Coexistence of periodic modulation of quasiparticle states and superconductivity in Bi2Sr2CaCu2O8+delta

Tunable Non-Fermi Liquid Phase from Coupling to Two-Level Systems

We study a controlled large-N theory of electrons coupled to dynamical two-level systems (TLSs) via spatially random interactions. Such a physical situation arises when electrons scatter off low-energy excitations in a metallic glass, such as a charge or stripe glass. Our theory is governed by a non-Gaussian saddle point, which maps to the celebrated spin-boson model. By tuning the coupling strength we find that the model crosses over from a Fermi liquid at weak coupling to an extended region of non-Fermi liquid behavior at strong coupling, and realizes a marginal Fermi liquid at the crossover. Our results are valid for generic space dimensions d>1.

Universal Stripe Symmetry of Short-Range Charge Density Waves in Cuprate Superconductors

The omnipresence of charge density waves (CDWs) across almost all cuprate families underpins a common organizing principle. However, a longstanding debate of whether its spatial symmetry is stripe or checkerboard remains unresolved. While CDWs in lanthanum- and yttrium-based cuprates possess a stripe symmetry, distinguishing these two scenarios is challenging for the short-range CDW in bismuth-based cuprates. Here, high-resolution resonant inelastic x-ray scattering is employed to uncover the spatial symmetry of the CDW in Bi2 Sr2 - x Lax CuO6 + δ . Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes are found in reciprocal space. Based on Fourier transform analysis of real-space models, the results are interpreted as evidence of unidirectional charge stripes, hosted by mutually 90°-rotated anisotropic domains. This work paves the way for a unified symmetry and microscopic description of CDW order in cuprates.

Critical nematic correlations throughout the superconducting doping range in Bi2-zPbzSr2-yLayCuO6+x

Charge modulations have been widely observed in cuprates, suggesting their centrality for understanding the high-T_c superconductivity in these materials. However, the dimensionality of these modulations remains controversial, including whether their wavevector is unidirectional or bidirectional, and also whether they extend seamlessly from the surface of the material into the bulk. Material disorder presents severe challenges to understanding the charge modulations through bulk scattering techniques. We use a local technique, scanning tunneling microscopy, to image the static charge modulations on Bi_2-zPb_zSr_2-yLa_yCuO_6+x. The ratio of the phase correlation length ξ_CDW to the orientation correlation length ξ_orient points to unidirectional charge modulations. By computing new critical exponents at free surfaces including that of the pair connectivity correlation function, we show that these locally 1D charge modulations are actually a bulk effect resulting from classical 3D criticality of the random field Ising model throughout the entire superconducting doping range.

Stabilization of three-dimensional charge order through interplanar orbital hybridization in PrxY1-xBa2Cu3O6+δ

The shape of 3d-orbitals often governs the electronic and magnetic properties of correlated transition metal oxides. In the superconducting cuprates, the planar confinement of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${d}_{{x}^{2}-{y}^{2}}$$\end{document}dx2−y2 orbital dictates the two-dimensional nature of the unconventional superconductivity and a competing charge order. Achieving orbital-specific control of the electronic structure to allow coupling pathways across adjacent planes would enable direct assessment of the role of dimensionality in the intertwined orders. Using Cu L₃ and Pr M₅ resonant x-ray scattering and first-principles calculations, we report a highly correlated three-dimensional charge order in Pr-substituted YBa₂Cu₃O₇, where the Pr f-electrons create a direct orbital bridge between CuO₂ planes. With this we demonstrate that interplanar orbital engineering can be used to surgically control electronic phases in correlated oxides and other layered materials.

External perturbations can induce 3D charge order in cuprates, but the 3D correlation length is limited and the mechanism is not well understood. Ruiz et al. show that Pr substitution in YBa₂Cu₃O₇ enhances interplanar orbital coupling and stabilizes coherent 3D charge order that coexists with superconductivity.

Enhanced charge density wave coherence in a light-quenched, high-temperature superconductor

Superconductivity and charge density waves (CDWs) are competitive, yet coexisting, orders in cuprate superconductors. To understand their microscopic interdependence, a probe capable of discerning their interaction on its natural length and time scale is necessary. We use ultrafast resonant soft x-ray scattering to track the transient evolution of CDW correlations in YBa₂Cu₃O_6+x after the quench of superconductivity by an infrared laser pulse. We observe a nonthermal response of the CDW order characterized by a near doubling of the correlation length within ≈1 picosecond of the superconducting quench. Our results are consistent with a model in which the interaction between superconductivity and CDWs manifests inhomogeneously through disruption of spatial coherence, with superconductivity playing the dominant role in stabilizing CDW topological defects, such as discommensurations.

Anisotropic gapping of topological Weyl rings in the charge-density-wave superconductor InxTaSe2

Topological materials and topological phases have recently become a hot topic in condensed matter physics. In this work, we report an In-intercalated transition-metal dichalcogenide In_xTaSe₂ (named 112 system), a topological nodal-line semimetal in the presence of both charge density wave (CDW) and superconductivity. In the x = 0.58 sample, the 2×3 commensurate CDW (CCDW) and the 2×2 CCDW are observed below 116 and 77 K, respectively. Consistent with theoretical calculations, the spin-orbital coupling gives rise to two twofold-degenerate nodal rings (Weyl rings) connected by drumhead surface states, confirmed by angle-resolved photoemission spectroscopy. Our results suggest that the 2×2 CCDW ordering gaps out one Weyl ring in accordance with the CDW band folding, while the other Weyl ring remains gapless with intact surface states. In addition, superconductivity emerges at 0.91 K, with the upper critical field deviating from the s-wave behavior at low temperature, implying possibly unconventional superconductivity. Therefore, we think this type of the 112 system may possess abundant physical states and offer a platform to investigate the interplay between CDW, nontrivial band topology and superconductivity.

Charge ordering in high-temperature superconductors visualized by scanning tunneling microscopy

Since the discovery of stripe order in La_1.6-x Nd_0.4Sr _x CuO₄ superconductors in 1995, charge ordering in cuprate superconductors has been intensively studied by various experimental techniques. Among these studies, scanning tunneling microscope (STM) plays an irreplaceable role in determining the real space structures of charge ordering. STM imaging of different families of cuprates over a wide range of doping levels reveal similar checkerboard-like patterns, indicating that such a charge ordered state is likely a ubiquitous and intrinsic characteristic of cuprate superconductors, which may shed light on understanding the mechanism of high-temperature superconductivity. In another class of high-temperature superconductors, iron-based superconductors, STM studies reveal several charge ordered states as well, but their real-space patterns and the interplay with superconductivity are markedly different among different materials. In this paper, we present a brief review on STM studies of charge ordering in these two classes of high-temperature superconductors. Possible origins of charge ordering and its interplay with superconductivity will be discussed.

Charge-stripe crystal phase in an insulating cuprate

High-temperature (high-T_c) superconductivity in cuprates arises from carrier doping of an antiferromagnetic Mott insulator. This carrier doping leads to the formation of electronic liquid-crystal phases¹. The insulating charge-stripe crystal phase is predicted to form when a small density of holes is doped into the charge-transfer insulator state^1-3, but this phase is yet to be observed experimentally. Here, we use surface annealing to extend the accessible doping range in Bi-based cuprates and realize the lightly doped charge-transfer insulating state of the cuprate Bi₂Sr₂CaCu₂O_8+x. In this insulating state with a charge transfer gap on the order of ~1 eV, our spectroscopic imaging scanning tunnelling microscopy measurements provide strong evidence for a unidirectional charge-stripe order with a commensurate 4a₀ period along the Cu-O-Cu bond. Notably, this insulating charge-stripe crystal phase develops before the onset of the pseudogap and formation of the Fermi surface. Our work provides fresh insight into the microscopic origin of electronic inhomogeneity in high-T_c cuprates.

A tale of two metals: contrasting criticalities in the pnictides and hole-doped cuprates

The iron-based high temperature superconductors share a number of similarities with their copper-based counterparts, such as reduced dimensionality, proximity to states of competing order, and a critical role for 3d electron orbitals. Their respective temperature-doping phase diagrams also contain certain commonalities that have led to claims that the metallic and superconducting (SC) properties of both families are governed by their proximity to a quantum critical point (QCP) located inside the SC dome. In this review, we critically examine these claims and highlight significant differences in the bulk physical properties of both systems. While there is now a large body of evidence supporting the presence of a (magnetic) QCP in the iron pnictides, the situation in the cuprates is much less apparent, at least for the end point of the pseudogap phase. We argue that the opening of the normal state pseudogap in cuprates, so often tied to a putative QCP, arises from a momentum-dependent breakdown of quasiparticle coherence that sets in at much higher doping levels but which is driven by the proximity to the Mott insulating state at half filling. Finally, we present a new scenario for the cuprates in which this loss of quasiparticle integrity and its evolution with momentum, temperature and doping plays a key role in shaping the resultant phase diagram.

Stripe and Short Range Order in the Charge Density Wave of 1T-Cu_{x}TiSe_{2}

We study the impact of Cu intercalation on the charge density wave (CDW) in 1T-Cu_{x}TiSe_{2} by scanning tunneling microscopy and spectroscopy. Cu atoms, identified through density functional theory modeling, are found to intercalate randomly on the octahedral site in the van der Waals gap and to dope delocalized electrons near the Fermi level. While the CDW modulation period does not depend on Cu content, we observe the formation of charge stripe domains at low Cu content (x<0.02) and a breaking up of the commensurate order into 2×2 domains at higher Cu content. The latter shrink with increasing Cu concentration and tend to be phase shifted. These findings invalidate a proposed excitonic pairing as the primary CDW formation mechanism in this material.

The rate of quasiparticle recombination probes the onset of coherence in cuprate superconductors

In the underdoped copper-oxides, high-temperature superconductivity condenses from a nonconventional metallic ”pseudogap” phase that exhibits a variety of non-Fermi liquid properties. Recently, it has become clear that a charge density wave (CDW) phase exists within the pseudogap regime. This CDW coexists and competes with superconductivity (SC) below the transition temperature T_c, suggesting that these two orders are intimately related. Here we show that the condensation of the superfluid from this unconventional precursor is reflected in deviations from the predictions of BSC theory regarding the recombination rate of quasiparticles. We report a detailed investigation of the quasiparticle (QP) recombination lifetime, τ_qp, as a function of temperature and magnetic field in underdoped HgBa₂CuO_4+δ (Hg-1201) and YBa₂Cu₃O_6+x (YBCO) single crystals by ultrafast time-resolved reflectivity. We find that τ_qp(T ) exhibits a local maximum in a small temperature window near T_c that is prominent in underdoped samples with coexisting charge order and vanishes with application of a small magnetic field. We explain this unusual, non-BCS behavior by positing that T_c marks a transition from phase-fluctuating SC/CDW composite order above to a SC/CDW condensate below. Our results suggest that the superfluid in underdoped cuprates is a condensate of coherently-mixed particle-particle and particle-hole pairs.

Observation of a three-dimensional quasi-long-range electronic supermodulation in YBa2Cu3O(7-x)/La0.7Ca0.3MnO3 heterostructures

Recent developments in high-temperature superconductivity highlight a generic tendency of the cuprates to develop competing electronic (charge) supermodulations. While coupled with the lattice and showing different characteristics in different materials, these supermodulations themselves are generally conceived to be quasi-two-dimensional, residing mainly in individual CuO₂ planes, and poorly correlated along the c axis. Here we observed with resonant elastic X-ray scattering a distinct type of electronic supermodulation in YBa₂Cu₃O_7−x (YBCO) thin films grown epitaxially on La_0.7Ca_0.3MnO₃ (LCMO). This supermodulation has a periodicity nearly commensurate with four lattice constants in-plane, eight out of plane, with long correlation lengths in three dimensions. It sets in far above the superconducting transition temperature and competes with superconductivity below this temperature for electronic states predominantly in the CuO₂ plane. Our finding sheds light on the nature of charge ordering in cuprates as well as a reported long-range proximity effect between superconductivity and ferromagnetism in YBCO/LCMO heterostructures.

Understanding the nature of competing phases is a key to understanding the superconducting mechanism of unconventional superconductors. Here, the authors demonstrate a three-dimensional charge ordering state which competes with superconductivity in epitaxial YBa₂Cu₃O_7-x thin films grown on La_0.7Ca_0.3MnO₃ substrates.

Three-dimensional charge density wave order in YBa2Cu3O6.67 at high magnetic fields

Charge density wave (CDW) correlations have been shown to universally exist in cuprate superconductors. However, their nature at high fields inferred from nuclear magnetic resonance is distinct from that measured with x-ray scattering at zero and low fields. We combined a pulsed magnet with an x-ray free-electron laser to characterize the CDW in YBa2Cu3O6.67 via x-ray scattering in fields of up to 28 tesla. While the zero-field CDW order, which develops at temperatures below ~150 kelvin, is essentially two dimensional, at lower temperature and beyond 15 tesla, another three-dimensionally ordered CDW emerges. The field-induced CDW appears around the zero-field superconducting transition temperature; in contrast, the incommensurate in-plane ordering vector is field-independent. This implies that the two forms of CDW and high-temperature superconductivity are intimately linked.

Stripe-like nanoscale structural phase separation in superconducting BaPb(1-x)Bi(x)O3

The phase diagram of BaPb(1-x)Bi(x)O3 exhibits a superconducting dome in the proximity of a charge density wave phase. For the superconducting compositions, the material coexists as two structural polymorphs. Here we show, via high-resolution transmission electron microscopy, that the structural dimorphism is accommodated in the form of partially disordered nanoscale stripes. Identification of the morphology of the nanoscale structural phase separation enables determination of the associated length scales, which we compare with the Ginzburg-Landau coherence length. We find that the maximum Tc occurs when the superconducting coherence length matches the width of the partially disordered stripes, implying a connection between the structural phase separation and the shape of the superconducting dome.

Andreev-Bragg Reflection from an Amperian Superconductor

We show how an electrical measurement can detect the pairing of electrons on the same side of the Fermi surface (Amperian pairing), recently proposed by Patrick Lee for the pseudogap phase of high-Tc cuprate superconductors. Bragg scattering from the pair-density wave introduces odd multiples of 2k(F) momentum shifts when an electron incident from a normal metal is Andreev reflected as a hole. These Andreev-Bragg reflections can be detected in a three-terminal device, containing a ballistic Y junction between normal leads (1, 2) and the superconductor. The cross-conductance dI1/dV2 has the opposite sign for Amperian pairing than it has either in the normal state or for the usual BCS pairing.

Symmetry of charge order in cuprates

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

Superconductivity. Broken translational and rotational symmetry via charge stripe order in underdoped YBa₂Cu₃O(6+y)

After the discovery of stripelike order in lanthanum-based copper oxide superconductors, charge-ordering instabilities were observed in all cuprate families. However, it has proven difficult to distinguish between unidirectional (stripes) and bidirectional (checkerboard) charge order in yttrium- and bismuth-based materials. We used resonant x-ray scattering to measure the two-dimensional structure factor in the superconductor YBa2Cu3O(6+y) in reciprocal space. Our data reveal the presence of charge stripe order (i.e., locally unidirectional density waves), which may represent the true microscopic nature of charge modulation in cuprates. At the same time, we find that the well-established competition between charge order and superconductivity is stronger for charge correlations across the stripes than along them, which provides additional evidence for the intrinsic unidirectional nature of the charge order.

From quantum matter to high-temperature superconductivity in copper oxides

The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.

Charge order driven by Fermi-arc instability in Bi2Sr(2-x)La(x)CuO(6+δ)

The understanding of the origin of superconductivity in cuprates has been hindered by the apparent diversity of intertwining electronic orders in these materials. We combined resonant x-ray scattering (REXS), scanning-tunneling microscopy (STM), and angle-resolved photoemission spectroscopy (ARPES) to observe a charge order that appears consistently in surface and bulk, and in momentum and real space within one cuprate family, Bi2Sr(2-x)La(x)CuO(6+δ). The observed wave vectors rule out simple antinodal nesting in the single-particle limit but match well with a phenomenological model of a many-body instability of the Fermi arcs. Combined with earlier observations of electronic order in other cuprate families, these findings suggest the existence of a generic charge-ordered state in underdoped cuprates and uncover its intimate connection to the pseudogap regime.

Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates

Besides superconductivity, copper-oxide high-temperature superconductors are susceptible to other types of ordering. We used scanning tunneling microscopy and resonant elastic x-ray scattering measurements to establish the formation of charge ordering in the high-temperature superconductor Bi2Sr2CaCu2O(8+x). Depending on the hole concentration, the charge ordering in this system occurs with the same period as those found in Y-based or La-based cuprates and displays the analogous competition with superconductivity. These results indicate the similarity of charge organization competing with superconductivity across different families of cuprates. We observed this charge ordering to leave a distinct electron-hole asymmetric signature (and a broad resonance centered at +20 milli-electron volts) in spectroscopic measurements, indicating that it is likely related to the organization of holes in a doped Mott insulator.

Surface-enhanced charge-density-wave instability in underdoped Bi2Sr(2-x)La(x)CuO(6+δ)

Neutron and X-ray scattering experiments have provided mounting evidence for spin and charge ordering phenomena in underdoped cuprates. These range from early work on stripe correlations in Nd-LSCO to the latest discovery of charge-density-waves in YBa2Cu3O(6+x). Both phenomena are characterized by a pronounced dependence on doping, temperature and an externally applied magnetic field. Here, we show that these electron-lattice instabilities exhibit also a previously unrecognized bulk-surface dichotomy. Surface-sensitive electronic and structural probes uncover a temperature-dependent evolution of the CuO2 plane band dispersion and apparent Fermi pockets in underdoped Bi2 Sr(2-x) La(x) CuO(6+δ) (Bi2201), which is directly associated with an hitherto-undetected strong temperature dependence of the incommensurate superstructure periodicity below 130 K. In stark contrast, the structural modulation revealed by bulk-sensitive probes is temperature-independent. These findings point to a surface-enhanced incipient charge-density-wave instability, driven by Fermi surface nesting. This discovery is of critical importance in the interpretation of single-particle spectroscopy data, and establishes the surface of cuprates and other complex oxides as a rich playground for the study of electronically soft phases.

Scanning tunnelling microscopy imaging of symmetry-breaking structural distortion in the bismuth-based cuprate superconductors

A complicating factor in unravelling the theory of high-temperature (high-T(c)) superconductivity is the presence of a 'pseudogap' in the density of states, the origin of which has been debated since its discovery. Some believe the pseudogap is a broken symmetry state distinct from superconductivity, whereas others believe it arises from short-range correlations without symmetry breaking. A number of broken symmetries have been imaged and identified with the pseudogap state, but it remains crucial to disentangle any electronic symmetry breaking from the pre-existing structural symmetry of the crystal. We use scanning tunnelling microscopy to observe an orthorhombic structural distortion across the cuprate superconducting Bi(2)Sr(2)Ca(n-1)Cu(n)O(2n+4+x) (BSCCO) family tree, which breaks two-dimensional inversion symmetry in the surface BiO layer. Although this inversion-symmetry-breaking structure can impact electronic measurements, we show from its insensitivity to temperature, magnetic field and doping, that it cannot be the long-sought pseudogap state. To detect this picometre-scale variation in lattice structure, we have implemented a new algorithm that will serve as a powerful tool in the search for broken symmetry electronic states in cuprates, as well as in other materials.

Method for detecting superconducting stripes in high-temperature superconductors based on nonlinear resistivity measurements

We theoretically study the effect that stripelike superconducting inclusions would have on the nonlinear resistivity in single crystals. Even if the stripe orientation varies throughout the sample between two orthogonal directions due to twinning, we predict that there should be a universal dependence of the nonlinear resistivity on the angle between the applied current and the crystal axes. This prediction can be used to test the existence of superconducting stripes at and above the superconducting transition temperature in cuprate superconductors.

Optical nonreciprocity in magnetic structures related to high-Tc superconductors

Rotation of the plane of polarization of reflected light (Kerr effect) is a direct manifestation of broken time-reversal symmetry and is generally associated with the appearance of a ferromagnetic moment. Here I identify magnetic structures that may arise within the unit cell of cuprate superconductors that generate polarization rotation despite the absence of a net moment. For these magnetic symmetries the Kerr effect is mediated by magnetoelectric coupling, which can arise when antiferromagnetic order breaks inversion symmetry. The structures identified are candidates for a time-reversal breaking phase in the pseudogap regime of the cuprates.

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.

Fluctuating stripes at the onset of the pseudogap in the high-T(c) superconductor Bi(2)Sr(2)CaCu(2)O(8+x)

Doped Mott insulators have a strong propensity to form patterns of holes and spins often referred to as stripes. In copper oxides, doping also gives rise to the pseudogap state, which can be transformed into a high-temperature superconducting state with sufficient doping or by reducing the temperature. A long-standing issue has been the interplay between the pseudogap, which is generic to all hole-doped copper oxide superconductors, and stripes, whose static form occurs in only one family of copper oxides over a narrow range of the phase diagram. Here we report observations of the spatial reorganization of electronic states with the onset of the pseudogap state in the high-temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+x), using spectroscopic mapping with a scanning tunnelling microscope. We find that the onset of the pseudogap phase coincides with the appearance of electronic patterns that have the predicted characteristics of fluctuating stripes. As expected, the stripe patterns are strongest when the hole concentration in the CuO(2) planes is close to 1/8 (per copper atom). Although they demonstrate that the fluctuating stripes emerge with the onset of the pseudogap state and occur over a large part of the phase diagram, our experiments indicate that the stripes are a consequence of pseudogap behaviour rather than its cause.

Electron cotunneling into a Kondo lattice

Motivated by recent experimental interest in tunneling into heavy-electron materials, we present a theory for electron tunneling into a Kondo lattice. The passage of an electron into a Kondo lattice is accompanied by a simultaneous spin flip of the localized moments via cotunneling mechanism. We compute the tunneling current with the large-N mean field theory. In the absence of disorder, differential tunneling conductance exhibits two peaks separated by the hybridization gap. Disorder effects lead to the smearing of the gap resulting in a Fano line shape.

Gap-inhomogeneity-induced electronic states in superconducting Bi2Sr2CaCu2O(8+delta)

In this Letter, we analyze, using scanning tunneling spectroscopy, the density of electronic states in nearly optimally doped Bi2Sr2CaCu2O(8+delta) in zero magnetic field. Focusing on the superconducting gap, we find patches of what appear to be two different phases in a background of some average gap, one with a relatively small gap and sharp large coherence peaks and one characterized by a large gap with broad weak coherence peaks. We compare these spectra with calculations of the local density of states for a simple phenomenological model in which a 2xi0 x 2xi0 patch with an enhanced or suppressed d-wave gap amplitude is embedded in a region with a uniform average d-wave gap.