Distinct Fermi-Momentum-Dependent Energy Gaps in Deeply Underdoped Bi2212

Band-selective gap opening by a C 4-symmetric order in a proximity-coupled heterostructure Sr2VO3FeAs

Complex electronic phases in strongly correlated electron systems are manifested by broken symmetries in the low-energy electronic states. Some mysterious phases, however, exhibit intriguing energy gap opening without an apparent signature of symmetry breaking (e.g., high-T_C cuprates and heavy fermion superconductors). Here, we report an unconventional gap opening in a heterostructured, iron-based superconductor Sr₂VO₃FeAs across a phase transition at T ₀ ∼150 K. Using angle-resolved photoemission spectroscopy, we identify that a fully isotropic gap opens selectively on one of the Fermi surfaces with finite warping along the interlayer direction. This band selectivity is incompatible with conventional gap opening mechanisms associated with symmetry breaking. These findings, together with the unusual field-dependent magnetoresistance, suggest that the Kondo-type proximity coupling of itinerant Fe electrons to localized V spin plays a role in stabilizing the exotic phase, which may serve as a distinct precursor state for unconventional superconductivity.

Cooper Pair Density of Bi2Sr2CaCu2O8+ x in Atomic scale at 4.2 K

In pursuit of the elusive mechanism of high- T _C superconductors (HTSC), spectroscopic imaging scanning tunneling microscopy (SI-STM) is an indispensable tool for surveying local properties of HTSC. Since a conventional STM utilizes metal tips, which allow the examination of only quasiparticles and not superconducting (SC) pairs, Josephson tunneling using STM has been demonstrated by many authors in the past. An atomically resolved scanning Josephson tunneling microscopy (SJTM), however, was realized only recently on Bi₂Sr₂CaCu₂O_{8+ x} (Bi-2212) below 50 mK and on the Pb(110) surface at 20 mK. Here we report the atomically resolved SJTM on Bi₂Sr₂CaCu₂O_{8+ x} at 4.2 K using Bi-2212 tips created in situ. The I- V characteristics show clear zero bias conductance peaks following Ambegaokar-Baratoff (AB) theory. A gap map was produced for the first time using an atomically resolved Josephson critical current map I _C( r) and AB theory. Surprisingly, we found that this new gap map is anticorrelated to the gap map produced by a conventional method relying on the coherence peaks. Quasiparticle resonance due to a single isolated zinc atom impurity was also observed by SJTM, indicating that atomically resolved SJTM was achieved at 4.2 K. Our result provides a starting point for realizing SJTM at even higher temperatures, rendering possible investigation of the existence of SC pairs in HTSC above the T _C.

Origin of the Fermi arcs in cuprates: a dual role of quasiparticle and pair excitations

Angle resolved photoemission spectroscopy (ARPES) mesurements in cuprates have given key information on the temperature and angle dependence of the gap (d-wave order parameter, Fermi arcs and pseudogap). We show that these features can be understood in terms of a Bose condensation of interacting pairons (preformed hole pairs which form in their local antiferromagnetic environment). Starting from the basic properties of the pairon wavefunction, we derive the corresponding k-space spectral function. The latter explains the variation of the ARPES spectra as a function of temperature and angle up to T ^*, the onset temperature of pairon formation. While Bose excitations dominate at the antinode, the fermion excitations dominate around the nodal direction, giving rise to the Fermi arcs at finite temperature. This dual role is the key feature distinguishing cuprate from conventional superconductivity.

Disorder induced power-law gaps in an insulator-metal Mott transition

A correlated material in the vicinity of an insulator-metal transition (IMT) exhibits rich phenomenology and a variety of interesting phases. A common avenue to induce IMTs in Mott insulators is doping, which inevitably leads to disorder. While disorder is well known to create electronic inhomogeneity, recent theoretical studies have indicated that it may play an unexpected and much more profound role in controlling the properties of Mott systems. Theory predicts that disorder might play a role in driving a Mott insulator across an IMT, with the emergent metallic state hosting a power-law suppression of the density of states (with exponent close to 1; V-shaped gap) centered at the Fermi energy. Such V-shaped gaps have been observed in Mott systems, but their origins are as-yet unknown. To investigate this, we use scanning tunneling microscopy and spectroscopy to study isovalent Ru substitutions in Sr3(Ir1-xRux)2O7 (0 ≤ x ≤ 0.5) which drive the system into an antiferromagnetic, metallic state. Our experiments reveal that many core features of the IMT, such as power-law density of states, pinning of the Fermi energy with increasing disorder, and persistence of antiferromagnetism, can be understood as universal features of a disordered Mott system near an IMT and suggest that V-shaped gaps may be an inevitable consequence of disorder in doped Mott insulators.

Universal spectral signatures in pnictides and cuprates: the role of quasiparticle-pair coupling

Understanding the physical properties of a large variety of high-T _c superconductors (SC), the cuprate family as well as the more recent iron-based superconductors, is still a major challenge. In particular, these materials exhibit the 'peak-dip-hump' structure in the quasiparticle density of states (DOS). The origin of this structure is explained within our pair-pair interaction (PPI) model: The non-superconducting state consists of incoherent pairs, a 'Cooper-pair glass' which, due to the PPI, undergoes a Bose-like condensation below T _c to the coherent SC state. We derive the equations of motion for the quasiparticle operators showing that the DOS 'peak-dip-hump' is caused by the coupling between quasiparticles and excited pair states, or 'super-quasiparticles'. The renormalized SC gap function becomes energy-dependent and non retarded, reproducing accurately the experimental spectra of both pnictides and cuprates, despite the large difference in gap value.

Unconventional high-Tc superconductivity in fullerides

A3C60 molecular superconductors share a common electronic phase diagram with unconventional high-temperature superconductors such as the cuprates: superconductivity emerges from an antiferromagnetic strongly correlated Mott-insulating state upon tuning a parameter such as pressure (bandwidth control) accompanied by a dome-shaped dependence of the critical temperature, Tc However, unlike atom-based superconductors, the parent state from which superconductivity emerges solely by changing an electronic parameter-the overlap between the outer wave functions of the constituent molecules-is controlled by the C60 (3-) molecular electronic structure via the on-molecule Jahn-Teller effect influence of molecular geometry and spin state. Destruction of the parent Mott-Jahn-Teller state through chemical or physical pressurization yields an unconventional Jahn-Teller metal, where quasi-localized and itinerant electron behaviours coexist. Localized features gradually disappear with lattice contraction and conventional Fermi liquid behaviour is recovered. The nature of the underlying (correlated versus weak-coupling Bardeen-Cooper-Schrieffer theory) s-wave superconducting states mirrors the unconventional/conventional metal dichotomy: the highest superconducting critical temperature occurs at the crossover between Jahn-Teller and Fermi liquid metal when the Jahn-Teller distortion melts.This article is part of the themed issue 'Fullerenes: past, present and future, celebrating the 30th anniversary of Buckminster Fullerene'.

A universal explanation of tunneling conductance in exotic superconductors

A longstanding mystery in understanding cuprate superconductors is the inconsistency between the experimental data measured by scanning tunneling spectroscopy (STS) and angle-resolved photoemission spectroscopy (ARPES). In particular, the gap between prominent side peaks observed in STS is much bigger than the superconducting gap observed by ARPES measurements. Here, we reconcile the two experimental techniques by generalising a theory which was previously applied to zero-dimensional mesoscopic Kondo systems to strongly correlated two-dimensional (2D) exotic superconductors. We show that the side peaks observed in tunneling conductance measurements in all these materials have a universal origin: They are formed by coherence-mediated tunneling under bias and do not directly reflect the underlying density of states (DOS) of the sample. We obtain theoretical predictions of the tunneling conductance and the density of states of the sample simultaneously and show that for cuprate and pnictide superconductors, the extracted sample DOS is consistent with the superconducting gap measured by ARPES.

Applications of VUV extra-focus mechanism: high-performance dual-mode monochromator from VUV to soft X-ray

A new monochromator scheme is presented in which an extra-focus constant-included-angle varied-line-spacing cylindrical-grating monochromator (extra-focus CIA-VCGM) is conveniently combined with a variable-included-angle varied-line-spacing plane-grating monochromator (VIA-VPGM). This dual-mode solution delivers high performance in the energy range from vacuum ultraviolet (VUV) to soft X-ray. The resolving power and the efficiency of this dual-mode grating monochromator are analyzed in detail based on realistic parameters. Comparisons with the commonly used variable-included-angle plane-grating monochromator and normal-incidence monochromator (VIA-PGM/NIM) hybrid monochromator are made.

A new extra-focus monochromator designed for high-performance VUV beamlines

A new monochromator called an extra-focus constant-included-angle varied-line-spacing (VLS) cylindrical-grating monochromator (extra-focus CIA-VCGM) is described. This monochromator is based on the Hettrick-Underwood scheme where the plane VLS grating is replaced by a cylindrical one in order to zero the defocus at three reference photon energies in the vacuum-ultraviolet range. It has a simple mechanical structure and a fixed focus spot with high performance over a wide energy range. Furthermore, its mechanical compatibility with a standard VLS plane-grating monochromator allows convenient extension into the soft-X-ray range.

Pairing and the phase diagram of the normal coherence length ξN(T, x) above Tc of La(2-x)Sr(x)CuO4 thin films probed by the Josephson effect

The long range proximity effect in high-T_c c-axis Josephson junctions with a high-T_c barrier of lower T_c is still a puzzling phenomenon. It leads to supercurrents in junctions with much thicker barriers than would be allowed by the conventional proximity effect. Here we measured the T − x (Temperature-doping level) phase diagram of the barrier coherence length ξ_N(T, x), and found an enhancement of ξ_N at moderate under-doping and high temperatures. This indicates that a possible origin of the long range proximity effect in the cuprate barrier is the conjectured pre-formed pairs in the pseudogap regime, which increase the length scale over which superconducting correlations survive in the seemingly normal barrier. In more details, we measured the supercurrents I_c of Superconducting - Normal - Superconducting SNS c-axis junctions, where S was optimally doped Y Ba₂Cu₃O_7−δ below T_c (90 K) and N was La_2−xSr_xCuO₄ above its T_c (<25 K) but in the pseudogap regime. From the exponential decay of I_c(T) ∝ exp[−d/ξ_N(T)], where d is the barrier thickness, the ξ_N(T) values were extracted. By repeating these measurements for different barrier doping levels x, the whole phase diagram of ξ_N(T, x) was obtained.

Size and symmetry of the superconducting gap in the f.c.c. Cs3C60 polymorph close to the metal-Mott insulator boundary

The alkali fullerides, A(3)C(60) (A = alkali metal) are molecular superconductors that undergo a transition to a magnetic Mott-insulating state at large lattice parameters. However, although the size and the symmetry of the superconducting gap, Δ, are both crucial for the understanding of the pairing mechanism, they are currently unknown for superconducting fullerides close to the correlation-driven magnetic insulator. Here we report a comprehensive nuclear magnetic resonance (NMR) study of face-centred-cubic (f.c.c.) Cs(3)C(60) polymorph, which can be tuned continuously through the bandwidth-controlled Mott insulator-metal/superconductor transition by pressure. When superconductivity emerges from the insulating state at large interfullerene separations upon compression, we observe an isotropic (s-wave) Δ with a large gap-to-superconducting transition temperature ratio, 2Δ0/k(B)T(c) = 5.3(2) [Δ0 = Δ(0 K)]. 2Δ0/k(B)T(c) decreases continuously upon pressurization until it approaches a value of ~3.5, characteristic of weak-coupling BCS theory of superconductivity despite the dome-shaped dependence of Tc on interfullerene separation. The results indicate the importance of the electronic correlations for the pairing interaction as the metal/superconductor-insulator boundary is approached.

Doping dependence of low-energy quasiparticle excitations in superconducting Bi2212

: The doping-dependent evolution of the d-wave superconducting state is studied from the perspective of the angle-resolved photoemission spectra of a high-Tc cuprate, Bi2Sr2CaCu2 O8+δ (Bi2212). The anisotropic evolution of the energy gap for Bogoliubov quasiparticles is parametrized by critical temperature and superfluid density. The renormalization of nodal quasiparticles is evaluated in terms of mass enhancement spectra. These quantities shed light on the strong coupling nature of electron pairing and the impact of forward elastic or inelastic scatterings. We suggest that the quasiparticle excitations in the superconducting cuprates are profoundly affected by doping-dependent screening.

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.

Doping-dependent photon scattering resonance in the model high-temperature superconductor HgBa2CuO4+δ revealed by Raman scattering and optical ellipsometry

We study the model high-temperature superconductor HgBa(2)CuO(4+δ) with electronic Raman scattering and optical ellipsometry over a wide doping range. The dependence of the resonant Raman cross section on the incident photon energy changes drastically as a function of doping, in a manner that corresponds to a rearrangement of the interband optical transitions seen with ellipsometry. This doping-dependent Raman resonance allows us to reconcile the apparent discrepancy between Raman and x-ray detection of magnetic fluctuations in superconducting cuprates. Intriguingly, the strongest variation occurs across the doping level where the antinodal superconducting gap appears to reach its maximum.

Universal features in the photoemission spectroscopy of high-temperature superconductors

The energy gap for electronic excitations is one of the most important characteristics of the superconducting state, as it directly reflects the pairing of electrons. In the copper-oxide high-temperature superconductors (HTSCs), a strongly anisotropic energy gap, which vanishes along high-symmetry directions, is a clear manifestation of the d-wave symmetry of the pairing. There is, however, a dramatic change in the form of the gap anisotropy with reduced carrier concentration (underdoping). Although the vanishing of the gap along the diagonal to the square Cu-O bond directions is robust, the doping dependence of the large gap along the Cu-O directions suggests that its origin might be different from pairing. It is thus tempting to associate the large gap with a second-order parameter distinct from superconductivity. We use angle-resolved photoemission spectroscopy to show that the two-gap behavior and the destruction of well-defined electronic excitations are not universal features of HTSCs, and depend sensitively on how the underdoped materials are prepared. Depending on cation substitution, underdoped samples either show two-gap behavior or not. In contrast, many other characteristics of HTSCs, such as the dome-like dependence of on doping, long-lived excitations along the diagonals to the Cu-O bonds, and an energy gap at the Brillouin zone boundary that decreases monotonically with doping while persisting above (the pseudogap), are present in all samples, irrespective of whether they exhibit two-gap behavior or not. Our results imply that universal aspects of high- superconductivity are relatively insensitive to differences in the electronic states along the Cu-O bond directions.

Formation of gapless Fermi arcs and fingerprints of order in the pseudogap state of cuprate superconductors

We use angle-resolved photoemission spectroscopy and a new quantitative approach based on the partial density of states to study properties of seemingly disconnected portions of the Fermi surface (FS) that are present in the pseudogap state of cuprates called Fermi arcs. We find that the normal state FS collapses very abruptly into Fermi arcs at the pseudogap temperature (T*). Surprisingly, the length of the Fermi arcs remains constant over an extended temperature range between T* and T(pair), consistent with the presence of an ordered state below T*. These arcs collapse again at the temperature below which pair formation occurs (T(pair)) either to a point or a very short arc, whose length is limited by our experimental resolution. The tips of the arcs span between points defining a set of wave vectors in momentum space, which are the fingerprints of the ordered state that causes the pseudogap.

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-T_c cuprates, because anisotropic evolution of a d-wave-like superconducting gap with underdoping has been difficult to formulate along with a critical temperature T_c. Here we show that a nodal-gap energy 2Δ_N closely follows 8.5 k_BT_c with underdoping and is also proportional to the product of an antinodal gap energy Δ^* and a square-root superfluid density √P_s for Bi₂Sr₂CaCu₂O_8+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 T_c.

In conventional superconductors, the critical temperature is proportional to the superconducting energy gap, but this is not so in unconventional superconductors. Anzai et al. identify an alternative relationship involving nodal and antinodal gaps in an underdoped cuprate superconductor.

Robust nodal d-wave spectrum in simulations of a strongly fluctuating competing order in underdoped cuprate superconductors

We resolve an existing discrepancy between convincing evidence for competing order in underdoped cuprates and spectroscopic data consistent with a homogeneous d-wave superconductor in the very same compounds. Specifically, we show that fluctuations of the competing order generate strongly inhomogeneous states whose spectra are almost indistinguishable from the pure d-wave superconductor. This is in contrast to the commonly studied case of homogeneously coexisting order, which typically generates a reconstructed Fermi surface with closed Fermi pockets. The signatures of the fluctuating competing order can be found mainly in a splitting of the antinodal band, and, for strong magnetic order, in small induced nodal gaps similar to those found in recent experiments on underdoped La(2-x)Sr(x)CuO4.

Low-doping anomalies in high-Tc cuprate superconductors as evidence of a spin-fluctuation-mediated superconducting state

We present a theoretical study of the impact of spin fluctuations on electronic properties when these fluctuations are soft and strong, as in low-doped cuprates. We show that they play a triple role: they mediate d pairing, destroy the coherence of antinodal electrons, and create a spin density wave pseudogap. The competition between these effects is responsible for numerous electron anomalies close to those observed experimentally in the low-doping superconducting state.

Phase competition in trisected superconducting dome

A detailed phenomenology of low energy excitations is a crucial starting point for microscopic understanding of complex materials, such as the cuprate high-temperature superconductors. Because of its unique momentum-space discrimination, angle-resolved photoemission spectroscopy (ARPES) is ideally suited for this task in the cuprates, where emergent phases, particularly superconductivity and the pseudogap, have anisotropic gap structure in momentum space. We present a comprehensive doping- and temperature-dependence ARPES study of spectral gaps in Bi(2)Sr(2)CaCu(2)O(8+δ), covering much of the superconducting portion of the phase diagram. In the ground state, abrupt changes in near-nodal gap phenomenology give spectroscopic evidence for two potential quantum critical points, p = 0.19 for the pseudogap phase and p = 0.076 for another competing phase. Temperature dependence reveals that the pseudogap is not static below T(c) and exists p > 0.19 at higher temperatures. Our data imply a revised phase diagram that reconciles conflicting reports about the endpoint of the pseudogap in the literature, incorporates phase competition between the superconducting gap and pseudogap, and highlights distinct physics at the edge of the superconducting dome.

Pairing mechanism for the high-TC superconductivity: symmetries and thermodynamic properties

The pairing mechanism for the high-Tc superconductors based on the electron-phonon (EPH) and electron-electron-phonon (EEPH) interactions has been presented. On the fold mean-field level, it has been proven, that the obtained s-wave model supplements the predictions based on the BCS van Hove scenario. In particular: (i) For strong EEPH coupling and T < T(C) the energy gap (Δtot) is very weak temperature dependent; up to the critical temperature Δtot extends into the anomalous normal state to the Nernst temperature. (ii) The model explains well the experimental dependence of the ratio R(1) ≡ 2Δ(tot)(0)/k(B)T(C) on doping for the reported superconductors in the terms of the few fundamental parameters. In the presented paper, the properties of the d-wave superconducting state in the two-dimensional system have been also studied. The obtained results, like for s-wave, have shown the energy gap amplitude crossover from the BCS to non-BCS behavior, as the value of the EEPH potential increases. However, for T > T(C) the energy gap amplitude extends into the anomalous normal state to the pseudogap temperature. Finally, it has been presented that the anisotropic model explains the dependence of the ratio R(1) on doping for the considered superconductors.

d-Wave Superconductivity and s-Wave Charge Density Waves: Coexistence between Order Parameters of Different Origin and Symmetry

A review of the theory describing the coexistence between d-wave superconductivity and s-wave charge-density-waves (CDWs) is presented. The CDW gapping is identified with pseudogapping observed in high-Tc oxides. According to the cuprate specificity, the analysis is carried out for the two-dimensional geometry of the Fermi surface (FS). Phase diagrams on the σ0 − α plane—here, σ0 is the ratio between the energy gaps in the parent pure CDW and superconducting states, and the quantity 2α is connected with the degree of dielectric (CDW) FS gapping—were obtained for various possible configurations of the order parameters in the momentum space. Relevant tunnel and photoemission experimental data for high-Tc oxides are compared with theoretical predictions. A brief review of the results obtained earlier for the coexistence between s-wave superconductivity and CDWs is also given.

The phase diagram for coexisting d-wave superconductivity and charge-density waves: cuprates and beyond

Phase diagrams of d-wave superconductivity characterized by an order parameter Δ coexisting with charge-density waves (CDWs) characterized by an order parameter Σ were constructed for the two-dimensional Fermi surface (FS) appropriate to, e.g., cuprates. CDWs were considered as an origin of the pseudogap appearing at antinodal FS sections of the d(x2-y2) superconductor. Two types of the Σ-reentrance were found: with the temperature, T, and with the opening of the CDW sector, 2α. The angular plots in the momentum space for the resulting gap profile over the FS ('gap roses') were obtained. The gap patterns are rather involved, giving insight into the difficulties of the interpretation of photoemission spectra. It was shown that the Σ-Δ coexistence region exists even for the complete dielectric gapping due to the distinction between the superconducting and CDW order parameter symmetries. The checkerboard and unidirectional CDW configurations were examined, and both the phase diagrams and the behavior with T and α of the order parameters were found to differ. A more general case with a non-zero mismatch angle β between the superconducting lobes and the CDW sectors was analyzed, the case β = π/4 corresponding to the d(xy) symmetry of the superconducting order parameter. The phase diagrams were found to be sensitive to β-variations, showing that internal strains and external pressure can drastically affect the behavior of Σ(T) and Δ(T).

Reaffirming the d(x2-y2) superconducting gap using the autocorrelation angle-resolved photoemission spectroscopy of Bi1.5Pb0.55Sr1.6La0.4CuO(6+δ)

Knowledge of the gap function is important to understand the pairing mechanism for high-temperature (T(c)) superconductivity. However, Fourier transform scanning tunneling spectroscopy (FT STS) and angle-resolved photoemission spectroscopy (ARPES) in the cuprates have reported contradictory gap functions, with FT-STS results deviating strongly from a canonical d(x2-y2) form. By applying an "octet model" analysis to autocorrelation ARPES, we reveal that a contradiction occurs because the octet model does not consider the effects of matrix elements and the pseudogap. This reaffirms the canonical d(x2-y2) superconducting gap around the node, which can be directly determined from ARPES. Further, our study suggests that the FT-STS reported fluctuating superconductivity around the node at far above T(c) is not necessary to explain the existence of the quasiparticle interference at low energy.

From a single-band metal to a high-temperature superconductor via two thermal phase transitions

The nature of the pseudogap phase of cuprate high-temperature superconductors is a major unsolved problem in condensed matter physics. We studied the commencement of the pseudogap state at temperature T* using three different techniques (angle-resolved photoemission spectroscopy, polar Kerr effect, and time-resolved reflectivity) on the same optimally doped Bi2201 crystals. We observed the coincident, abrupt onset at T* of a particle-hole asymmetric antinodal gap in the electronic spectrum, a Kerr rotation in the reflected light polarization, and a change in the ultrafast relaxational dynamics, consistent with a phase transition. Upon further cooling, spectroscopic signatures of superconductivity begin to grow close to the superconducting transition temperature (T(c)), entangled in an energy-momentum-dependent manner with the preexisting pseudogap features, ushering in a ground state with coexisting orders.

Evidence of a precursor superconducting phase at temperatures as high as 180 K in RBa2Cu3O(7-δ) (R=Y, Gd, Eu) superconducting crystals from infrared spectroscopy

We show that a multilayer analysis of the infrared c-axis response of RBa2Cu3O(7-δ) (R=Y, Gd, Eu) provides important new information about the anomalous normal-state properties of underdoped cuprate high temperature superconductors. In addition to competing correlations which give rise to a pseudogap that depletes the low-energy electronic states below T*≫T(c), it enables us to identify the onset of a precursor superconducting state below T(ons)>T(c). We map out the doping phase diagram of T(ons) which reaches a maximum of 180 K at strong underdoping and present magnetic field dependent data which confirm our conclusions.

Insensitivity of the superconducting gap to variations in the critical temperature of Zn-substituted Bi2Sr2CaCu2O(8+δ) superconductors

The phase diagram of the superconducting high-T(c) cuprates is governed by two energy scales: T*, the temperature below which a gap is opened in the excitation spectrum, and T(c), the superconducting transition temperature. The way these two energy scales are reflected in the low-temperature energy gap is being intensively debated. Using Zn substitution and carefully controlled annealing we prepared a set of samples having the same T* but different T(c)'s, and measured their gap using angle-resolved photoemission spectroscopy (ARPES). We show that T(c) is not related to the gap shape or size, but it controls the size of the coherence peak at the gap edge.

Theory of extrinsic and intrinsic tunnelling in cuprate superconductors

There has been a huge theoretical and experimental push to try to illuminate the mechanism behind the high-temperature superconductivity of copper oxides. Cuprates are distinguishable from conventional metallic superconductors in originating from the doping of the parent charge-transfer insulators. The superconducting parts are weakly coupled two-dimensional doped layers held together by the parent lattice. Apart from their high-T(c) they have other characteristic features including the 'superconducting' gap (SG) which develops below the superconducting critical temperature and can be seen in extrinsic and intrinsic tunnelling experiments as well as using high-resolution angle-resolved photoemission (ARPES); there also exists another energy gap, the 'pseudogap' (PG), which is a large anomalous gap that exists well above T(c). We present a brief review of recent theories behind the pseudogap and discuss in detail one specific (polaronic) approach which explains the SG, PG and unusual tunnelling characteristics of cuprate superconductors.

Carrier-concentration dependence of the pseudogap ground state of superconducting Bi₂Sr(₂-x)La(x)CuO(₆+δ) revealed by ⁶³,⁶⁵Cu-nuclear magnetic resonance in very high magnetic fields

We report the results of the Knight shift by ⁶³,⁶⁵Cu-NMR measurements on single-layered copper-oxide Bi₂Sr(₂-x)La(x)CuO(₆+δ) conducted under very high magnetic fields up to 44 T. The magnetic field suppresses superconductivity completely, and the pseudogap ground state is revealed. The ⁶³Cu-NMR Knight shift shows that there remains a finite density of states at the Fermi level in the zero-temperature limit, which indicates that the pseudogap ground state is a metallic state with a finite volume of Fermi surface. The residual density of states in the pseudogap ground state decreases with decreasing doping (increasing x) but remains quite large even at the vicinity of the magnetically ordered phase of x ≥ 0.8, which suggests that the density of states plunges to zero upon approaching the Mott insulating phase.

Enhanced superconducting gaps in the trilayer high-temperature Bi2Sr2Ca2Cu3O(10+δ) cuprate superconductor

We report the first observation of the multilayer band splitting in the optimally doped trilayer cuprate Bi2Sr2Ca2Cu3O(10+δ) (Bi2223) by angle-resolved photoemission spectroscopy. The observed energy bands and Fermi surfaces are originated from the outer and inner CuO2 planes (OP and IP). The OP band is overdoped with a large d-wave gap around the node of Δ0∼43  meV while the IP is underdoped with an even large gap of Δ0∼60  meV. These energy gaps are much larger than those for the same doping level of the double-layer cuprates, which leads to the large Tc in Bi2223. We propose possible origins of the large superconducting gaps for the OP and IP: (1) minimal influence of out-of-plane disorder and a proximity effect and (2) interlayer tunneling of Cooper pairs between the OP and IP.

Doping-dependent nodal fermi velocity of the high-temperature superconductor Bi2Sr2CaCu2O(8+δ) revealed using high-resolution angle-resolved photoemission spectroscopy

The improved resolution of laser-based angle-resolved photoemission spectroscopy (ARPES) allows reliable access to fine structures in the spectrum. We present a systematic, doping-dependent study of a recently discovered low-energy kink in the nodal dispersion of Bi2Sr2CaCu2O(8+δ) (Bi-2212), which demonstrates the ubiquity and robustness of this kink in underdoped Bi-2212. The renormalization of the nodal velocity due to this kink becomes stronger with underdoping, revealing that the nodal Fermi velocity is nonuniversal, in contrast with assumed phenomenology. This is used together with laser ARPES measurements of the gap velocity (v2) to resolve discrepancies with thermal conductivity measurements.

Evolution of the dynamical pairing across the phase diagram of a strongly correlated high-temperature superconductor

We study the dynamics of the Cooper pairing across the T = 0 phase diagram of the two-dimensional Hubbard model, relevant for high-temperature superconductors, using a cluster extension of dynamical mean-field theory. We find that the superconducting pairing function evolves from an unconventional form in the overdoped region into a more conventional boson-mediated retarded form in the underdoped region of the phase diagram. The boson, however, promotes the rise of a pseudogap in the electron density of states rather than a superconducting gap as in the standard theory of superconductivity. We discuss our results in terms of Mott-related phenomena, and we show that they can be observed in tunneling experiments.

Universal versus material-dependent two-gap behaviors of the high-Tc cuprate superconductors: angle-resolved photoemission study of La2-xSrxCuO4

We have investigated the doping and temperature dependences of the pseudogap and superconducting gap in the single-layer cuprate La2-xSrxCuO4 by angle-resolved photoemission spectroscopy. The results clearly exhibit two distinct energy and temperature scales, namely, the gap around (pi, 0) of magnitude Delta* and the gap around the node characterized by the d-wave order parameter Delta0. In comparison with Bi2212 having higher Tc's, Delta0 is smaller, while Delta* and T* are similar. This result suggests that Delta* and T* are approximately material-independent properties of a single CuO2 plane, in contrast to the material-dependent Delta0, representing the pairing strength.

Evolution of a pairing-induced pseudogap from the superconducting gap of (Bi,Pb)2Sr2CuO6

We have performed an ultrahigh-resolution angle-resolved photoemission spectroscopy study of slightly overdoped (Bi,Pb)2Sr2CuO6 to elucidate the origin of the pseudogap. By using a newly developed xenon-plasma light source, we determined the comprehensive momentum and temperature dependencies of the superconducting gap and the pseudogap. We found that the antinodal pseudogap persists far above the superconducting transition temperature and is smoothly connected to the nodal gap. The characteristic temperature of the pseudogap scales well with the superconducting gap size irrespective of the momentum location. The present experimental results point to the pairing origin of the pseudogap.

Superconducting pairing through the spin resonance mode in high-temperature cuprate superconductors

We find that the spin resonance mode mediator scenario can explain important anomalies observed in the superconducting (SC) high-T_{c} cuprates: the famous low energy nodal kink with its doping dependence, the U-shaped form of the SC gap angular dependence, the anomalous form of electron density of states, the high absolute value of the SC gap, and some other unconventional properties.

Two energy gaps and Fermi-surface "arcs" in NbSe2

Using angle-resolved photoemission spectroscopy, we report on the direct observation of the energy gap in 2H-NbSe2 caused by the charge-density waves (CDW). The gap opens in the regions of the momentum space connected by the CDW vectors, which implies a nesting mechanism of CDW formation. In remarkable analogy with the pseudogap in cuprates, the detected energy gap also exists in the normal state (T>T0) where it breaks the Fermi surface into "arcs," it is nonmonotonic as a function of temperature with a local minimum at the CDW transition temperature (T0), and it forestalls the superconducting gap by excluding the nested portions of the Fermi surface from participating in superconductivity.

A brief update of angle-resolved photoemission spectroscopy on a correlated electron system

In this paper, we briefly summarize the capabilities of state-of-the-art angle-resolved photoemission spectroscopy (ARPES) in the field of experimental condensed matter physics. Due to the advancement of the detector technology and the high flux light sources, ARPES has become a powerful tool to study the low energy excitations of solids, especially those novel quantum materials in which many-body physics are at play. To benchmark today's state-of-the-art ARPES technique, we demonstrate that the precision of today's ARPES has advanced to a regime comparable to the bulk-sensitive de Haas-van Alphen (dHvA) measurements. Finally, as an example of new discoveries driven by the advancement of the ARPES technique, we summarize some of our recent ARPES measurements on underdoped high-T(c) superconducting cuprates, which have provided further insight into the complex pseudogap problem.

Valence bond glass theory of electronic disorder and the pseudogap state of high-temperature cuprate superconductors

We show that the low-energy fluctuations of the valence bond due to the superexchange are pinned by the electronic disorder from off-stoichiometric dopants, leading to a valence bond glass (VBG) pseudogap phase in underdoped high-T_{c} cuprates. The antinodal Fermi surface sections are gapped out, giving rise to a normal state Fermi arc whose length shrinks with underdoping. Below T_{c}, the superexchange interaction induces a d-wave superconducting gap that coexists with the VBG pseudogap. The evolution of the local and momentum-space spectroscopy with doping and temperature captures the salient properties of the pseudogap phenomena and the electronic disorder.

Competition between the pseudogap and superconductivity in the high-T(c) copper oxides

In a classical Bardeen-Cooper-Schrieffer superconductor, pairing and coherence of electrons are established simultaneously below the critical transition temperature (T(c)), giving rise to a gap in the electronic energy spectrum. In the high-T(c) copper oxide superconductors, however, a pseudogap extends above T(c). The relationship between the pseudogap and superconductivity is one of the central issues in this field. Spectral gaps arising from pairing precursors are qualitatively similar to those caused by competing electronic states, rendering a standard approach to their analysis inconclusive. The issue can be settled, however, by studying the correlation between the weights associated with the pseudogap and superconductivity spectral features. Here we report a study of two spectral weights using angle-resolved photoemission spectroscopy. The weight of the superconducting coherent peak increases away from the node following the trend of the superconducting gap, but starts to decrease in the antinodal region. This striking non-monotonicity reveals the presence of a competing state. We demonstrate a direct correlation, for different values of momenta and doping, between the loss in the low-energy spectral weight arising from the opening of the pseudogap and a decrease in the spectral weight associated with superconductivity. We therefore conclude that the pseudogap competes with the superconductivity by depleting the spectral weight available for pairing.

Emergence of preformed Cooper pairs from the doped Mott insulating state in Bi2Sr2CaCu2O8+delta

Superconductors are characterized by an energy gap that represents the energy needed to break the pairs of electrons (Cooper pairs) apart. At temperatures considerably above those associated with superconductivity, the high-transition-temperature copper oxides have an additional 'pseudogap'. It has been unclear whether this represents preformed pairs of electrons that have not achieved the coherence necessary for superconductivity, or whether it reflects some alternative ground state that competes with superconductivity. Paired electrons should display particle-hole symmetry with respect to the Fermi level (the energy of the highest occupied level in the electronic system), but competing states need not show such symmetry. Here we report a photoemission study of the underdoped copper oxide Bi(2)Sr(2)CaCu(2)O(8+delta) that shows the opening of a symmetric gap only in the anti-nodal region, contrary to the expectation that pairing would take place in the nodal region. It is therefore evident that the pseudogap does reflect the formation of preformed pairs of electrons and that the pairing occurs only in well-defined directions of the underlying lattice.

Evidence for a competition between the superconducting state and the pseudogap state of (BiPb)2(SrLa)2CuO6+delta from muon spin rotation experiments

The in-plane magnetic penetration depth lambda ab in optimally doped (BiPb)2(SrLa)2CuO6+delta (OP Bi2201) was studied by means of muon-spin rotation. The measurements of lambda ab(-2)(T) are inconsistent with a simple model of a d-wave order parameter and a uniform quasiparticle weight around the Fermi surface. The data are well described assuming the angular gap symmetry obtained in ARPES experiments [Phys. Rev. Lett. 98, 267004 (2007)], which suggest that the superconducting gap in OP Bi2201 exists only in segments of the Fermi surface near the nodes. The remaining parts of the Fermi surface, which are strongly affected by the pseudogap state, do not contribute significantly to the superconducting condensate.

Coexistence of competing orders with two energy gaps in real and momentum space in the high temperature superconductor Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta}

Through a combined scanning tunneling microscopy and angle-resolved photoemission spectroscopy study, we report the observation of two distinct gaps (a small and a large gap) that coexist both in real space and in the antinodal region of momentum space, below the superconducting transition temperature (T_{c}) of Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta}. We show that the small gap is associated with superconductivity. The large-gap persists above T_{c}, and seems linked to observed charge ordering. We find a strong correlation between the large and small gaps suggesting that they are affected by similar physical processes.

Direct observation of the coexistence of the pseudogap and superconducting quasiparticles in Bi2Sr2CaCu2O8 + y by time-resolved optical spectroscopy

We report the ultrafast optical response of quasiparticles (QPs) in both the pseudogap (PG) and superconducting (SC) states of an underdoped Bi2Sr2CaCu2O8 + y (Bi2212) single crystal measured with the time-resolved pump-probe technique. At a probe energy variant planck's over omegapr = 1.55 eV, it is found that the reflectivity change DeltaR/R changes its sign at exactly Tc, which allows the direct separation of the charge dynamics of PG and SC QPs. Further systematic investigations indicate that the transient signals associated with PG and SC QPs depend on the probe beam energy and polarization. By tuning them below Tc, two distinct components can be detected simultaneously, providing evidence for the coexistence of PG and SC QPs.

Evolution with hole doping of the electronic excitation spectrum in the cuprate superconductors

The recent scanning tunnelling results of Alldredge and co-workers on Bi-2212 and of Hanaguri and co-workers on Na-CCOC (Ca(2-x)Na(x)CuO(2)Cl(2)) are examined from the perspective of the Bardeen-Cooper-Schrieffer (BCS)/Bose-Einstein condensation boson-fermion resonant crossover model for the mixed-valence high temperature superconductor (HTSC) cuprates. The model specifies the two energy scales controlling the development of HTSC behaviour and the dichotomy often now alluded to between nodal and antinodal phenomena in the HTSC cuprates. An indication is extracted from the data as to how the choice of the particular HTSC system sees these two basic energy scales ([Formula: see text], the local pair binding energy, and Δ(sc), the nodal BCS-like gap parameter) evolve with doping and change in the degree of metallization of the structurally and electronically perturbed mixed-valent environment.

How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+delta

The antiferromagnetic ground state of copper oxide Mott insulators is achieved by localizing an electron at each copper atom in real space (r-space). Removing a small fraction of these electrons (hole doping) transforms this system into a superconducting fluid of delocalized Cooper pairs in momentum space (k-space). During this transformation, two distinctive classes of electronic excitations appear. At high energies, the mysterious 'pseudogap' excitations are found, whereas, at lower energies, Bogoliubov quasi-particles-the excitations resulting from the breaking of Cooper pairs-should exist. To explore this transformation, and to identify the two excitation types, we have imaged the electronic structure of Bi(2)Sr(2)CaCu(2)O(8+delta) in r-space and k-space simultaneously. We find that although the low-energy excitations are indeed Bogoliubov quasi-particles, they occupy only a restricted region of k-space that shrinks rapidly with diminishing hole density. Concomitantly, spectral weight is transferred to higher energy r-space states that lack the characteristics of excitations from delocalized Cooper pairs. Instead, these states break translational and rotational symmetries locally at the atomic scale in an energy-independent way. We demonstrate that these unusual r-space excitations are, in fact, the pseudogap states. Thus, as the Mott insulating state is approached by decreasing the hole density, the delocalized Cooper pairs vanish from k-space, to be replaced by locally translational- and rotational-symmetry-breaking pseudogap states in r-space.