Cuprate High-temperature Superconductors Research Articles

Orbital Approach to High Temperature Superconductivity

High temperature superconductivity in cuprates is explained in terms of 3d-orbital capture in copper. In elemental Cu 3d-orbital capture abstracts an electron from the 4 s2 valence orbital, and leaves it as 4 s1. This is known since Cu occurs in Group IB of the Periodic Table. This forms an electron vacancy, or hole, in the valence shell. Therefore, the energy of 3d-orbital capture is stronger than the energy of unpairing of a paired-spin 4 s2 orbital. In cuprates 3d-orbital capture abstracts an electron from a Cu-O covalent bond, and leaves a hole in the excited state orbital. By electron-hole migration the excited state orbital leads to a coordinate covalent bond. This leads to superconductivity. The 3d-orbital process accounts for superconductivity and insulator behavior in cuprates. These results lend credence to the statement that 3d-orbital capture in copper is the cause of high temperature superconductivity.

Synthesis and Physicochemical Properties of Er0.5Dy0.5Ba2Cu3O6.83 Cuprate High-Temperature Superconductor

Synthesis and Physicochemical Properties of Er_0.5Dy_0.5Ba₂Cu₃O_6.83 Cuprate High-Temperature Superconductor

MICROWAVE RADIO PHYSICS OF UNCONVENTIONAL SUPERCONDUCTORS

The paper presents a review of main results obtained by the authors in the process of microwave (MW) investigations on unconventional superconductors and developments of MW devices based on cuprate high-temperature superconductors (HTS) carried out over the course of the past 10-15 years. Experimental investigations were carried out by the methods of impedance measurements of superconductor samples. For this purpose the authors have developed two measuring techniques in the mm wavelength range: on the base of quasioptical sapphire resonators and using a feature of the polarized wave p-field reflection from the superconductor surface at a grazing angle of incidence. Epitaxial films of the YBa2Cu3O7–δ cuprate superconductor and Fe-containing superconductors in the form of Ba(Fe0.926Co0.074)2As2 pnictide single crystals and FeSexTe1–x (x = 0.5 and 0.7) chalcogenide epitaxial films have been investigated. The results of the MW response of electrodynamic structures with the investigated samples were used as a base for finding the complex conductivity including the fluctuation one. In general, the results obtained confirm the scenario of the slit function d-wave symmetry for cuprate superconductors and s-wave symmetry for Fe-based superconductors. However, further investigations are required as there is a number of features and effects, namely: abnormal frequency dependence of the residual surface resistance in YBa2Cu3O7–δ in the form of ω3./2, increase of the quasi-particle conductivity with temperature decreasing after the critical one and avalanche-like transition from the superconducting state to the strongly dissipative state in the coplanar transmission line. New MW devices based on cuprate HTS films in the mm wave range 1) quasioptical sapphire resonator with radial slit and HTS end walls for investigation of Fe-based superconductors in the mm wave range: 1) quasioptical sapphire resonator with a radial slit and HTS end walls for investigation of Fe-based superconductors in the form of small (1-2 mm in the a-b plane) samples; 2) quasioptical planar resonator; 3) band-pass filter with an E-plane insertion in the cross-type waveguide. A possibility of noncontact testing the homogeneity properties of massive superconductors at room temperature is shown. The temperature dependence of the complex conductivity of YBa2Cu3O7-(Ba (Fe0.926Co0.074)2As2 and FeSexTe1-x (x = 0.5 and 0.7) superconductors as well as the corresponding physical quantities have been obtained, that enables one to judge about the evidence of relevant scenarios of the wave symmetry in the slit function of investigated superconductors. However, a number of revealed features and effects require further study. A possibility of developing large-scale MW HTS-based devices operating at frequencies up to 40 GHz was experimentally confirmed.

Probing the energy gap of high-temperature cuprate superconductors by resonant inelastic x-ray scattering

The determination of the symmetry of the energy gap is crucial for research on the microscopic mechanisms of unconventional superconductivity. Here, we demonstrate experimentally that high-resolution resonant inelastic X-ray scattering at the Cu L3 edge can serve as a momentum-resolved, bulk-sensitive probe of the superconducting gap. We studied two optimally doped cuprates Bi2Sr2CaCu2O8+δ and Bi2Sr2Ca2Cu3O10+δ, in which we observe a strongly momentum dependent reduction of the spectral weight upon entering the superconducting state, with a maximum for momenta connecting antinodal regions of the Fermi surface. Based on a comparison with the calculated charge susceptibility and electronic Raman scattering data, we interpret our observation as a renormalization of the non-local charge susceptibility due to the superconducting gap opening. Our data demonstrate the methodological potential of resonant inelastic X-ray scattering as a versatile probe of the energy gap of high-temperature superconductors, including buried interfaces in heterostructures which are inaccessible to angle-resolved photoemission spectroscopy.

Plaquette Valence Bond Theory of Cuprate High-Temperature Superconductivity

We investigate the phenomenon of high-temperature superconductivity within a strong coupling perspective. The occurence is traced to a quantum critical point that is in the phase diagram of the plaquette's t; t0-Hubbard model. We develop a bottom-up approach combining several methods, i.e. exact diagonalization of an isolated plaquette, the Lanczos-method for a plaquette within a bath and cluster dynamical Mean-Field theory with continuous time quantum Monte-Carlo solver to embedd the plaquette in a lattice environment. The quantum critical point is located where the N = 2; 3; 4-sectors of the plaquette cross. This point is also found to show optimal doping. The wave order turns out to be largest at the localized-itinerant transition of the electrons. Furthermore, we present an explenation for the pseudo-gap phenomenon, that is explained by a soft mode related to local singlets of the plaquette. The theory presented here is similar to the resonating valence bond theory, but stresses the importance of local singlets.

Emergence of superconductivity from fully incoherent normal state in an iron-based superconductor (Ba0.6K0.4)Fe2As2

In unconventional superconductors, it is generally believed that understanding the physical properties of the normal state is a pre-requisite for understanding the superconductivity mechanism. In conventional superconductors like niobium or lead, the normal state is a Fermi liquid with a well-defined Fermi surface and well-defined quasipartcles along the Fermi surface. Superconductivity is realized in this case by the Fermi surface instability in the superconducting state and the formation and condensation of the electron pairs (Cooper pairing). The high temperature cuprate superconductors, on the other hand, represent another extreme case that superconductivity can be realized in the underdoped region where there is neither well-defined Fermi surface due to the pseudogap formation nor quasiparticles near the antinodal regions in the normal state. Here we report a novel scenario that superconductivity is realized in a system with well-defined Fermi surface but without quasiparticles along the Fermi surface in the normal state. High resolution laser-based angle-resolved photoemission measurements have been performed on an optimally-doped iron-based superconductor (Ba0.6K0.4)Fe2As2. We find that, while sharp superconducting coherence peaks emerge in the superconducting state on the hole-like Fermi surface sheets, no quasiparticle peak is present in the normal state. Its electronic behaviours deviate strongly from a Fermi liquid system. The superconducting gap of such a system exhibits an unusual temperature dependence that it is nearly a constant in the superconducting state and abruptly closes at Tc. These observations have provided a new platform to study unconventional superconductivity in a non-Fermi liquid system.

Three-dimensional collective charge excitations in electron-doped copper oxide superconductors.

High-temperature copper oxide superconductors consist of stacked CuO2 planes, with electronic band structures and magnetic excitations that are primarily two-dimensional1,2, but with superconducting coherence that is three-dimensional. This dichotomy highlights the importance of out-of-plane charge dynamics, which has been found to be incoherent in the normal state3,4 within the limited range of momenta accessible by optics. Here we use resonant inelastic X-ray scattering to explore the charge dynamics across all three dimensions of the Brillouin zone. Polarization analysis of recently discovered collective excitations (modes) in electron-doped copper oxides5-7 reveals their charge origin, that is, without mixing with magnetic components5-7. The excitations disperse along both the in-plane and out-of-plane directions, revealing its three-dimensional nature. The periodicity of the out-of-plane dispersion corresponds to the distance between neighbouring CuO2 planesrather than to the crystallographic c-axis lattice constant, suggesting that the interplane Coulomb interaction is responsible for the coherent out-of-plane charge dynamics. The observed properties are hallmarks of the long-sought 'acoustic plasmon', which is a branch of distinct charge collective modes predicted for layered systems8-12 and argued to play a substantial part in mediating high-temperature superconductivity10-12.

Coupling between dynamic magnetic and charge-order correlations in the cuprate superconductor Nd2−xCexCuO4

Charge order has now been observed in several cuprate high-temperature superconductors. We report a resonant inelastic x-ray scattering experiment on the electron-doped cuprate Nd$_{2-x}$Ce$_{x}$CuO$_4$ that demonstrates the existence of dynamic correlations at the charge order wave vector. Upon cooling we observe a softening in the electronic response, which has been predicted to occur for a d-wave charge order in electron-doped cuprates. At low temperatures, the energy range of these excitations coincides with that of the dispersive magnetic modes known as paramagnons. Furthermore, measurements where the polarization of the scattered photon is resolved indicate that the dynamic response at the charge order wave vector primarily involves spin-flip excitations. Overall, our findings indicate a coupling between dynamic magnetic and charge-order correlations in the cuprates.

Ultrathin Bismuth Film on High-Temperature Cuprate Superconductor Bi2Sr2CaCu2O8+δ as a Candidate of a Topological Superconductor.

One of the key challenges in condensed-matter physics is to establish a topological superconductor that hosts exotic Majorana fermions. Although various heterostructures consisting of conventional BCS (Bardeen-Cooper-Schrieffer) superconductors as well as doped topological insulators were intensively investigated, no conclusive evidence for Majorana fermions has been provided. This is mainly because of their very low superconducting transition temperatures ( Tc) and small superconducting-gap magnitude. Here, we report a possible realization of topological superconductivity at very high temperatures in a hybrid of Bi(110) ultrathin film and copper oxide superconductor Bi2Sr2CaCu2O8+δ (Bi2212). Using angle-resolved photoemission spectroscopy and scanning tunneling microscopy, we found that three-bilayer-thick Bi(110) on Bi2212 exhibits a proximity-effect-induced s-wave energy gap as large as 7.5 meV which persists up to Tc of Bi2212 (85 K). The small Fermi energy and strong spin-orbit coupling of Bi(110), together with the large pairing gap and high Tc, make this system a prime candidate for exploring stable Majorana fermions at very high temperatures.

Candidate theory for the strange metal phase at a finite-energy window

We propose a lattice model for strongly interacting electrons with the potential to explain the main phenomenology of the strange metal phase in the cuprate high temperature superconductors. Our model is motivated by the recently developed "tetrahedron" rank-3 tensor model that mimics much of the physics of the better-known Sachdev-Ye-Kitaev (SYK) model. Our electron model has the following advantageous properties: (1) it only needs one orbital per site on the square lattice; (2) it does not require any quenched random interaction; (3) it has local interactions and respects all the symmetries of the system; (4) the soluble limit of this model has a longitudinal DC resistivity that scales linearly with temperature within a finite temperature window; (5) again the soluble limit of this model has a fermion pairing instability in the infrared, which can lead to either superconductivity or a "pseudogap" phase. The linear$-T$ longitudinal resistivity and the pairing instability originate from the generic scaling feature of the SYK model and the tetrahedron tensor model.

Location of the oxygen dopant in the high temperature superconductor HgBa2CuO[formula omitted] from 199Hg NMR

In the high temperature cuprate superconductor, HgBa2CuO4+δ, it has been determined that the dopant oxygen, Oδ, resides in the Hg-plane. Here we present a systematic investigation of the 199Hg NMR spectrum as a function of dopant oxygen concentration, δ. At high doping levels we observe four distinct 199Hg resonance peaks which follow a binomial distribution in δ corresponding to zero, one, two, and three nearest neighbor Oδ atoms. Additionally, we have measured a linear dependence of the peak frequencies on doping and suggest that these measurements might be theoretically amenable.

Charge trapping and super-Poissonian noise centres in a cuprate superconductor

The electronic properties of cuprate high temperature superconductors in their normal state are very two-dimensional: while transport in the ab plane is perfectly metallic, it is insulating along the c-axis, with ratios between the two exceeding 10^4. This anisotropy has been identified as one of the mysteries of the cuprates early on, and while widely different proposals exist for its microscopic origin, little is known empirically on the microscopic scale. Here, we elucidate the properties of the insulating layers with a newly developed scanning noise spectroscopy technique that can spatially map not only the current but also the current fluctuations in time. We discover atomic-scale noise centers that exhibit MHz current fluctuations 40 times the expectation from Poissonian noise, more than what has been observed in mesoscopic systems. Such behaviour can only happen in highly polarizable insulators and represents strong evidence for trapping of charge in the charge reservoir layers. Our measurements suggest a picture of metallic layers separated by polarizable insulators within a three-dimensional superconducting state.

Self-energies and quasiparticle scattering interference

The cuprate high-temperature superconductors are known to host a wide array of effects due to interactions and disorder. In this work, we look at some of the consequences of these effects which can be visualized by scanning tunneling spectroscopy. These interaction and disorder effects can be incorporated into a mean-field description by means of a self-energy appearing in the Green's function. We first examine the quasiparticle scattering interference spectra in the superconducting state at optimal doping as temperature is increased. Assuming agreement with angle-resolved photoemission experiments which suggest that the scattering rate depends on temperature, resulting in the filling of the $d$-wave gap, we find that the peaks predicted by the octet model become progressively smeared as temperature is increased. When the scattering rate is of the same order of magnitude as the superconducting gap, the spectral function shows Fermi-arc-like patterns, while the power spectrum of the local density of states shows the destruction of the octet-model peaks. We next consider the normal state properties of the optimally-doped cuprates. We model this by adding a marginal Fermi liquid self-energy to the normal-state propagator, and consider the dependence of the QPI spectra on frequency, temperature, and doping. We demonstrate that the MFL self-energy leads to a smearing of the caustics appearing in the normal-state QPI power spectrum as either temperature or frequency is increased at fixed doping. The smearing is found to be more prominent in the MFL case than in an ordinary Fermi liquid. We also consider the case of a marginal Fermi liquid with a strongly momentum-dependent self-energy which gives rise to a visible "nodal-antinodal" dichotomy at the normal state, and discuss how the spectra as seen in ARPES and STS differ from both an isotropic metal and a broadened $d$-wave superconductor.

Spin excitation spectrum of high-temperature cuprate superconductors from finite cluster simulations

A cluster of spins 1/2 of a finite size can be regarded as a basic building block of a spin texture in high-temperature cuprate superconductors. If this texture has the character of a network of weakly coupled spin clusters, then spin excitation spectra of finite clusters are expected to capture the principal features of the experimental spin response. We calculate spin excitation spectra of several clusters of spins 1/2 coupled by Heisenberg interaction. We find that the calculated spectra exhibit a high degree of variability representative of the actual phenomenology of cuprates, while, at the same time, reproducing a number of important features of the experimentally measured spin response. Among such features are the spin gap, the broad peak around ≃ (40–70) meV and the sharp peak at zero frequency. The latter feature emerges due to transitions inside the ground-state multiplet of the so-called ‘uncompensated’ clusters with an odd number of spins.

Percolative nature of the direct-current paraconductivity in cuprate superconductors

Despite extraordinary scientific efforts over the past three decades, the cuprate high-temperature superconductors continue to pose formidable challenges. A pivotal problem, essential for understanding both the normal and superconducting states, is to clarify the nature of the superconducting pre-pairing above the bulk transition temperature Tc. Different experimental probes have given conflicting results, in part due to difficulties in discerning the superconducting response from the complex normal-state behavior. Moreover, it has proven challenging to separate common properties of the cuprates from compound-specific idiosyncrasies. Here we investigate the paraconductivity—the superconducting contribution to the direct-current (dc) conductivity—of the simple-tetragonal model cuprate material HgBa2CuO4+δ. We are able to separate the superconducting and normal-state responses by taking advantage of the Fermi-liquid nature of the normal state in underdoped HgBa2CuO4+δ; the robust and simple quadratic temperature-dependence of the normal-state resistivity enables us to extract the paraconductivity above the macroscopic Tc with great accuracy. We find that the paraconductivity exhibits unusual exponential temperature dependence, and that it can be quantitatively explained by a simple superconducting percolation model. Consequently, the emergence of superconductivity in this model system is dominated by the underlying intrinsic gap inhomogeneity. Motivated by these insights, we reanalyze published results for two other cuprates and find exponential behavior as well, with nearly the same characteristic temperature scale. The universal intrinsic gap inhomogeneity is not only essential for understanding the supercoducting precursor, but will also have to be taken into account in the analysis of other bulk measurements of the cuprates.

Majorana Corner Modes in a High-Temperature Platform.

We introduce two-dimensional topological insulators in proximity to high-temperature cuprate or iron-based superconductors as high-temperature platforms of Majorana Kramers pairs of zero modes. The proximity-induced pairing at the helical edge state of the topological insulator serves as a Dirac mass, whose sign changes at the sample corner because of the pairing symmetry of high-T_{c} superconductors. This sign changing naturally creates at each corner a pair of Majorana zero modes protected by time-reversal symmetry. Conceptually, this is a topologically trivial superconductor-based approach for Majorana zero modes. We provide quantitative criteria and suggest candidate materials for this proposal.

Impurity induced renormalized phonon spectrum of cuprate superconductors

The potential problem of anharmonic lattice vibrations in high-temperature superconductors (HTS) using the most suitable Born–Mayer–Huggins (BMH) potential has been taken up to investigate the renormalized phonon density of states (RPDOS). In order to develop the suitable results, the many body theory using quantum dynamical approach of Green’s function (GF) via an almost complete Hamiltonian (without using BCS type Hamiltonian) has been incorporated which includes harmonic electron and phonon Hamiltonian, electron–phonon interaction Hamiltonian, anharmonic and defect Hamiltonian. The derivation of anharmonic phonon GF for modified form of BMH potential enables to evaluate the renormalized and perturbed mode phonon frequencies of solids. The expressions obtained for the RPDOS can be resolved into diagonal and nondiagonal parts of which the nondiagonal part chiefly depends on impurities and disappears in pure crystals. A large number of new features are investigated in the light of this formulation followed by the numerical analysis for the energy spectrum of representative cuprate HTS YBa2Cu3O[Formula: see text]. The inclusion of defects, anharmonicities and electron–phonon interactions in the cuprate superconductors substantially modifies the scenario of RPDOS and reveals a large number of unexplained peaks in the spectrum.

Topological Scenario for High-Temperature Superconductivity in Cuprates

The structure of the joint phase diagram of high-temperature superconducting cuprates has been studied within the theory of fermion condensation. Prerequisites of the topological rearrangement of the Landau state with the formation of a flat band adjacent to the nominal Fermi surface have been established. The related non-Fermi-liquid behavior of cuprates in the normal phase has been studied with focus on the non-Fermi-liquid behavior of the resistivity ρ(T), including the observed crossover from the linear temperature behavior ρ(T, x) = A1(x)T at doping levels x below the critical value x c h corresponding to the boundary of the superconducting region to the quadratic temperature behavior at x > x c h , which is incompatible with predictions of the conventional quantum-critical-point scenario. It has been demonstrated that the slope of the coefficient A1(x) is universal and is the same on both boundaries of the joint phase diagram of cuprates in agreement with available experimental data. It has also been shown that the fermion condensate is responsible for pairing in the D-wave state in cuprates. The effective Coulomb repulsion in the Cooper channel, which prevents the existence of superconductivity in normal metals in the S channel, leads to high-temperature superconductivity in the D channel.

The Vanishing Superfluid Density in Cuprates—and Why It Matters

Recently, we have released the results of a comprehensive study of a couple thousand single-crystal La2−xSrxCuO4 films, covering densely the entire overdoped side of the phase diagram (Božovic et al. Nature 536, 309–311, 2016; Wu et al. Nature 547, 432–435, 2017). Here, we review the key experimental findings, place them in the context of other important well-established facts and observations, and discuss their implications for our understanding of high-temperature superconductivity in cuprates. We conclude that it involves some new physics that requires going beyond the standard Fermi liquid description of the normal state and Bardeen-Cooper-Schrieffer description of the superconducting state.

Relationship between Magnetic Anisotropy below Pseudogap Temperature and Short-Range Antiferromagnetic Order in High-Temperature Cuprate Superconductor

The central issue in high-temperature cuprate superconductors is the pseudogap state appearing below the pseudogap temperature $T^*$, which is well above the superconducting transition temperature. In this study, we theoretically investigate the rapid increase of the magnetic anisotropy below the pseudogap temperature detected by the recent torque-magnetometry measurements on YBa$_2$Cu$_3$O$_y$ [Y. Sato et al., Nat. Phys., 13, 1074 (2017)]. Applying the spin Green's function formalism including the Dzyaloshinskii--Moriya interaction arising from the buckling of the CuO$_2$ plane, we obtain results that are in good agreement with the experiment and find a scaling relationship. Our analysis suggests that the characteristic temperature associated with the magnetic anisotropy, which coincides with $T^*$, is not a phase transition temperature but a crossover temperature associated with the short-range antiferromagnetic order.