Graphene has shown great application potential as the host material for next-generation electronic devices. However, despite its intriguing properties, one of the biggest hurdles for graphene to be useful as an electronic material is the lack of an energy gap in its electronic spectra. This, for example, prevents the use of graphene in making transistors. Although several proposals have been made to open a gap in graphene's electronic spectra, they all require complex engineering of the graphene layer. Here, we show that when graphene is epitaxially grown on SiC substrate, a gap of approximately 0.26 eV is produced. This gap decreases as the sample thickness increases and eventually approaches zero when the number of layers exceeds four. We propose that the origin of this gap is the breaking of sublattice symmetry owing to the graphene-substrate interaction. We believe that our results highlight a promising direction for bandgap engineering of graphene.

Films of iron selenide (FeSe) one unit cell thick grown on strontium titanate (SrTiO3 or STO) substrates have recently shown superconducting energy gaps opening at temperatures close to the boiling point of liquid nitrogen (77 kelvin), which is a record for the iron-based superconductors. The gap opening temperature usually sets the superconducting transition temperature Tc, as the gap signals the formation of Cooper pairs, the bound electron states responsible for superconductivity. To understand why Cooper pairs form at such high temperatures, we examine the role of the SrTiO3 substrate. Here we report high-resolution angle-resolved photoemission spectroscopy results that reveal an unexpected characteristic of the single-unit-cell FeSe/SrTiO3 system: shake-off bands suggesting the presence of bosonic modes, most probably oxygen optical phonons in SrTiO3 (refs 5, 6, 7), which couple to the FeSe electrons with only a small momentum transfer. Such interfacial coupling assists superconductivity in most channels, including those mediated by spin fluctuations. Our calculations suggest that this coupling is responsible for raising the superconducting gap opening temperature in single-unit-cell FeSe/SrTiO3.

The phase diagram of hole-doped copper oxides shows four different electronic phases existing at zero temperature. Familiar among these are the Mott insulator, high-transition-temperature superconductor and metallic phases. A fourth phase, of unknown identity, occurs at light doping along the zero-temperature bound of the 'pseudogap' regime 1 . This regime is rich in peculiar electronic phenomena 1 , prompting numerous proposals that it contains some form of hidden electronic order. Here we present low-temperature electronic structure imaging studies of a lightly hole-doped copper oxide: Ca 2−x Na x CuO 2 Cl 2 . Tunnelling spectroscopy (at energies |E|>100 meV) reveals electron extraction probabilities greatly exceeding those for injection, as anticipated for a doped Mott insulator. However, for |E|<100 meV, the spectrum exhibits a V-shaped energy gap centred on E=0. States within this gap undergo intense spatial modulations, with the spatial correlations of a four CuO 2 -unit-cell square 'checkerboard', independent of energy. Intricate atomic-scale electronic structure variations also exist within the checkerboard. These data are consistent with an unanticipated crystalline electronic state, possibly the hidden electronic order, existing in the zero-temperature pseudogap regime of Ca 2−x Na x CuO 2 Cl 2 .Scanning tunnelling microscopy (STM) has recently emerged as a suitable technique to search for 'hidden' electronic order in the copper oxides. Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212) studies where high-transition-temperature (T c ) superconductivity (HTSC) was 2 suppressed to reveal the pseudogap have been especially fruitful. The prototypical study yielded a pseudogap-like conductance spectrum (V-shaped without coherence peaks) associated with a 'checkerboard' approximately four CuO 2 unit cells square of localdensity-of-states (LDOS) modulations surrounding vortex cores 2 . Similar phenomena were discovered throughout the sample above T c (ref.3), and within strongly underdoped nano-regions exhibiting pseudogap-like spectra 4 (see Fig. 1c). Underdoped Bi-2212 therefore shows a tendency towards checkerboard electronic modulations when HTSC is suppressed. However, it is unclear whether these checkerboard modulations in Bi-2212 represent a true electronic phase, because they exhibit [2][3][4] (1) a variety of dopingdependent incommensurate wavevectors, (2) very weak intensities, and (3) To search for electronic order hidden in the pseudogap while avoiding these uncertainties, we decided to study a simpler and less disordered copper oxide at lower doping and temperature. We chose Ca 2−x Na x CuO 2 Cl 2 (Na-CCOC), a material whose parent compound Ca 2 CuO 2 Cl 2 is a canonical Mott insulator 8 . Within its undistorted tetragonal crystal structure (Fig. 1b), all the CuO 2 planes are crystallographically identical. Sodium substitution for Ca destroys the Mott insulator state, producing first a nodal metal 9 in the zero-temperature pseudogap (ZTPG) regime, and eventually HTSC for x≥0. 10 (refs 10, 11). Crucially, Na-CCOC ...

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

Scanning tunneling spectroscopy of the high-Tc superconductor Bi2Sr2CaCu2O8+delta reveals weak, incommensurate, spatial modulations in the tunneling conductance. Images of these energy-dependent modulations are Fourier analyzed to yield the dispersion of their wavevectors. Comparison of the dispersions with photoemission spectroscopy data indicates that quasiparticle interference, due to elastic scattering between characteristic regions of momentum-space, provides a consistent explanation for the conductance modulations, without appeal to another order parameter. These results refocus attention on quasiparticle scattering processes as potential explanations for other incommensurate phenomena in the cuprates. The momentum-resolved tunneling spectroscopy demonstrated here also provides a new technique with which to study quasiparticles in correlated materials.

The electronic structure of simple crystalline solids can be completely described in terms either of local quantum states in real space (r-space), or of wave-like states defined in momentum-space (k-space). However, in the copper oxide superconductors, neither of these descriptions alone may be sufficient. Indeed, comparisons between r-space and k-space studies of Bi2Sr2CaCu2O8+delta (Bi-2212) reveal numerous unexplained phenomena and apparent contradictions. Here, to explore these issues, we report Fourier transform studies of atomic-scale spatial modulations in the Bi-2212 density of states. When analysed as arising from quasiparticle interference, the modulations yield elements of the Fermi-surface and energy gap in agreement with photoemission experiments. The consistency of numerous sets of dispersing modulations with the quasiparticle interference model shows that no additional order parameter is required. We also explore the momentum-space structure of the unoccupied states that are inaccessible to photoemission, and find strong similarities to the structure of the occupied states. The copper oxide quasiparticles therefore apparently exhibit particle-hole mixing similar to that of conventional superconductors. Near the energy gap maximum, the modulations become intense, commensurate with the crystal, and bounded by nanometre-scale domains. Scattering of the antinodal quasiparticles is therefore strongly influenced by nanometre-scale disorder.

The randomness of dopant atom distributions in cuprate high-critical temperature superconductors has long been suspected to cause nanoscale electronic disorder. In the superconductor Bi2Sr2CaCu2O8+delta, we identified populations of atomic-scale impurity states whose spatial densities follow closely those of the oxygen dopant atoms. We found that the impurity-state locations are strongly correlated with all manifestations of the nanoscale electronic disorder. This disorder occurs via an unanticipated mechanism exhibiting high-energy spectral weight shifts, with associated strong superconducting coherence peak suppression but very weak scattering of low-energy quasi-particles.

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