The Ground State of the Pseudogap in Cuprate Superconductors

Evidence of striped electronic phases in a structurally modulated superlattice

The electronic properties of crystals can be manipulated by superimposing spatially periodic electric, magnetic or structural modulations. Long-wavelength modulations incommensurate with the atomic lattice are particularly interesting1, exemplified by recent advances in two-dimensional (2D) moiré materials2,3. Bulk van der Waals (vdW) superlattices4-8 hosting 2D interfaces between minimally disordered layers represent scalable bulk analogues of artificial vdW heterostructures and present a complementary venue to explore incommensurately modulated 2D states. Here we report the bulk vdW superlattice SrTa2S5 realizing an incommensurate one-dimensional (1D) structural modulation of 2D transition metal dichalcogenide (TMD) H-TaS2 layers. High-quality electronic transport in the H-TaS2 layers, evidenced by quantum oscillations, is made anisotropic by the modulation and exhibits commensurability oscillations paralleling lithographically modulated 2D systems9-11. We also find unconventional, clean-limit superconductivity in SrTa2S5 with a pronounced suppression of interlayer relative to intralayer coherence. The in-plane magnetic field dependence of interlayer critical current, together with electron diffraction from the structural modulation, suggests superconductivity12-14 in SrTa2S5 is spatially modulated and mismatched between adjacent TMD layers. With phenomenology suggestive of pair-density wave superconductivity15-17, SrTa2S5 may present a pathway for microscopic evaluation of this unconventional order18-21. More broadly, SrTa2S5 establishes bulk vdW superlattices as versatile platforms to address long-standing predictions surrounding modulated electronic phases in the form of nanoscale vdW devices12,13 to macroscopic crystals22,23.

Revealing the frequency-dependent oscillations in the nonlinear terahertz response induced by the Josephson current

Nonlinear responses of superconductors to intense terahertz radiation has been an active research frontier. Using terahertz pump-terahertz probe spectroscopy, we investigate the c-axis nonlinear optical response of a high-temperature superconducting cuprate. After excitation by a single-cycle terahertz pump pulse, the reflectivity of the probe pulse oscillates as the pump-probe delay is varied. Interestingly, the oscillatory central frequency scales linearly with the probe frequency, a fact widely overlooked in pump-probe experiments. By theoretically solving the nonlinear optical reflection problem on the interface, we show that our observation is well explained by the Josephson-type third-order nonlinear electrodynamics, together with the emission coefficient from inside the material into free space. The latter results in a strong enhancement of the emitted signal whose physical frequency is around the Josephson plasma edge. Our result offers a benchmark for and new insights into strong-field terahertz spectroscopy of related quantum materials.

Emergent superconducting fluctuations in compressed kagome superconductor CsV3Sb5

The recent discovery of superconductivity (SC) and charge density wave (CDW) in kagome metals AV₃Sb₅ (A = K, Rb, Cs) provides an ideal playground for the study of emergent electronic orders. Application of moderate pressure leads to a two-dome-shaped SC phase regime in CsV₃Sb₅ accompanied by the destabilizing of CDW phase. Nonetheless, the nature of this pressure-tuned SC state and its interplay with the CDW are yet to be explored. Here, we perform soft point-contact spectroscopy (SPCS) measurements in CsV₃Sb₅ to investigate the evolution of superconducting order parameter with pressure. Surprisingly, we find that the superconducting gap is significantly enhanced between the two SC domes, at which the zero-resistance temperature is suppressed and the transition is remarkably broadened. Moreover, the temperature-dependence of the SC gap in this pressure range severely deviates from the conventional Bardeen-Cooper-Schrieffer (BCS) behavior, evidencing for strong Cooper pair phase fluctuations. These findings reveal the complex intertwining of the CDW with SC in the compressed CsV₃Sb₅, suggesting striking parallel to the cuprate superconductor La_2-xBa_xCuO₄. Our results point to the essential role of charge degree of freedom in the development of intertwining electronic orders, and thus provide new constraints for theories.

Future Study of Dense Superconducting Hydrides at High Pressure

The discovery of a record high superconducting transition temperature (Tc) of 288 K in a pressurized hydride inspires new hope to realize ambient-condition superconductivity. Here, we give a perspective on the theoretical and experimental studies of hydride superconductivity. Predictions based on the BCS-Eliashberg-Midgal theory with the aid of density functional theory have been playing a leading role in the research and guiding the experimental realizations. To date, about twenty hydrides experiments have been reported to exhibit high-Tc superconductivity and their Tc agree well with the predicted values. However, there are still some controversies existing between the predictions and experiments, such as no significant transition temperature broadening observed in the magnetic field, the experimental electron-phonon coupling beyond the Eliashberg-Midgal limit, and the energy dependence of density of states around the Fermi level. To investigate these controversies and the origin of the highest Tc in hydrides, key experiments are required to determine the structure, bonding, and vibrational properties associated with H atoms in these hydrides.

Topological Doping and Superconductivity in Cuprates: An Experimental Perspective

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La2−xBaxCuO4 with x=1/8. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates.

Kinetic 2D Crystals via Topochemical Approach

The designing of novel materials is a fascinating and innovative pathway in materials science. Particularly, novel layered compounds have tremendous influence in various research fields. Advanced fundamental studies covering various aspects, including reactants and synthetic methods, are required to obtain novel layered materials with unique physical and chemical properties. Among the promising synthetic techniques, topochemical approaches have afforded the platform for widening the extent of novel 2D materials. Notably, the synthesis of binary layered materials is considered as a major scientific breakthrough after the synthesis of graphene as they exhibit a wide spectrum of material properties with varied potential applicability. In this review, a comprehensive overview of the progress in the development of metastable layered compounds is presented. The various metastable layered compounds synthesized from layered ternary bulk materials through topochemical approaches are listed, followed by the descriptions of their mechanisms, structural analyses, characterizations, and potential applications. Finally, an essential research direction concerning the synthesis of new materials is indicated, wherein the possible application of topochemical approaches in unprecedented areas is explored.

Overdoping Graphene beyond the van Hove Singularity

At very high doping levels the van Hove singularity in the π^{*} band of graphene becomes occupied and exotic ground states possibly emerge, driven by many-body interactions. Employing a combination of ytterbium intercalation and potassium adsorption, we n dope epitaxial graphene on silicon carbide past the π^{*} van Hove singularity, up to a charge carrier density of 5.5×10^{14}  cm^{-2}. This regime marks the unambiguous completion of a Lifshitz transition in which the Fermi surface topology has evolved from two electron pockets into a giant hole pocket. Angle-resolved photoelectron spectroscopy confirms these changes to be driven by electronic structure renormalizations rather than a rigid band shift. Our results open up the previously unreachable beyond-van-Hove regime in the phase diagram of epitaxial graphene, thereby accessing an unexplored landscape of potential exotic phases in this prototype two-dimensional material.

Phase Separation and Pairing Fluctuations in Oxide Materials

The microscopic mechanism of charge instabilities and the formation of inhomogeneous states in systems with strong electron correlations is investigated. We demonstrate that within a strong coupling expansion the single-band Hubbard model shows an instability towards phase separation and extend the approach also for an analysis of phase separation in the Hubbard-Kanamori hamiltonian as a prototypical multiband model. We study the pairing fluctuations on top of an inhomogeneous stripe state where superconducting correlations in the extended s-wave and d-wave channels correspond to (anti)bound states in the two-particle spectra. Whereas extended s-wave fluctuations are relevant on the scale of the local interaction parameter U, we find that d-wave fluctuations are pronounced in the energy range of the active subband which crosses the Fermi level. As a result, low energy spin and charge fluctuations can transfer the d-wave correlations from the bound states to the low energy quasiparticle bands. Our investigations therefore help to understand the coexistence of stripe correlations and d-wave superconductivity in cuprates.

Enhanced Electron-Phonon Coupling for Charge-Density-Wave Formation in La_{1.8-x}Eu_{0.2}Sr_{x}CuO_{4+δ}

Charge density wave (CDW) correlations are prevalent in all copper-oxide superconductors. While CDWs in conventional metals are driven by coupling between lattice vibrations and electrons, the role of the electron-phonon coupling (EPC) in cuprate CDWs is strongly debated. Using Cu L_{3} edge resonant inelastic x-ray scattering, we study the CDW and Cu-O bond-stretching phonons in the stripe-ordered cuprate La_{1.8-x}Eu_{0.2}Sr_{x}CuO_{4+δ}. We investigate the interplay between charge order and EPC as a function of doping and temperature and find that the EPC is enhanced in a narrow momentum region around the CDW ordering vector. By detuning the incident photon energy from the absorption resonance, we extract an EPC matrix element at the CDW ordering vector of M≃0.36  eV, which decreases to M≃0.30  eV at high temperature in the absence of the CDW. Our results suggest a feedback mechanism in which the CDW enhances the EPC which, in turn, further stabilizes the CDW.

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.

Tuning from failed superconductor to failed insulator with magnetic field

Do charge modulations compete with electron pairing in high-temperature copper oxide superconductors? We investigated this question by suppressing superconductivity in a stripe-ordered cuprate compound at low temperature with high magnetic fields. With increasing field, loss of three-dimensional superconducting order is followed by reentrant two-dimensional superconductivity and then an ultraquantum metal phase. Circumstantial evidence suggests that the latter state is bosonic and associated with the charge stripes. These results provide experimental support to the theoretical perspective that local segregation of doped holes and antiferromagnetic spin correlations underlies the electron-pairing mechanism in cuprates.

Disorder raises the critical temperature of a cuprate superconductor

With the discovery of charge-density waves (CDWs) in most members of the cuprate high-temperature superconductors, the interplay between superconductivity and CDWs has become a key point in the debate on the origin of high-temperature superconductivity. Some experiments in cuprates point toward a CDW state competing with superconductivity, but others raise the possibility of a CDW-superconductivity intertwined order or more elusive pair-density waves (PDWs). Here, we have used proton irradiation to induce disorder in crystals of [Formula: see text] and observed a striking 50% increase of [Formula: see text], accompanied by a suppression of the CDWs. This is in sharp contrast with the behavior expected of a d-wave superconductor, for which both magnetic and nonmagnetic defects should suppress [Formula: see text] Our results thus make an unambiguous case for the strong detrimental effect of the CDW on bulk superconductivity in [Formula: see text] Using tunnel diode oscillator (TDO) measurements, we find indications for potential dynamic layer decoupling in a PDW phase. Our results establish irradiation-induced disorder as a particularly relevant tuning parameter for the many families of superconductors with coexisting density waves, which we demonstrate on superconductors such as the dichalcogenides and [Formula: see text].

Phase diagram of Bi2Sr2CaCu2O8+δ revisited

In cuprate superconductors, the doping of carriers into the parent Mott insulator induces superconductivity and various other phases whose characteristic temperatures are typically plotted versus the doping level p. In most materials, p cannot be determined from the chemical composition, but it is derived from the superconducting transition temperature, Tc, using the assumption that the Tc dependence on doping is universal. Here, we present angle-resolved photoemission studies of Bi2Sr2CaCu2O8+δ, cleaved and annealed in vacuum or in ozone to reduce or increase the doping from the initial value corresponding to Tc = 91 K. We show that p can be determined from the underlying Fermi surfaces and that in-situ annealing allows mapping of a wide doping regime, covering the superconducting dome and the non-superconducting phase on the overdoped side. Our results show a surprisingly smooth dependence of the inferred Fermi surface with doping. In the highly overdoped regime, the superconducting gap approaches the value of 2Δ0 = (4 ± 1)kBTc.

A High Rigidity and Precision Scanning Tunneling Microscope with Decoupled XY and Z Scans

A new scan-head structure for the scanning tunneling microscope (STM) is proposed, featuring high scan precision and rigidity. The core structure consists of a piezoelectric tube scanner of quadrant type (for XY scans) coaxially housed in a piezoelectric tube with single inner and outer electrodes (for Z scan). They are fixed at one end (called common end). A hollow tantalum shaft is coaxially housed in the XY-scan tube and they are mutually fixed at both ends. When the XY scanner scans, its free end will bring the shaft to scan and the tip which is coaxially inserted in the shaft at the common end will scan a smaller area if the tip protrudes short enough from the common end. The decoupled XY and Z scans are desired for less image distortion and the mechanically reduced scan range has the superiority of reducing the impact of the background electronic noise on the scanner and enhancing the tip positioning precision. High quality atomic resolution images are also shown.

Complementary Response of Static Spin-Stripe Order and Superconductivity to Nonmagnetic Impurities in Cuprates

We report muon-spin rotation and neutron-scattering experiments on nonmagnetic Zn impurity effects on the static spin-stripe order and superconductivity of the La214 cuprates. Remarkably, it was found that, for samples with hole doping x≈1/8, the spin-stripe ordering temperature T_{so} decreases linearly with Zn doping y and disappears at y≈4%, demonstrating a high sensitivity of static spin-stripe order to impurities within a CuO_{2} plane. Moreover, T_{so} is suppressed by Zn in the same manner as the superconducting transition temperature T_{c} for samples near optimal hole doping. This surprisingly similar sensitivity suggests that the spin-stripe order is dependent on intertwining with superconducting correlations.

Remarkable Stability of Charge Density Wave Order in La_{1.875}Ba_{0.125}CuO_{4}

The occurrence of charge-density-wave (CDW) order in underdoped cuprates is now well established, although the precise nature of the CDW and its relationship with superconductivity is not. Theoretical proposals include contrasting ideas such as that pairing may be driven by CDW fluctuations or that static CDWs may intertwine with a spatially modulated superconducting wave function. We test the dynamics of CDW order in La_{1.825}Ba_{0.125}CuO_{4} by using x-ray photon correlation spectroscopy at the CDW wave vector, detected resonantly at the Cu L_{3} edge. We find that the CDW domains are strikingly static, with no evidence of significant fluctuations up to 2 ¾  h. We discuss the implications of these results for some of the competing theories.

Fermi arcs vs. Fermi pockets in electron-doped perovskite iridates

We report on an angle resolved photoemission (ARPES) study of bulk electron-doped perovskite iridate, (Sr_1−xLa_x)₃Ir₂O₇. Fermi surface pockets are observed with a total electron count in keeping with that expected from La substitution. Depending on the energy and polarization of the incident photons, these pockets show up in the form of disconnected “Fermi arcs”, reminiscent of those reported recently in surface electron-doped Sr₂IrO₄. Our observed spectral variation is consistent with the coexistence of an electronic supermodulation with structural distortion in the system.

Fluctuation Effects in Symmetric Diblock Copolymer-Homopolymer Ternary Mixtures near the Lamellar-Disorder Transition

We have systematically mapped the phase behavior of a series of symmetric CE/C/E ternary copolymer/homopolymer mixtures, where C is poly(cyclohexylethylene) and E is poly(ethylene), identifying the location in composition of the technologically important bicontinuous microemulsion (BμE) channel as a function of diblock molecular weight. The lamellar-to-disorder transition, characterized by dynamic mechanical spectroscopy, small-angle X-ray scattering, and optical transmission measurements, exhibits increasingly second-order behavior as the BμE state is approached with increasing homopolymer content. Real-space transmission electron microscopy images obtained from rapidly frozen specimens evidence the development of large-scale fluctuating smectic correlations in the disordered state as the order-disorder transition is approached. This discovery provides fresh insights into the unexplained role of fluctuations in the formation of the BμE in ternary mixtures formed from binary blends of homopolymers that display an Ising-like critical point and a symmetric diblock copolymer governed by a weak, fluctuation-induced, first-order phase transition.

Absence of a proximity effect for a thin-films of a Bi2Se3 topological insulator grown on top of a Bi2Sr2CaCu2O(8+δ) cuprate superconductor

Proximity-induced superconductivity in a 3D topological insulator represents a new avenue for observing zero-energy Majorana fermions inside vortex cores. Relatively small gaps and low transition temperatures of conventional s-wave superconductors put hard constraints on these experiments. Significantly larger gaps and higher transition temperatures in cuprate superconductors might be an attractive alternative to considerably relax these constraints, but it is not clear whether the proximity effect would be effective in heterostructures involving cuprates and topological insulators. Here, we present angle-resolved photoemission studies of thin Bi(2)Se(3) films grown in situ on optimally doped Bi(2)Sr(2)CaCu(2)O(8+δ) substrates that show the absence of proximity-induced gaps on the surfaces of Bi(2)Se(3) films as thin as a 1.5 quintuple layer. These results suggest that the superconducting proximity effect between a cuprate superconductor and a topological insulator is strongly suppressed, likely due to a very short coherence length along the c axis, incompatible crystal and pairing symmetries at the interface, small size of the topological surface state's Fermi surface, and adverse effects of a strong spin-orbit coupling in the topological material.

Negative oxygen isotope effect on the static spin stripe order in superconducting La(2-x)Ba(x)CuO(4) (x=1/8) observed by muon-spin rotation

Large negative oxygen-isotope (^{16}O and ^{18}O) effects (OIEs) on the static spin-stripe-ordering temperature T_{so} and the magnetic volume fraction V_{m} were observed in La_{2-x}Ba_{x}CuO_{4}(x=1/8) by means of muon-spin-rotation experiments. The corresponding OIE exponents were found to be α_{T_{so}}=-0.57(6) and α_{V_{m}}=-0.71(9), which are sign reversed to α_{T_{c}}=0.46(6) measured for the superconducting transition temperature T_{c}. This indicates that the electron-lattice interaction is involved in the stripe formation and plays an important role in the competition between bulk superconductivity and static stripe order in the cuprates.

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

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

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.

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.

Magneto-optical measurements of a cascade of transitions in superconducting La1.875Ba0.125CuO4 single crystals

Recent experiments on the original cuprate high-temperature superconductor, La(2-x)Ba(x)CuO4, revealed a remarkable sequence of phase transitions. Here we investigate such crystals with the polar Kerr effect, which is sensitive to time-reversal-symmetry breaking. Concurrent birefringence measurements accurately locate the structural phase transitions from high-temperature tetragonal to low-temperature orthorhombic, and then to lower-temperature tetragonal, at which temperature strong Kerr signal onsets. Hysteretic behavior of the Kerr signal suggests that time-reversal symmetry is already broken well above room temperature, an effect that was previously observed in high quality YBa2Cu3O(6+x) crystals.

Towards resolution of the Fermi surface in underdoped high-Tc superconductors

We survey recent experimental results including quantum oscillations and complementary measurements probing the electronic structure of underdoped cuprates, and theoretical proposals to explain them. We discuss quantum oscillations measured at high magnetic fields in the underdoped cuprates that reveal a small Fermi surface section, comprising quasiparticles that obey Fermi-Dirac statistics, unaccompanied by other states of comparable thermodynamic mass at the Fermi level. The location of the observed Fermi surface section at the nodes is indicated by a body of evidence including the collapse in Fermi velocity measured by quantum oscillations, which is found to be associated with the nodal density of states observed in angular resolved photoemission, the persistence of quantum oscillations down to low fields in the vortex state, the small value of density of states from heat capacity and the multiple frequency quantum oscillation pattern consistent with nodal magnetic breakdown of bilayer-split pockets. A nodal Fermi surface pocket is further consistent with the observation of a density of states at the Fermi level concentrated at the nodes in photoemission experiments, and the antinodal pseudogap observed by photoemission, optical conductivity, nuclear magnetic resonance (NMR) Knight shift, as well as other complementary diffraction, transport and thermodynamic measurements. One of the possibilities considered is that the small Fermi surface pockets observed at high magnetic fields can be understood in terms of Fermi surface reconstruction by a form of small wavevector charge order, observed over long lengthscales in experiments such as NMR and x-ray scattering, potentially accompanied by an additional mechanism to gap the antinodal density of states.

Unusual Nernst effect suggesting time-reversal violation in the striped cuprate superconductor La(2-x)Ba(x)CuO4

The striped cuprate La(2-x)Ba(x)CuO(4) (x=1/8) undergoes several transitions below the charge-ordering temperature T(co)=54  K. From Nernst experiments, we find that, below T(co), there exists a large, anomalous Nernst signal e(N,even)(H,T) that is symmetric in field H, and remains finite as H→0. The time-reversal violating signal suggests that, below T(co), vortices of one sign are spontaneously created to relieve interlayer phase frustration.

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.

Protected nodal electron pocket from multiple-Q ordering in underdoped high temperature superconductors

A multiple wave vector (Q) reconstruction of the Fermi surface is shown to yield a profoundly different electronic structure to that characteristic of single wave vector reconstruction, despite their proximity in energy. We consider the specific case in which ordering is generated by Q(x)=[2πa,0] and Q(y)=[0,2πb] (in which a=b=1/4)-similar to those identified in neutron diffraction and scanning tunneling microscopy experiments-and more generally show that an isolated pocket adjacent to the nodal point k(nodal)=[±π/2,±π/2] is a protected feature of such a multiple-Q model, potentially corresponding to the nodal "Fermi arcs" observed in photoemission and the small size of the electronic heat capacity found in high magnetic fields-importantly, containing electron carriers which can yield negative Hall and Seebeck coefficients observed in high magnetic fields.

Structural origin of apparent Fermi surface pockets in angle-resolved photoemission of Bi₂Sr(2-x)La(x)CuO(6+δ)

We observe apparent hole pockets in the Fermi surfaces of single-layer Bi-based cuprate superconductors from angle-resolved photoemission. From detailed low-energy electron diffraction measurements and an analysis of the angle-resolved photoemission polarization dependence, we show that these pockets are not intrinsic but arise from multiple overlapping superstructure replicas of the main and shadow bands. We further demonstrate that the hole pockets reported recently from angle-resolved photoemission [Meng et al., Nature (London) 462, 335 (2009)] have a similar structural origin and are inconsistent with an intrinsic hole pocket associated with the electronic structure of a doped CuO₂ plane.

Polar nanodomains and giant converse magnetoelectric effect in charge-ordered Fe2OBO3

The magnetoelectric coupling and polar nanodomains in the charge-ordered Fe2OBO3 have been extensively studied from room temperature down to 100 K. In situ TEM investigations demonstrate that the charge-ordering transition characterized by an incommensurate modulation could evidently result in remarkable polar nanodomains at low temperatures. This kind of nanodomain could play a critical role in triggering a high dielectric constant and notable dielectric dispersion as observed in Fe2OBO3. Moreover, measurements of the magnetoelectric coupling under electrical field demonstrate the existence of giant electrically induced changes in magnetization around the magnetic transition.

Superconductivity in strongly repulsive fermions: the role of kinetic-energy frustration

We discuss a physical mechanism of a non-BCS nature which can stabilize a superconducting state in a strongly repulsive electronic system. By considering the two-dimensional Hubbard model with spatially modulated electron hoppings, we demonstrate how kinetic-energy frustration can lead to robust d-wave superconductivity at arbitrarily large on-site repulsion. This phenomenon should be observable in experiments using fermionic atoms, e.g. 40K, in specially prepared optical lattices.

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.

Effects of thermal phase fluctuations in a two-dimensional superconductor: an exact result for the spectral function

We consider the single particle spectral function for a two-dimensional clean superconductor in a regime of strong critical thermal phase fluctuations. In the limit where the maximum of the superconducting gap is much smaller than the Fermi energy we obtain an exact expression for the spectral function integrated over the momentum component perpendicular to the Fermi surface.

Dynamic cluster quantum Monte Carlo simulations of a two-dimensional Hubbard model with stripelike charge-density-wave modulations: interplay between inhomogeneities and the superconducting state

Using dynamic cluster quantum Monte Carlo simulations, we study the superconducting behavior of a 1/8 doped two-dimensional Hubbard model with imposed unidirectional stripelike charge-density-wave modulation. We find a significant increase of the pairing correlations and critical temperature relative to the homogeneous system when the modulation length scale is sufficiently large. With a separable form of the irreducible particle-particle vertex, we show that optimized superconductivity is obtained for a moderate modulation strength due to a delicate balance between the modulation enhanced pairing interaction, and a concomitant suppression of the bare particle-particle excitations by a modulation reduction of the quasiparticle weight.

Towards a two-dimensional superconducting state of La(2-x)Sr(x)CuO4 in a moderate external magnetic field

We report a novel aspect of the competition and coexistence between magnetism and superconductivity in the high-T(c) cuprate La(2-x)Sr(x)CuO4 (La214). With a modest magnetic field applied H parallel c axis, we monitored the infrared signature of pair tunneling between the CuO2 planes and discovered the complete suppression of interlayer coupling in a series of underdoped La214 single crystals. We find that the in-plane superconducting properties remain intact, in spite of enhanced magnetism in the planes.

Spectral and optical properties in the antiphase stripe phase of the cuprate superconductors

We investigate the superconducting order parameter, the spectral and optical properties in a stripe model with spin-(charge-) domain-derived scattering potential V(s) (V(c)). We show that the charge-domain-derived scattering is less effective than the spin scattering on the suppression of superconductivity. For [Formula: see text], the spectral weight concentrates on the (π,0) antinodal region and a finite energy peak appears in the optical conductivity with the disappearance of the Drude peak. But for V(s)≈V(c), the spectral weight concentrates on the (π/2,π/2) nodal region and a residual Drude peak exists in the optical conductivity without the finite energy peak. These results consistently account for the divergent observations in the ARPES and optical conductivity experiments in several high- T(c) cuprates and suggest that the 'insulating' and 'metallic' properties are intrinsic to the stripe state, depending on the relative strength of the spin- and charge-domain-derived scattering potentials.

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.

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.

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.

Temperature dependence of the gap size near the brillouin-zone nodes of HgBa2CuO4+delta superconductors

Although more than 20 years have passed, the identification of the superconducting order parameter in cuprates is still under debate. Here, we show that the gap size near the nodes is a good candidate for the order parameter: it scales with the critical temperature Tc over a wide doping range and displays a significant temperature dependence below Tc in both the underdoped and the overdoped regimes. In contrast, the gap size at the antinodes does not scale with Tc in the underdoped regime and appears to be controlled by the pseudogap which persists below Tc.

Enhancement of the superconducting transition temperature of La2-xSrxCuO4 bilayers: role of pairing and phase stiffness

The superconducting transition temperature T(c) of bilayers comprising underdoped La(2-x)Sr(x)CuO(4) films capped by a thin heavily overdoped metallic La(1.65)Sr(0.35)CuO(4) layer, is found to increase with respect to T(c) of the bare underdoped films. The highest T(c) is achieved for x=0.12, close to the "anomalous" 1/8 doping level, and exceeds that of the optimally doped bare film. Our data suggest that the enhanced superconductivity is confined to the interface between the layers. We attribute the effect to a combination of the high pairing scale in the underdoped layer with an enhanced phase stiffness induced by the overdoped film.

Dynamical layer decoupling in a stripe-ordered high-T(c) superconductor

In the stripe-ordered state of a strongly correlated two-dimensional electronic system, under a set of special circumstances, the superconducting condensate, like the magnetic order, can occur at a nonzero wave vector corresponding to a spatial period double that of the charge order. In this case, the Josephson coupling between near neighbor planes, especially in a crystal with the special structure of La(2-x)Ba(x)CuO(4), vanishes identically. We propose that this is the underlying cause of the dynamical decoupling of the layers recently observed in transport measurements at x = 1/8.

Charge order superstructure with integer iron valence in Fe(2)OBO(3)

Solution-grown single crystals of Fe(2)OBO(3) were characterized by specific heat, Mössbauer spectroscopy, and x-ray diffraction. A peak in the specific heat at 340 K indicates the onset of charge order. Evidence for a doubling of the unit cell at low temperature is presented. Combining structural refinement of diffraction data and Mössbauer spectra, domains with diagonal charge order are established. Bond-valence-sum analysis indicates integer valence states of the Fe ions in the charge ordered phase, suggesting Fe(2)OBO(3) is the clearest example of ionic charge order so far.