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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$_{2-z}$Pb$_z$Sr$_{2-y}$La$_y$CuO$_{6+x}$. By comparing the phase correlation length $\xi_{\mathrm{CDW}}$ with the orientation correlation length $\xi_{\mathrm{orient}}$, we show that the charge modulations are more consistent with an underlying unidirectional wave vector. Using cluster techniques, we show that these locally 1D charge modulations are actually a bulk effect resulting from 3D criticality throughout the entire superconducting doping range.

Ever since the discovery of graphene and subsequent explosion of interest in single atom thick materials, studying their mechanical properties has been an active area of research. New length scales often necessitate a rethinking of physical laws, making such studies crucial for understanding and ultimately utilizing novel material properties. Here we report on the investigation of nanoscale periodic ripples in suspended, single layer graphene sheets by scanning tunneling microscopy and atomistic scale simulations. Unlike the sinusoidal ripples found in classical fabrics, we find that graphene forms triangular ripples, where bending is limited to a narrow region on the order of a few unit cell dimensions at the apex of each ripple. This non-classical bending profile results in graphene behaving like a bizarre fabric, which regardless of how it is draped, always buckles at the same angle. Investigating the origin of such non-classical mechanical properties, we find that unlike a thin classical fabric, both in-plane and out-of-plane deformations occur in a graphene sheet. These two modes of deformation compete with each other, resulting in a strain-locked optimal buckling configuration when draped. Electronically, we see that this in-plane deformation generates pseudo electric fields creating a ~3 nm wide pnp heterojunction purely by strain modulation., Comment: 34 pages, 5 figures and supplementary section

Strain engineering of graphene takes advantage of one of the most dramatic responses of Dirac electrons enabling their manipulation via strain-induced pseudo-magnetic fields. Numerous theoretically proposed devices, such as resonant cavities and valley filters, as well as novel phenomena, such as snake states, could potentially be enabled via this effect. These proposals, however, require strong, spatially oscillating magnetic fields while to date only the generation and effects of pseudo-gauge fields which vary at a length scale much larger than the magnetic length have been reported. Here we create a periodic pseudo-gauge field profile using periodic strain that varies at the length scale comparable to the magnetic length and study its effects on Dirac electrons. A periodic strain profile is achieved by pulling on graphene with extreme (>10%) strain and forming nanoscale ripples, akin to a plastic wrap pulled taut at its edges. Combining scanning tunneling microscopy and atomistic calculations, we find that spatially oscillating strain results in a new quantization different from the familiar Landau quantization observed in previous studies. We also find that graphene ripples are characterized by large variations in carbon-carbon bond length, directly impacting the electronic coupling between atoms, which within a single ripple can be as different as in two different materials. The result is a single graphene sheet that effectively acts as an electronic superlattice. Our results thus also establish a novel approach to synthesize an effective 2D lateral heterostructure - by periodic modulation of lattice strain., Comment: 18 pages, 5 figures and supplementary information

We use scanning tunneling microscopy (STM) to study magnetic Fe impurities intentionally doped into the high-temperature superconductor Bi$_{2}$Sr$_{2}$Ca$_{2}$CuO$_{8+\delta}$. Our spectroscopic measurements reveal that Fe impurities introduce low-lying resonances in the density of states at \Omega$_{1}$ $\approx$ 4meV and \Omega$_{2}$ $\approx$ 15 meV allowing us to determine that, despite having a large magnetic moment, potential scattering of quasiparticles by Fe impurities dominates magnetic scattering. In addition, using high-resolution spatial characterizations of the local density of states near and away from Fe impurities, we detail the spatial extent of impurity affected regions as well as provide a local view of impurity-induced effects on the superconducting and pseudogap states. Our studies of Fe impurities, when combined with a reinterpretation of earlier STM work in the context of a two-gap scenario, allow us to present a unified view of the atomic-scale effects of elemental impurities on the pseudogap and superconducting states in hole-doped cuprates; this may help resolve a previously assumed dichotomy between the effects of magnetic and non-magnetic impurities in these materials.

The unclear relationship between cuprate superconductivity and the pseudogap state remains an impediment to understanding the high transition temperature (Tc) superconducting mechanism. Here we employ magnetic-field-dependent scanning tunneling microscopy to provide phase-sensitive proof that d-wave superconductivity coexists with the pseudogap on the antinodal Fermi surface of an overdoped cuprate. Furthermore, by tracking the hole doping (p) dependence of the quasiparticle interference pattern within a single Bi-based cuprate family, we observe a Fermi surface reconstruction slightly below optimal doping, indicating a zero-field quantum phase transition in notable proximity to the maximum superconducting Tc. Surprisingly, this major reorganization of the system's underlying electronic structure has no effect on the smoothly evolving pseudogap., Comment: For higher-resolution figures, please see the published version

The competition between proximate electronic phases produces a complex phenomenology in strongly correlated systems. In particular, fluctuations associated with periodic charge or spin modulations, known as density waves, may lead to exotic superconductivity in several correlated materials. However, density waves have been difficult to isolate in the presence of chemical disorder, and the suspected causal link between competing density wave orders and high temperature superconductivity is not understood. Here we use scanning tunneling microscopy to image a previously unknown unidirectional (stripe) charge density wave (CDW) smoothly interfacing with the familiar tri-directional (triangular) CDW on the surface of the stoichiometric superconductor NbSe$_2$. Our low temperature measurements rule out thermal fluctuations, and point to local strain as the tuning parameter for this quantum phase transition. We use this discovery to resolve two longstanding debates about the anomalous spectroscopic gap and the role of Fermi surface nesting in the CDW phase of NbSe$_2$. Our results highlight the importance of local strain in governing phase transitions and competing phenomena, and suggest a new direction of inquiry for resolving similarly longstanding debates in cuprate superconductors and other strongly correlated materials., Comment: PNAS in press

A complicating factor in unraveling the theory of high-temperature (high-Tc) superconductivity is the presence of a "pseudogap" in the density of states, whose origin has been debated since its discovery [1]. Some believe the pseudogap is a broken symmetry state distinct from superconductivity [2-4], while others believe it arises from short-range correlations without symmetry breaking [5,6]. A number of broken symmetries have been imaged and identified with the pseudogap state [7,8], but it remains crucial to disentangle any electronic symmetry breaking from pre-existing structural symmetry of the crystal. We use scanning tunneling microscopy (STM) to observe an orthorhombic structural distortion across the cuprate superconducting Bi2Sr2Can-1CunO2n+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 picometer-scale variation in lattice structure, we have implemented a new algorithm which will serve as a powerful tool in the search for broken symmetry electronic states in cuprates, as well as in other materials., Comment: 4 figures

Particle-wave duality suggests we think of electrons as waves stretched across a sample, with wavevector k proportional to their momentum. Their arrangement in "k-space," and in particular the shape of the Fermi surface, where the highest energy electrons of the system reside, determine many material properties. Here we use a novel extension of Fourier transform scanning tunneling microscopy to probe the Fermi surface of the strongly inhomogeneous Bi-based cuprate superconductors. Surprisingly, we find that rather than being globally defined, the Fermi surface changes on nanometer length scales. Just as shifting tide lines expose variations of water height, changing Fermi surfaces indicate strong local doping variations. This discovery, unprecedented in any material, paves the way for an understanding of other inhomogeneous characteristics of the cuprates, like the pseudogap magnitude, and highlights a new approach to the study of nanoscale inhomogeneity in general.

The discovery of high temperature superconductivity in La[O1-xFx]FeAs at the beginning of this year [1] has generated much excitement and has led to the rapid discovery of similar compounds with as high as 55 K transition temperatures [2]. The high superconducting transition temperatures are seemingly incompatible with the electron-phonon driven pairing of conventional superconductors, resulting in wide speculation as to the mechanism and nature of the superconductivity in these materials. Here we report results of the first scanning tunneling microscopy study of the 32 K superconductor (Sr1-xKx)Fe2As2. We find two distinct topographic regions on the sample, one with no apparent atomic corrugation, and another marked by a stripe-like modulation at double the atomic periodicity. In the latter the stripes appear to modulate the local density of states, occasionally revealing a Delta = 10 mV gap with a shape consistent with unconventional (non-s wave) superconductivity., Comment: 5 pages, 4 figures Minor changes: fixed unit cell size, added references

One of the main challenges in understanding high TC superconductivity is to disentangle the rich variety of states of matter that may coexist, cooperate, or compete with d-wave superconductivity. At center stage is the pseudogap phase, which occupies a large portion of the cuprate phase diagram surrounding the superconducting dome [1]. Using scanning tunneling microscopy, we find that a static, non-dispersive, "checkerboard"-like electronic modulation exists in a broad regime of the cuprate phase diagram and exhibits strong doping dependence. The continuous increase of checkerboard periodicity with hole density strongly suggests that the checkerboard originates from charge density wave formation in the anti-nodal region of the cuprate Fermi surface. These results reveal a coherent picture for static electronic orderings in the cuprates and shed important new light on the nature of the pseudogap phase., Comment: 5 pages, 4 figures

The nature of the pseudogap state, observed above the superconducting transition temperature TC in many high temperature superconductors, is the center of much debate. Recently, this discussion has focused on the number of energy gaps in these materials. Some experiments indicate a single energy gap, implying that the pseudogap is a precursor state. Others indicate two, suggesting that it is a competing or coexisting phase. Here we report on temperature dependent scanning tunneling spectroscopy of Pb-Bi2Sr2CuO6+x. We have found a new, narrow, homogeneous gap that vanishes near TC, superimposed on the typically observed, inhomogeneous, broad gap, which is only weakly temperature dependent. These results not only support the two gap picture, but also explain previously troubling differences between scanning tunneling microscopy and other experimental measurements., Comment: 6 pages

Microscopy (STM). At all dopings, the low energy density-of-states modulations are analyzed according to a simple model of quasiparticle interference and found to be consistent with Fermi-arc superconductivity. The superconducting coherence-peaks, ubiquitous in near-optimal tunneling spectra, are destroyed with strong underdoping and a new spectral type appears. Exclusively in regions exhibiting this new spectrum, we find local `checkerboard' charge-order with wavevector Q=(2pi/4.5a,0);(0,2pi/4.5a)+15%. Surprisingly, this order coexists harmoniously with the the low energy, Comment: 4 pages 4 figures in jpeg format. version with hegher res embedded figures can be found at: http://people.ccmr.cornell.edu/~jcdavis/files/mcelroy040620.pdf

We use novel STM techniques in concert to study the doping dependence of electronic structure in Bi-2212. At all dopings, the low energy states are relatively homogenous except for dispersive density-of-states modulations whose properties are used to elucidate the momentum-space characteristics of quasi-particles. The superconductive coherence-peaks, ubiquitous in near-optimal tunneling spectra, are destroyed with strong underdoping. A new spectral type, likely characteristic of the zero temperature pseudogap regime, appears in these samples. Exclusively in regions exhibiting this new spectrum, we find a quasi periodic modulations in dI/dV as well as in topograph with Q(2pi/4.5a,0) and (0,2pi/4.5a)+-15%. This is consistent with the existence of a local charge density modulation at these wave vectors. Surprisingly, this state coexists harmoniously with the low energy nodal quasi-particles. We discuss the relevance of these findings to the cuprate phase diagram and to the relationship between the pseudogap and superconductivity., Comment: higher resolutions of figures imbedded in .pdf can be downloaded at: http://people.ccmr.cornell.edu/~jcdavis/files/nodalqp_co.pdf

Scanning tunneling microscopy is used to image the additional quasiparticle states generated by quantized vortices in the high-Tc superconductor Bi2Sr2CaCu2O8+d. They exhibit a Cu-O bond oriented 'checkerboard' pattern, with four unit cell (4a0) periodicity and a ~30 angstrom decay length. These electronic modulations may be related to the magnetic field-induced, 8a0 periodic, spin density modulations of decay length ~70 angstroms recently discovered in La1.84Sr0.16CuO4. The proposed explanation is a spin density wave localized surrounding each vortex core. General theoretical principles predict that, in the cuprates, a localized spin modulation of wavelength L should be associated with a corresponding electronic modulation of wavelength L/2, in good agreement with our observations., Comment: 10 pages, 3 figures

Granular superconductivity occurs when microscopic superconducting grains are separated by non-superconducting regions through which they communicate by Josephson tunneling to establish the macroscopic superconducting state [1]. Although crystals of the cuprate high-Tc superconductors are not granular in a structural sense, theory indicates that at low hole densities the holes can become concentrated at some locations resulting in hole-rich superconducting domains [2-5]. Granular superconductivity due to Josephson tunneling through 'undoped' regions between such domains would represent a new paradigm for the underdoped cuprates. Here we report studies of the spatial interrelationships between STM tunneling spectra in underdoped Bi2Sr2CaCu2O8+x. They reveal an apparent spatial segregation of the electronic structure into ~3nm diameter domains (with superconducting characteristics and local energy gap delta<50 meV) in an electronically distinct background. To explore whether this represents nanoscale segregation of two distinct electronic phases, we employ scattering-resonances at Ni impurity atoms [6] as 'markers' for the local existence of superconductivity [7-9]. No Ni-resonances are detected in any regions where delta>50(2.5) meV. These observations suggest that underdoped Bi2Sr2CaCu2O8+x is a mixture of two different short-range electronic orders with the long-range characteristics of a granular superconductor., Comment: To appear in Nature

The parent compounds of the copper oxide high-Tc superconductors are unusual insulators. Superconductivity arises when they are properly doped away from stoichiometry1. In Bi2Sr2CaCu2O8+x, superconductivity results from doping with excess oxygen atoms, which introduce positive charge carriers (holes) into the CuO2 planes, where superconductivity is believed to originate. The role of these oxygen dopants is not well understood, other than the fact that they provide charge carriers. However, it is not even clear how these charges distribute in the CuO2 planes. Accordingly, many models of high-Tc superconductors simply assume that the charge carriers introduced by doping distribute uniformly, leading to an electronically homogeneous system, as in ordinary metals. Here we report the observation of an electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x using scanning tunnelling microscopy/spectroscopy. This inhomogeneity is manifested as spatial variations in both the local density of states spectrum and the superconducting energy gap. These variations are correlated spatially and vary on a surprisingly short length scale of ~ 14 Angs. Analysis suggests that the inhomogeneity observed is a consequence of proximity to a Mott insulator resulting in poor screening of the charge potentials associated with the oxygen ions left behind in the BiO plane after doping. Hence this experiment is a direct probe of the local nature of the superconducting state, which is not easily accessible by macroscopic measurements., Comment: 6 pages, 4 figures

In conventional superconductors, magnetic interactions and magnetic impurity atoms are destructive to superconductivity. By contrast, in some unconventional systems, e.g. superfluid 3He and superconducting UGe2, superconductivity or superfluidity is actually mediated by magnetic interactions. A magnetic mechanism has also been proposed for high temperature superconductivity (HTSC) in which an electron magnetically polarizes its environment resulting in an attractive pairing-interaction for oppositely polarized spins. Since a magnetic impurity atom would apparently not disrupt such a pairing-interaction, it has also been proposed that the weaker influences on HTSC of magnetic Ni impurity atoms compared to those of non-magnetic Zn are evidence for a magnetic mechanism. Here we use scanning tunneling microscopy (STM) to determine directly the influence of individual Ni atoms on the electronic structure of Bi2Sr2CaCu2O8+d. Two local d-wave impurity-states are observed at each Ni. Analysis of their energies surprisingly reveals that the primary quasiparticle scattering effects of Ni atoms are due to non-magnetic interactions. Nonetheless, we also demonstrate that a magnetic moment coexists with unimpaired superconductivity at each Ni site. We discuss the implications of these phenomena, and those at Zn, for the pairing-mechanism., Comment: 13 pages, 4 figures

We report on low temperature scanning tunneling microscopy (STM) studies of the electronic structure of vortex cores in Bi2Sr2CaCu2O8+d (BSCCO). At the vortex core center, an enhanced density-of-states (DOS) is observed at energies near 7 meV. Spectroscopic imaging at these energies reveals an exponential decay of these 'core states' with a decay length of 2.2(3) nm. The four-fold symmetry sometimes predicted for d-wave vortices is not seen in spectroscopic vortex images. A locally nodeless order parameter induced by the magnetic field may be consistent with these measurements., Comment: Submitted to Physical Review Letters. Address correspondence to jcdavis@socrates.berkeley.edu

Although their crystal structures are complex, all high temperature superconductors contain some crystal planes consisting of only Cu and O atoms in a square lattice. Superconductivity is believed to originate from strongly interacting electrons in these CuO2 planes. Substitution of a single impurity atom at a Cu site creates a simple but powerful perturbation to these interactions. Detailed knowledge of the effects of such an impurity atom on the superconducting order parameter and on the quasi-particle local density of states (LDOS) could allow competing theories of high temperature superconductivity (HTSC) to be tested at the atomic scale. The fundamental implications of results from numerous bulk measurements on samples doped with impurity atoms could also be clarified with such data. Here we describe scanning tunneling microscopy studies of the effects of individual Zn impurity atoms located at the Cu site in the high-Tc superconductor Bi2Sr2CaCu2O8+delta. Tunneling spectroscopy shows intense quasi-particle scattering resonances at the Zn sites, coincident with strong suppression of superconductivity within about 1.5 nm. Imaging of the quasi-particle LDOS at these sites reveals the long sought four-fold symmetric "quasi-particle cloud" aligned with the d-wave gap nodes. Several unexpected phenomena, which can shed new light on the atomic-scale response of HTSC to a probe impurity atom, are also observed., Comment: 18 pages, 4 figures