Novel neutron resonance mode in dx2-y2-wave superconductors

Bosonic excitation spectra of superconductingBi2Sr2CaCu2O8+δandYBa2Cu3O6+xextracted from scanning tunneling spectra

A detailed interpretation of scanning tunneling spectra obtained on unconventional superconductors enables one to gain information on the pairing boson. Decisive for this approach are inelastic tunneling events. Due to the lack of momentum conservation in tunneling from or to the sharp tip, those are enhanced in the geometry of a scanning tunneling microscope compared to planar tunnel junctions. This work extends the method of obtaining the bosonic excitation spectrum by deconvolution from tunneling spectra to nodald-wave superconductors. In particular, scanning tunneling spectra of slightly underdopedBi2Sr2CaCu2O8+δwith aTcof 82 K and optimally dopedYBa2Cu3O6+xwith aTcof 92 K reveal a resonance mode in their bosonic excitation spectrum atΩres≈63 meVandΩres≈61 meVrespectively. In both cases, the overall shape of the bosonic excitation spectrum is indicative of predominant spin scattering with a resonant mode atΩres<2Δand overdamped spin fluctuations for energies larger than 2Δ. To perform the deconvolution of the experimental data, we implemented an efficient iterative algorithm that significantly enhances the reliability of our analysis.

Calculation of an Enhanced A_{1g} Symmetry Mode Induced by Higgs Oscillations in the Raman Spectrum of High-Temperature Cuprate Superconductors

In superconductors the Anderson-Higgs mechanism allows for the existence of a collective amplitude (Higgs) mode which can couple to eV light mainly in a nonlinear Raman-like process. The experimental nonequilibrium results on isotropic superconductors have been explained going beyond the BCS theory including the Higgs mode. Furthermore, in anisotropic d-wave superconductors strong interaction effects with other modes are expected. Here we calculate the Raman contribution of the Higgs mode from a new perspective, including many-body Higgs oscillations effects and their consequences in conventional, spontaneous Raman spectroscopy. Our results suggest a significant contribution to the intensity of the A_{1g} symmetry Raman spectrum in d-wave superconductors. In order to test our theory, we predict the presence of measurable characteristic oscillations in THz quench-optical probe time-dependent reflectivity experiments.

Disappearance of superconductivity due to vanishing coupling in the overdoped Bi[Formula: see text]Sr[Formula: see text]CaCu[Formula: see text]O[Formula: see text]

In cuprate superconductors, superconductivity is accompanied by a plethora of orders and phenomena that complicate our understanding of superconductivity in these materials. Prominent in the underdoped regime, these orders weaken or vanish with overdoping. Here, we approach the superconducting phase from the more conventional overdoped side. We present angle-resolved photoemission spectroscopy studies of Bi[Formula: see text]Sr[Formula: see text]CaCu[Formula: see text]O[Formula: see text], cleaved and annealed in ozone to increase the doping all the way to the non-superconducting phase. We show that the mass renormalization in the antinodal region of the Fermi surface that possibly reflects the pairing, weakens with doping and completely disappears precisely where superconductivity disappears. This is the evidence that in the overdoped regime, superconductivity is determined primarily by the coupling strength. A doping dependence and an abrupt disappearance above the transition temperature eliminate phononic mechanism of the observed renormalization and identify the onset of spin-fluctuations as its likely origin.

Nature of the spin resonance mode in CeCoIn5

Spin-fluctuation-mediated unconventional superconductivity can emerge at the border of magnetism, featuring a superconducting order parameter that changes sign in momentum space. Detection of such a sign-change is experimentally challenging, since most probes are not phase-sensitive. The observation of a spin resonance mode (SRM) from inelastic neutron scattering is often seen as strong phase-sensitive evidence for a sign-changing superconducting order parameter, by assuming the SRM is a spin-excitonic bound state. Here we show that for the heavy fermion superconductor CeCoIn5, its SRM defies expectations for a spin-excitonic bound state, and is not a manifestation of sign-changing superconductivity. Instead, the SRM in CeCoIn5 likely arises from a reduction of damping to a magnon-like mode in the superconducting state, due to its proximity to magnetic quantum criticality. Our findings emphasize the need for more stringent tests of whether SRMs are spin-excitonic, when using their presence to evidence sign-changing superconductivity.

Evidence of a Nodal Line in the Superconducting Gap Symmetry of Noncentrosymmetric ThCoC_{2}

The newly discovered noncentrosymmetric superconductor ThCoC_{2} exhibits numerous types of unconventional behavior in the field dependent heat capacity data. Here we present the first measurement of the gap symmetry of ThCoC_{2} by muon spin rotation and relaxation (μSR) measurements. The temperature dependence of the magnetic penetration depth measured using the transverse field μSR experiment reveals the evidence of a nodal pairing symmetry. To understand this finding, we carry out calculations of the superconducting pairing eigenvalue and eigenfunction (pairing symmetry) due to the spin-fluctuation mechanism by directly implementing the ab initio band structures. We find that the system possesses a single Fermi surface with considerable three dimensionality and a strong nesting along the k_{z} direction. Such nesting promotes a superconducting state with a cosk_{z}-like pairing symmetry with a prominent nodal line on the k_{z}=±π/2 plane. The result agrees well with the experimental data.

Imaging the real space structure of the spin fluctuations in an iron-based superconductor

Spin fluctuations are a leading candidate for the pairing mechanism in high temperature superconductors, supported by the common appearance of a distinct resonance in the spin susceptibility across the cuprates, iron-based superconductors and many heavy fermion materials. The information we have about the spin resonance comes almost exclusively from neutron scattering. Here we demonstrate that by using low-temperature scanning tunnelling microscopy and spectroscopy we can characterize the spin resonance in real space. We show that inelastic tunnelling leads to the characteristic dip-hump feature seen in tunnelling spectra in high temperature superconductors and that this feature arises from excitations of the spin fluctuations. Spatial mapping of this feature near defects allows us to probe non-local properties of the spin susceptibility and to image its real space structure.

The knowledge of how spin fluctuations affect high-Tc superconductivity comes exclusively from neutron scattering. Here, Chi et al. establish characteristic excitation features of the spin fluctuations in real space from the scanning tunnelling spectra in an iron-based superconductor.

Robust upward dispersion of the neutron spin resonance in the heavy fermion superconductor Ce1-xYbxCoIn5

The neutron spin resonance is a collective magnetic excitation that appears in the unconventional copper oxide, iron pnictide and heavy fermion superconductors. Although the resonance is commonly associated with a spin-exciton due to the d(s±)-wave symmetry of the superconducting order parameter, it has also been proposed to be a magnon-like excitation appearing in the superconducting state. Here we use inelastic neutron scattering to demonstrate that the resonance in the heavy fermion superconductor Ce1-xYbxCoIn5 with x=0, 0.05 and 0.3 has a ring-like upward dispersion that is robust against Yb-doping. By comparing our experimental data with a random phase approximation calculation using the electronic structure and the momentum dependence of the -wave superconducting gap determined from scanning tunnelling microscopy (STM) for CeCoIn5, we conclude that the robust upward-dispersing resonance mode in Ce1-xYbxCoIn5 is inconsistent with the downward dispersion predicted within the spin-exciton scenario.

Charge orders, magnetism and pairings in the cuprate superconductors

We review the recent developments in the field of cuprate superconductors with special focus on the recently observed charge order in the underdoped compounds. We introduce new theoretical developments following the study of the antiferromagnetic quantum critical point in two dimensions, in which preemptive orders in both charge and superconducting (SC) sectors emerge, that are in turn related by an SU(2) symmetry. We consider the implications of this proliferation of orders in the underdoped region, and provide a study of the type of fluctuations which characterize the SU(2) symmetry. We identify an intermediate energy scale where the SC fluctuations are dominant and argue that they are unstable towards the formation of a resonant excitonic state at the pseudogap temperature T (*). We discuss the implications of this scenario for a few key experiments.

Superconducting pairing and the pseudogap in the nematic dynamical stripe phase of La2-xSrxCuO4

Fully absorption coefficient corrected Raman spectra were obtained in La2-xSrxCuO4. The B1g spectra have a Fleury-Loudon type two-magnon peak (resonant term) whose energy decreases from 3180 cm(-1) (394 meV) to 440 cm(-1) (55 meV) on increasing the carrier density from x = 0 to 0.25, while the B2g spectra have a 1000-3500 cm(-1) (124-434 meV) hump (hill) whose lower-edge energy increases from x = 0 to 0.115 and then stays constant to x = 0.25. The B2g hump is assigned to the electronic scattering (non-resonant term) of the spectral function with magnetic self-energy. The completely different carrier density dependence arises from anisotropic magnetic excitations of spin-charge stripes. The B1g spectra were assigned to the sum of k ∥  and k⊥ stripe excitations and the B2g spectra to k⊥ stripe excitations according to the calculation by Seibold and Lorenzana (2006 Phys. Rev. B 73 144515). The k ∥  and k⊥ stripe excitations in fluctuating spin-charge stripes were separately detected for the first time. The appearance of only k⊥ stripe excitations in the electronic scattering arises from the charge hopping perpendicular to the stripe. This is the same direction as the Burgers vector of the edge dislocation in metal. The successive charge hopping in the Burgers vector direction across the charge stripes may cause Cooper pairs as predicted by Zaanen et al (2004 Ann. Phys. 310 181). Indeed, this is supported by the experimental fact that the superconducting coherent length coincides with the inter-charge stripe distance in the wide carrier density range. The one-directional charge hopping perpendicular to the stripe causes the flat Fermi surface and the pseudogap near (π,0) and (0,π), but the states around (π/2,π/2) cannot be produced. The low-energy Raman scattering disclosed that the electronic states at the Fermi arc around (π/2,π/2) are coupled to the A1g soft phonon of the tetragonal-orthorhombic phase transition. This suggests that the Fermi arc is produced by the electron-phonon interaction. All the present Raman data suggest that Cooper pairs are formed at moving edge dislocations of dynamical charge stripes.

Hour-glass magnetic spectrum in a stripeless insulating transition metal oxide

An hour-glass-shaped magnetic excitation spectrum appears to be a universal characteristic of the high-temperature superconducting cuprates. Fluctuating charge stripes or alternative band structure approaches are able to explain the origin of these spectra. Recently, an hour-glass spectrum has been observed in an insulating cobaltate, thus favouring the charge stripe scenario. Here we show that neither charge stripes nor band structure effects are responsible for the hour-glass dispersion in a cobaltate within the checkerboard charge-ordered regime of La(2-x)Sr(x)CoO(4). The search for charge stripe ordering reflections yields no evidence for charge stripes in La(1.6)Sr(0.4)CoO(4), which is supported by our phonon studies. With the observation of an hour-glass-shaped excitation spectrum in this stripeless insulating cobaltate, we provide experimental evidence that the hour-glass spectrum is neither necessarily connected to charge stripes nor to band structure effects, but instead, probably intimately coupled to frustration and arising chiral or non-collinear magnetic correlations.

Collective spin excitations in the singlet-correlated band model: a comparison with resonant inelastic x-ray scattering

We analyse the spin excitations near the optimal doping of superconducting layered cuprates taking into account both the local and the itinerant spin components self-consistently. The obtained expression allows us to reproduce well the basic features of the resonant inelastic x-ray scattering and neutron scattering data experiments using a reasonable set of tight-binding parameters corresponding to the angle-resolved photoemission spectroscopy data. We also find that the spin excitation branch along the (0,0) - (0,π) symmetry direction in the first Brillouin zone shows a splitting at T < Tc. Possible experiments for verification of that prediction are briefly discussed.

Commensurate magnetic excitations induced by band splitting and Fermi surface topology in n-type cuprates

The antiferromagnetic correlation plays an important role in high-Tc superconductors. Considering this effect, the magnetic excitations in n-type cuprates near the optimal doping are studied within the spin-density-wave description. The magnetic excitations are commensurate in the low-energy regime and further develop into spin-wave-like dispersion at higher energy, consistent with the inelastic neutron scattering measurements. We clearly demonstrate that the commensurability originates from the band splitting and Fermi surface topology. The commensurability is a normal state property and has nothing to do with d-wave superconductivity. Our results strongly suggest the essential role of antiferromagnetic correlations in the cuprates.

Disorder, cluster spin glass, and hourglass spectra in striped magnetic insulators

Hourglass-shaped magnetic excitation spectra have been detected in a variety of doped transition-metal oxides with stripelike charge order. Compared to the predictions of spin-wave theory for perfect stripes, these spectra display a different intensity distribution and anomalous broadening. Here we show, based on a comprehensive modeling for La5/3Sr1/3CoO4, how quenched disorder in the charge sector causes frustration, and consequently cluster-glass behavior at low temperatures, in the spin sector. This spin-glass physics, which is insensitive to the detailed nature of the charge disorder, but sensitive to the relative strength of the magnetic interstripe coupling, ultimately determines the distribution of magnetic spectral weight: The excitation spectrum, calculated using spin waves in finite disordered systems, is found to match in detail the observed hour-glass spectrum.

Testing the sign-changing superconducting gap in iron-based superconductors with quasiparticle interference and neutron scattering

We present a phenomenological calculation of the quasiparticle interference (QPI) pattern and inelastic neutron scattering (INS) spectra in iron-pnictide and layered iron-selenide compounds by using material specific band structure and superconducting (SC) gap properties. As both the QPI and the INS spectra arise due to scattering of the Bogolyubov quasiparticles, they exhibit a one-to-one correspondence of the scattering vectors and the energy scales. We show that these two spectroscopies complement each other in such a way that a comparative study allows one to extract quantitative and unambiguous information about the underlying pairing structure and the phase of the SC gap. Due to the nodeless and isotropic nature of the SC gaps, both the QPI and INS maps are concentrated at only two energies in pnictide (two SC gaps) and one energy in iron-selenide, while the associated scattering vectors q for scattering of sign-changing and same sign of the SC gaps change between these spectroscopies. The results presented, particularly for the newly discovered iron-selenide compounds, can be used to test the nodeless d-wave pairing in this class of high temperature superconductor.

Toward a theory for low-frequency spin dynamics in plane copper oxide superconductors: crossover from localized spins to weak coupling charge carriers with doping

We explore for all wavevectors through the Brillouin zone the dynamic spin susceptibility χ(total)(+,-)(ω, q) that takes into account the interplay of localized and itinerant charge carriers. The imaginary part, Imχ(total)(+,-)(ω, q), has peaks at the antiferromagnetic wavevector Q = (π, π) and a diffusive-like, extremely narrow and sharp peak (symmetric ring of maxima |q| = q(0)) at very small wavevectors Q(0) is proportional to w/J ≈ 10(-6) with the nuclear magnetic/quadrupole resonance frequency ω and the superexchange coupling constant J. We demonstrate the capability of Imχ(total)(+,-)(ω, q) for plane copper (63)(1/T(1)) and oxygen (17)(1/T(1)) nuclear spin-lattice relaxation rate calculations from carrier free right up to optimally doped La(2 - x)Sr(x)CuO(4) and obtain the basic features of temperature and doping behavior for (63)(1/T(1)) in agreement with experimental observations.

Two energy scales in the magnetic resonance spectrum of electron and hole doped pnictide superconductors

We argue that a multiband superconductor with sign-changing gaps may have multiple spin resonances. We calculate the RPA-based spin resonance spectra of a pnictide superconductor by using the five-band tight-binding model or angle-resolved photoemission spectroscopy Fermi surface (FS) and experimental values of superconducting gaps. The resonance spectra split in both energy and momenta due to the effects of multiband and multiple gaps in s(±) pairing; the higher energy peak appears around the commensurate momenta due to scattering between α-FS to γ/δ-FS pockets. The second resonance is incommensurate, coming from β-FS to γ/δ-FS scatterings, and its q vector is doping-dependent and, hence, on the FS topology. Energies of both resonances ω(res)(1,2) are strongly doping-dependent and are proportional to the gap amplitudes at the contributing FSs.

Disorder-induced freezing of dynamical spin fluctuations in underdoped cuprate superconductors

We study the dynamical spin susceptibility of a correlated d-wave superconductor (dSC) in the presence of nonmagnetic disorder, using an unrestricted Hartree-Fock approach. This model provides a concrete realization of the notion that disorder slows down spin fluctuations, which eventually "freeze out." The evolution of disorder-induced spectral weight transfer agrees qualitatively with experimental observations on underdoped cuprate superconductors. For sufficiently large disorder concentrations, static spin density wave (SDW) order is created when droplets of magnetism nucleated by impurities overlap. We also study the disordered stripe state coexisting with a dSC and compare its magnetic fluctuation spectrum to that of the disorder-generated SDW phase.

Hidden quantum spin-gap state in the static stripe phase of high-temperature La2-xSrxCuO4 superconductors

Low-energy spin excitations were investigated in the static stripe phase of La2-xSrxCuO4 using elastic and inelastic neutron scattering on single crystals. For x=1/8 in which long-range static stripe order exists, an energy gap of E(g)=4 meV exists in the excitation spectrum in addition to strong quasielastic, incommensurate spin fluctuations associated with the static stripes. When x increases, the spectral weight of the spin fluctuations shifts from the quasielastic continuum to the excitation spectrum above E(g). The dynamic correlation length as a function of energy and the temperature evolution of the energy spectrum suggest a phase separation of two distinct magnetic phases in real space.

Magnetic resonance in the spin excitation spectrum of electron-doped cuprate superconductors

We study the emergence of a magnetic resonance in the superconducting state of the electron-doped cuprate superconductors. We show that the recently observed resonance peak in the electron-doped superconductor Pr0.88LaCe0.12CuO4-delta is consistent with an overdamped spin exciton located near the particle-hole continuum. We present predictions for the magnetic-field dependence of the resonance mode as well as its temperature evolution in those parts of the phase diagram where dx2-y2-wave superconductivity may coexist with an antiferromagnetic spin-density wave.

Neutron-spin resonance in the optimally electron-doped superconductor Nd1.85Ce0.15CuO4-delta

We use inelastic neutron scattering to probe magnetic excitations of an optimally electron-doped superconductor Nd1.85Ce0.15CuO4-delta above and below its superconducting transition temperature Tc=25 K. In addition to gradually opening a spin pseudogap at the antiferromagnetic ordering wave vector Q=(1/2,1/2,0), the effect of superconductivity is to form a resonance centered also at Q=(1/2,1/2,0) but at energies above the spin pseudogap. The intensity of the resonance develops like a superconducting order parameter, similar to those for hole-doped superconductors and electron-doped Pr0.88LaCe0.12CuO4. The resonance is therefore a general phenomenon of cuprate superconductors, and must be fundamental to the mechanism of high-Tc superconductivity.

Phenomenological theory of the underdoped phase of a high-Tc superconductor

We model the Fermi surface of the cuprates by one-dimensional nested parts near (0, pi) and (pi, 0) and unnested parts near the zone diagonals. Fermions in the nested regions form 1D spin liquids and develop spectral gaps below some approximately T*, but superconducting order is prevented by 1D phase fluctuations. We show that the Josephson coupling between these order parameters locks their relative phase at pi at the crossover scale T**<T*. Below T**, the system response becomes two dimensional, and the system displays Nernst effect. The remaining total phase gets locked at Tc<T**, at which the system develops a (quasi-) long-range superconducting order.

Spin excitations in fluctuating stripe phases of doped cuprate superconductors

Using a phenomenological lattice model of coupled spin and charge modes, we determine the spin susceptibility in the presence of fluctuating stripe charge order. We assume the charge fluctuations to be slow compared to those of the spins, and combine Monte Carlo simulations for the charge order parameter with exact diagonalization of the spin sector. Our calculations unify the spin dynamics of both static and fluctuating stripe phases and support the notion of a universal spin excitation spectrum in doped cuprate superconductors.

Constituents of the quasiparticle spectrum along the nodal direction of high-Tc cuprates

Applying the Kramers-Kronig consistent procedure, developed earlier, we investigate in detail the formation of the quasiparticle spectrum along the nodal direction of high-Tc cuprates. The heavily discussed "70 meV kink" on the renormalized dispersion exhibits a strong temperature and doping dependence when purified from structural effects such as bilayer splitting, diffraction replicas, etc. This dependence is well understood in terms of fermionic and bosonic constituents of the self-energy. The latter follows the evolution of the spin-fluctuation spectrum, emerging below some doping dependent temperature and sharpening below Tc, and is mainly responsible for the formation of the kink in question.

Kinks, nodal bilayer splitting, and interband scattering in YBa2Cu3O(6+x)

We apply the new-generation angle-resolved photoemission spectroscopy methodology to the most widely studied cuprate superconductor YBa2Cu3O(6+x). Considering the nodal direction, we found noticeable renormalization effects known as kinks both in the quasiparticle dispersion and scattering rate, the bilayer splitting, and evidence for strong interband scattering--all the characteristic features of the nodal quasiparticles detected earlier in Bi2Sr2CaCu2O(8+delta). The typical energy scale and the doping dependence of the kinks clearly point to their intimate relation with the spin-1 resonance seen in the neutron scattering experiments. Our findings strongly suggest a universality of the electron dynamics in the bilayer superconducting cuprates and a dominating role of the spin fluctuations in the formation of the quasiparticles along the nodal direction.

Effect of Zn and Ni impurities on the quasiparticle renormalization of superconducting Bi-2212

The Cu substitution by Zn and Ni impurities and its influence on the mass renormalization effects in angle-resolved photoelectron spectra (ARPES) of Bi2Sr2CaCu2O8-delta is addressed. We show that the nonmagnetic Zn atoms have a much stronger effect in both the nodal and antinodal parts of the Brillouin zone than magnetic Ni. The observed changes are consistent with the behavior of the spin resonance mode as seen by inelastic neutron scattering in YBCO. This strongly suggests that the "peak-dip-hump" and the kink in ARPES on the one side and neutron resonance on the other are closely related features.

Spin dynamics in the stripe phase of the cuprate superconductors

Within a model that supports stripe spin and charge order coexisting with a d(x2-y2)-wave superconducting phase, we study the self-consistently obtained electronic structure and the associated transverse dynamical spin susceptibility. In the coexisting phase of superconducting and static stripe order, the resulting particle-hole continuum can strongly damp parts of the low-energy spin-wave branches. This provides insight into recent inelastic neutron scattering data revealing the dispersion of the low-energy collective magnetic modes of lanthanum based cuprate superconductors.