its interplay with superconductivity.

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.

Itinerant effects and enhanced magnetic interactions in Bi-based multilayer cuprates

The cuprate high temperature superconductors exhibit a pronounced trend in which the superconducting transition temperature, $T_{\rm c}$, increases with the number of CuO$_2$ planes, $n$, in the crystal structure. We compare the magnetic excitation spectrum of Bi$_{2+x}$Sr$_{2-x}$CuO$_{6+\delta}$ (Bi-2201) and Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10 + \delta}$ (Bi-2223), with $n=1$ and $n=3$ respectively, using Cu $L_3$-edge resonant inelastic x-ray scattering (RIXS). Near the anti-nodal zone boundary we find the paramagnon energy in Bi-2223 is substantially higher than that in Bi-2201, indicating that multilayer cuprates host stronger effective magnetic exchange interactions, providing a possible explanation for the $T_{\rm c}$ vs.\ $n$ scaling. In contrast, the nodal direction exhibits very strongly damped, almost non-dispersive excitations. We argue that this implies that the magnetism in the doped cuprates is partially itinerant in nature.

Anisotropic softening of magnetic excitations along the nodal direction in superconducting cuprates.

The high-Tc cuprate superconductors are close to antiferromagnetic order. Recent measurements of magnetic excitations have reported an intriguing similarity to the spin waves--magnons--of the antiferromagnetic insulating parent compounds, suggesting that magnons may survive in damped, broadened form throughout the phase diagram. Here we show by resonant inelastic X-ray scattering on Bi(2)Sr(2)CaCu(2)O(8+δ) (Bi-2212) that the analogy with spin waves is only partial. The magnon-like features collapse along the nodal direction in momentum space and exhibit a photon energy dependence markedly different from the Mott-insulating case. These observations can be naturally described by the continuum of charge and spin excitations of correlated electrons. The persistence of damped magnons could favour scenarios for superconductivity built from quasiparticles coupled to spin fluctuations. However, excitation spectra composed of particle-hole excitations suggest that superconductivity emerges from a coherent treatment of electronic spin and charge in the form of quasiparticles with very strong magnetic correlations.

Field-Angle-Dependent Low-Energy Excitations around a Vortex in the Superconducting Topological Insulator CuxBi2Se3

We study the quasiparticle excitations around a single vortex in the superconducting topological insulator Cu$_{x}$Bi$_{2}$Se$_{3}$, focusing on a superconducting state with point nodes. Inspired by the recent Knight shift measurements, we propose two ways to detect the positions of point nodes, using an explicit formula of the density of states with Kramer-Pesch approximation in the quasiclassical treatment. The zero-energy local density of states around a vortex parallel to the $c$-axis has a twofold shape and splits along the nodal direction with increasing energy; these behaviors can be detected by the scanning tunneling microscopy. An angular dependence of the density of states with a rotating magnetic field on the $a$-$b$ plane has deep minima when the magnetic field is parallel to the directions of point nodes, which can be detected by angular-resolved heat capacity and thermal conductivity measurements. All the theoretical predictions are detectable via standard experimental techniques in magnetic fields.

Fermi surface evolution in the ensemble of spin-polarized quasiparticles in La2 − x Sr x CuO4

For the spin-fermion model, it has been shown that the concept of spin polarons makes it possible to reproduce fine details of the Fermi surface evolution in the nodal direction of La2 − x Sr x CuO4 occurring with changes in the doping level x. The physics here is determined by the spin-correlated hopping of charge carriers and by the doping dependence of the inverse magnetic correlation length.

Disappearance of nodal gap across the insulator–superconductor transition in a copper-oxide superconductor

The parent compound of the copper-oxide high-temperature superconductors is a Mott insulator. Superconductivity is realized by doping an appropriate amount of charge carriers. How a Mott insulator transforms into a superconductor is crucial in understanding the unusual physical properties of high-temperature superconductors and the superconductivity mechanism. Here we report high-resolution angle-resolved photoemission measurement on heavily underdoped Bi₂Sr₂-xLaxCuO(₆+δ) system. The electronic structure of the lightly doped samples exhibit a number of characteristics: existence of an energy gap along the nodal direction, d-wave-like anisotropic energy gap along the underlying Fermi surface, and coexistence of a coherence peak and a broad hump in the photoemission spectra. Our results reveal a clear insulator-superconductor transition at a critical doping level of ~0.10 where the nodal energy gap approaches zero, the three-dimensional antiferromagnetic order disappears, and superconductivity starts to emerge. These observations clearly signal a close connection between the nodal gap, antiferromagnetism and superconductivity.

Raman-scattering measurements and theory of the energy-momentum spectrum for underdoped Bi2Sr2CaCuO(8+δ) superconductors: evidence of an s-wave structure for the pseudogap.

We reveal the full energy-momentum structure of the pseudogap of underdoped high-Tc cuprate superconductors. Our combined theoretical and experimental analysis explains the spectral-weight suppression observed in the B2g Raman response at finite energies in terms of a pseudogap appearing in the single-electron excitation spectra above the Fermi level in the nodal direction of momentum space. This result suggests an s-wave pseudogap (which never closes in the energy-momentum space), distinct from the d-wave superconducting gap. Recent tunneling and photoemission experiments on underdoped cuprates also find a natural explanation within the s-wave pseudogap scenario.

Self-energy effects in electronic Raman spectra of doped cuprates due to magnetic fluctuations

We present results for magnetic excitations in doped copper oxides using the random phase approximation and itinerant electrons. In the [1,0] direction the observed excitations resemble dispersive quasi-particles both in the normal and superconducting state similar as in recent resonant inelastic X-ray scattering (RIXS) experiments. In the [1,1] direction the excitations form, except for the critical region near the antiferromagnetic wave vector ${\bf Q}=(\pi,\pi)$, only very broad continua. Using the obtained spin propagators we calculate electron self-energies and their effects on electronic Raman spectra. We show that the recently observed additional peak at about twice the pair breaking in B$_{1g}$ symmetry below T$_c$ in HgBa$_2$CuO$_{4+\delta}$ can be explained as a self-energy effect where a broken Cooper pair and a magnetic excitation appear as final states. The absence of this peak in B$_{2g}$ symmetry, which probes mainly electrons near the nodal direction, is explained by their small self-energies compared to those in the antinodal direction.

MECHANISM FOR EXCITING PLANETARY INCLINATION AND ECCENTRICITY THROUGH A RESIDUAL GAS DISK

Accordling to the theory of Kozai resonance, the initial mutual inclination between a small body and a massive planet in an outer circular orbit is as high as $\sim39.2^{\circ}$ for pumping the eccentricity of the inner small body. Here we show that, with the presence of a residual gas disk outside two planetary orbits, the inclination can be reduced as low as a few degrees. The presence of disk changes the nodal precession rates and directions of the planet orbits. At the place where the two planets achieve the same nodal processing rate, vertical secular resonance would occur so that mutual inclination of the two planets will be excited, which might trigger the Kozai resonance between the two planets further. However, in order to pump an inner Jupiter-like planet, the conditions required for the disk and the outer planet are relatively strict. We develop a set of evolution equations, which can fit the N-body simulation quite well but be integrated within a much shorter time. By scanning the parameter spaces using the evolution equations, we find that, a massive planet ($10M_J$) at 30AU with $6^o$ inclined to a massive disk ($50M_J$) can finally enter the Kozai resonance with an inner Jupiter around the snowline. And a $20^{\circ}$ inclination of the outer planet is required for flipping the inner one to a retrograde orbit. In multiple planet systems, the mechanism can happen between two nonadjacent planets, or inspire a chain reaction among more than two planets. This mechanism could be the source of the observed giant planets in moderate eccentric and inclined orbits, or hot-Jupiters in close-in, retrograde orbits after tidal damping.

Discerning electronic fingerprints of nodal and antinodal nestings and their phase coherences in doped cuprate superconductors

The complexity of competing orders in cuprates has recently been multiplied by a number of bulk evidences of charge ordering with wave vector that connects the antinodal region of the Fermi surface. This result contradicts many spectroscopic results of the nodal nesting. To resolve this issue, we carry out a unified study of the resulting electronic fingerprints of both nodal and antinodal nestings (NNs/ANs) and compare with angle-resolved photoemission, scanning tunneling spectroscopic data, as well as bulk-sensitive Hall-effect measurements. Our result makes several definitive distinctions between them in that while both nestings gap out the antinodal region, AN induces an additional quasiparticle gap below the Fermi level along the nodal direction, which is so far uncharted in spectroscopic data. Furthermore, we show that the Hall coefficient in the AN state obtains a discontinuous jump at the phase transition from an electronlike nodal pocket (negative value) to a large holelike Fermi surface (positive value), in contrast to a continuous transition in the available data. We conclude that individual NNs and ANs have difficulties in explaining all of the data. In this spirit, we study a possibility of coexisting NN and AN phases within a Ginsburg-Landau functional formalism. An interesting possibility of disorder pinned ``chiral'' charge ordering is finally discussed.

Model construction and superconductivity analysis of organic conductors β-(BDA-TTP)2MF6 (M = P, As, Sb and Ta) based on first-principles band calculation

We perform a first-principles band calculation for a group of quasi-two-dimensional organic conductors β-(BDA-TTP)2MF6 (M = P, As, Sb and Ta). The ab-initio calculation shows that the density of states is correlated with the bandwidth of the singly occupied (highest) molecular orbital, while it is not necessarily correlated with the unit-cell volume. The direction of the major axis of the cross section of the Fermi surface lies in the Γ–B-direction, which differs from that obtained by the extended Hückel calculation. Then, we construct a tight-binding model which accurately reproduces theab-initio band structure. The obtained transfer energies give a smaller dimerization than in the extended Hückel band. As to the difference in the anisotropy of the Fermi surface, the transfer energies along the inter-stacking direction are smaller than those obtained in the extended Hückel calculation. Assuming spin-fluctuation-mediated superconductivity, we apply random phase approximation to a two-band Hubbard model. This two-band Hubbard model is composed of the tight-binding model derived from the first-principles band structure and an on-site (intra-molecule) repulsive interaction taken as a variable parameter. The obtained superconducting gap changes sign four times along the Fermi surface like in a d-wave gap, and the nodal direction is different from that obtained in the extended Hückel model. Anion dependence of Tc is qualitatively consistent with the experimental observation.

Correlation between structural and transport properties in epitaxial films of Nd2 − xCexCuO4 ± δ

We present here a study on the influence of the oxygen reduction process on the structural and transport properties of epitaxial thin films of the electron-doped cuprate Nd2−xCexCuO4±δ. As is well known, the gradual removal from as-grown samples of a tiny percentage of excess oxygen ions leads to a drastic improvement of the metallic character of this system, which eventually becomes superconducting for suitable values of the cerium concentration, with a maximal critical temperature Tc≃25K. We find that the oxygen loss occurring in thermal treatments in the temperature range 500–850°C leads to a reduction of the disorder hindering conductance processes, but is insufficient to make the system become superconducting. On the other hand, as soon as the annealing temperature is raised above 850°C, superconductivity appears, and at the same time a systematic variation of the length of the unit cell along the c-axis direction is detected. This is a clear indication that the transition to the superconducting phase is always accompanied by a structural modification. A further salient feature characterizing samples annealed at high temperatures is the emergence of a linear contribution in the normal-state resistivity, which superimposes to the quadratic one already present in samples which are oxygen-reduced below 850°C. This contribution is probably associated with the formation of hole-like carriers located at hole pockets developing at the Fermi energy along the nodal direction in the Brillouin zone. We conjecture that the evolution of the electronic states with oxygen removal for a given cerium concentration close to optimal doping, is similar to the one taking place in optimally annealed samples where cerium concentration is raised from the underdoped to the lightly overdoped regime value.

Hole spectral functions in lightly doped quantum antiferromagnets

We study the hole and magnon spectral functions as a function of hole doping in the two-dimensional (2D) t-J and t-t'-t"-J models working within the limits of the spin-wave theory, by linearizing the hole-spin-deviation interaction and by adapting the non-crossing approximation (NCA). We find that the staggered magnetization decreases rather rapidly with doping and it goes to zero at a few percent of hole concentration in both t-J and the t-t'-t"-J model. We find that with doping, the residue of the quasiparticle peak at G=(pi/2,pi/2) decreases rapidly with doping and the spectral function is in agreement with high resolution angle-resolved photo-emission spectroscopy (ARPES) studies of the copper-oxide superconductors. The observed large shift of the chemical potential inside the Mott gap is found to be a result of broadening of the quasiparticle peak. We find pockets centered at G, similar to those observed by quantum oscillation measurements, (i) with an elliptical shape with large eccentricity along the anti-nodal direction in the case of the t-J model, and (ii) with an almost circular shape in the case of the t-t'-t"-J model. We also find that the spectral intensity distribution in the doped antiferromagnet has a waterfall-like patten along the nodal direction of the Brillouin zone, a feature that is also seen in ARPES measurements.