One of the main challenges in understanding high T C 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. Author ContributionsWDW, MCB and KC shared equal responsibility for all aspects of this project from instrument construction through data collection and analysis. TK grew the samples and helped refine the STM. TT and HI contributed to sample growth. YW contributed to analysis and writing of the manuscript. EWH advised.

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The unclear relationship between cuprate superconductivity and the pseudogap state remains an impediment to understanding the high transition temperature (T(c)) superconducting mechanism. Here, we used 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 quasi-particle interference pattern within a single bismuth-based cuprate family, we observed a Fermi surface reconstruction slightly below optimal doping, indicating a zero-field quantum phase transition in notable proximity to the maximum superconducting T(c). Surprisingly, this major reorganization of the system's underlying electronic structure has no effect on the smoothly evolving pseudogap.

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 tunnelling 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 nanometre 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, such as the pseudogap magnitude, and highlights a new approach to the study of nanoscale inhomogeneity in general.That high-temperature superconductors should show nanoscale inhomogeneity is unsurprising. In correlated electron materials, Coulomb repulsion between electrons hinders the formation of a homogeneous Fermi liquid, and complex real-space phase separation is ubiquitous 1 (Bi-2212; refs 3-5).This intrinsic inhomogeneity poses challenges to the interpretation of bulk or spatially averaged measurements. For example, angle-resolved photoemission spectroscopy (ARPES) is a powerful technique for studying k-space structure in the cuprates 6 . However, ARPES can provide only spatially averaged results, and uniting these with the nanoscale disordered electronic structure measured by STM remains a formidable task.Our approach to addressing this issue originates from discoveries by Fourier-transform STM (FT-STM), which has emerged as an important tool for studying the cuprates. These studies begin with the collection of a spectral survey, in which differential conductance spectra, proportional to local density of states (LDOS), are measured at a dense array of locations, creating a three-dimensional dataset of LDOS as a function of energy and position in the plane. By Fourier transforming constant-energy slices of these surveys, referred to as LDOS or conductance maps, FT-STM enables the study of two phenomena linked to the cuprate Fermi surface (FS) (Fig. 1b). First, non-dispersive wavevectors of the checkerboardlike charge order observed in many cuprates 7-10 are probably connected to the FS-nesting wavevectors near the antinodal (π,0) Brillouin zone boundary (see, for example, the arrow in Fig. 1b) 11 . Second, dispersive quasiparticle interference (QPI) patterns 12-14 originate from elastic scattering of quasiparticles on the FS near the nodal (π, π) direction 15 . Taken together, these phenomena provide complementary information about the cuprate FS. However, because these phenomena were previously characterized using Fourier transforms of large LDOS maps containing a wide range of energy gaps and spectra, previous FT-STM mapping of the FS was still sp...

We investigate the topological surface state properties at various surface cleaves in the topological insulator Bi2Se3, via first principles calculations and scanning tunneling microscopy/spectroscopy (STM/STS). While the typical surface termination occurs between two quintuple layers, we report the existence of a surface termination within a single quintuple layer where dangling bonds form with giant spin splitting owing to strong spin-orbit coupling. Unlike Rashba split states in a 2D electron gas, these states are constrained by the band topology of the host insulator with topological properties similar to the typical topological surface state, and thereby offer an alternative candidate for spintronics usage. We name these new states "topological dangling-bond states". The degree of the spin polarization of these states is greatly enhanced. Since dangling bonds are more chemically reactive, the observed topological dangling-bond states provide a new avenue for manipulating band dispersions and spin-textures by adsorbed atoms or molecules.

Strong electronic distortions are typically accompanied by structural distortions, and vice versa. Determining the relationship between these orders can be complicated, but a clue comes from their (co-)dependence on other parameters. In a cuprate superconductor, for example, both superconductivity and the pseudogap are highly dependent on doping, temperature, and magnetic field. Here, we investigate whether the structural symmetry in BSCCO is similarly dependent on these parameters, or whether it is an omnipresent background within which the electronic states evolve.Structural symmetries are traditionally measured by scattering experiments, such as xray or neutron scattering to determine bulk symmetries, or low energy electron diffraction (LEED) to determine surface symmetries. The structure of double layer Bi 2 Sr 2 CaCu 2 O 8+x (Bi-2212) is sketched in Fig. 1a. Although nearly tetragonal, a ∼0.5% difference between a and b axes 14 makes the true structure orthorhombic. However, despite numerous scattering experiments on BSCCO spanning two decades, the more detailed structure has remained enigmatic, due in part to an incommensurate structural "supermodulation" which pervades the bulk of these materials 14 , and to dopant disorder which leads Bi atoms to stochastically occupy inequivalent sites in different unit cells 15 . [18][19][20][21][22][23] . Thus, to investigate the role of structure in these broken symmetry electronic states, it is imperative to make atomic scale measurements of the structural symmetry.To undertake this investigation, we use three different home-built scanning tunneling microscopes. In each case, a sample is cleaved at low temperature in cryogenic ultra-high vacuum, and immediately inserted into the scanning head. BSCCO typically cleaves between two BiO mirror planes (Fig. 1a). Data was acquired at T=6K unless otherwise noted. The tip is rastered across the sample surface, while a feedback loop adjusts its height to maintain a constant tip-sample tunneling current. This results in a topographic image of the BiO surface.Temperature drift (typically < 10 mK), piezo hysteresis, and piezo nonlinearity, can lead to small but problematic warping of topographic images. Recently, Lawler et al introduced a ground-breaking algorithm to correct these picometer-scale drifts 7 . We show that Lawler's algorithm can also be used to remove subtle periodic noise (see Supplementary that the pseudogap is characterized by intra-unit-cell inversion symmetry breaking? To investigate this, we characterize the dependence of the structural distortion on parameters which are known to heavily influence electronic ordered states: doping, temperature, and magnetic field. Fig. 3a locates in a three-dimensional phase diagram the 21 datasets in which we measured the structure. The key results are summarized in Figs. 3b-d. We do not find a dependence of the structural distortion on doping, temperature, or field, across a wide range of values. We have measured the distortion both inside and outside the superconducting...

Abstract-The sum-frequency spectroscopy signatures of NH-(amide A) and C = O (amide I) groups, the amide segments in all proteins, are measured in thin films that consist of an ensemble of right-handed, helical poly--benzyl-L-glutamate (PBLG) macromolecules that are endgrafted and self-organized into a monomolecular film with a large degree of unidirectional order. Distinct sum-frequency spectral signatures associated with the amide A and the amide I bands are observed because of a strong noncentro-symmetry produced by intra-and intermolecular forces. Hydrogen bonding self-organizes amino and acidic groups within the molecular helical scaffold. In an endgrafted thin film, repulsive electrostatic forces between PBLG macromolecules stabilize the organization between molecules. The average orientation of the PBLG chain was measured. Imaging scans using sum-frequency generation, complemented by atomic force microscopy, were used to investigate the uniformity of orientation of the PBLG chains.

In conventional superconductors, the superconducting gap in the electronic excitation spectrum prevents scattering of low-energy electrons. In high-temperature superconductors (HTSs), an extra gap, the pseudogap 1 , develops well above the superconducting transition temperature T C . Here, we present a new avenue of investigating the pseudogap state, using scanning tunnelling microscopy (STM) of resonances generated by single-atom scatterers. Previous studies on the superconducting state of HTSs 2 have led to a fairly consistent picture in which potential scatterers, such as Zn, strongly suppress superconductivity in an atomic-scale region, while generating low-energy excitations with a spatial distribution-as imaged by STM 3,4 -indicative of the d-wave nature of the superconducting gap. Surprisingly, we find that similar native impurity resonances coexist spatially with the superconducting gap at low temperatures and survive virtually unchanged on warming through T C . These findings demonstrate that properties of impurity resonances in HTSs are not determined by the nature of the superconducting state, as previously suggested, but instead provide new insights into the pseudogap state.In d-wave superconductors, such as the high-temperature superconductors (HTSs), impurities act as pair breakers, giving rise to virtual bound states, or resonances, within the gap. For strong scatterers, these resonances lie close to the Fermi energy, and significantly modify bulk superconducting properties 5,6 . The local (atomic scale) effects of these resonances have been studied by several probes, such as nuclear magnetic resonance 7-11 (NMR) and muon spin relaxation (µSR) 12 . A variety of scanning tunnelling microscopy (STM) studies of impurity resonances in HTSs have been reported, including studies of native (unidentified) impurities 13,14 , intentionally doped Zn and Ni impurities 3,4 and intentionally placed surface impurities 15 . All of these STM studies demonstrated that impurity resonances are associated with an enhanced local density of states inside the gap, close to the Fermi energy. All of these studies were also carried out on Bi 2 Sr 2 CaCu 2 O 8+x (Bi-2212) near 4 K, significantly below T C .Here, we report on temperature-dependent STM studies of native impurities in overdoped (T C = 15 K) Bi 2−y Pb y Sr 2 CuO 6+x (Bi-2201). In addition to enabling comparison to previous studies in Bi-2212, Bi-2201 has the benefit of having a relatively low T C , thus enabling us to study impurity resonances below and above T C without the resonance being obscured by thermal broadening.To carry out the temperature-dependent measurements discussed here we have constructed an ultrahigh-vacuum STM with the ability to track atomically resolved regions-here surrounding individual impurities-over a wide range of temperatures. We begin our study at low temperatures, using an experimental methodology similar to that used in previous STM impurity studies 3,4 . We search for impurity resonances by recording a spectral survey, in which d...