Kenjiro K. Gomes

Designer Dirac fermions and topological phases in molecular graphene.

The observation of massless Dirac fermions in monolayer graphene has generated a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials. Both massless and massive Dirac fermions have been studied and proposed in a growing class of Dirac materials that includes bilayer graphene, surface states of topological insulators and iron-based high-temperature superconductors. Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atoms. Here we report the emergence of Dirac fermions in a fully tunable condensed-matter system—molecular graphene—assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface. Using low-temperature scanning tunnelling microscopy and spectroscopy, we embed the symmetries underlying the two-dimensional Dirac equation into electron lattices, and then visualize and shape the resulting ground states. These experiments show the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene. We then tune the quantum tunnelling between lattice sites locally to adjust the phase accrual of propagating electrons. Spatial texturing of lattice distortions produces atomically sharp p–n and p–n–p junction devices with two-dimensional control of Dirac fermion density and the power to endow Dirac particles with mass. Moreover, we apply scalar and vector potentials locally and globally to engender topologically distinct ground states and, ultimately, embedded gauge fields, wherein Dirac electrons react to ‘pseudo’ electric and magnetic fields present in their reference frame but absent from the laboratory frame. We demonstrate that Landau levels created by these gauge fields can be taken to the relativistic magnetic quantum limit, which has so far been inaccessible in natural graphene. Molecular graphene provides a versatile means of synthesizing exotic topological electronic phases in condensed matter using tailored nanostructures.

Visualizing pair formation on the atomic scale in the high- T c superconductor Bi 2 Sr 2 CaCu 2 O 8+ δ

Pairing of electrons in conventional superconductors occurs at the superconducting transition temperature Tc, creating an energy gap Δ in the electronic density of states (DOS). In the high-Tc superconductors, a partial gap in the DOS exists for a range of temperatures above Tc (ref. 2). A key question is whether the gap in the DOS above Tc is associated with pairing, and what determines the temperature at which incoherent pairs form. Here we report the first spatially resolved measurements of gap formation in a high-Tc superconductor, measured on Bi2Sr2CaCu2O8+δ samples with different Tc values (hole concentration of 0.12 to 0.22) using scanning tunnelling microscopy. Over a wide range of doping from 0.16 to 0.22 we find that pairing gaps nucleate in nanoscale regions above Tc. These regions proliferate as the temperature is lowered, resulting in a spatial distribution of gap sizes in the superconducting state. Despite the inhomogeneity, we find that every pairing gap develops locally at a temperature Tp, following the relation 2Δ/kBTp = 7.9 ± 0.5. At very low doping (≤0.14), systematic changes in the DOS indicate the presence of another phenomenon, which is unrelated and perhaps competes with electron pairing. Our observation of nanometre-sized pairing regions provides the missing microscopic basis for understanding recent reports of fluctuating superconducting response above Tc in hole-doped high-Tc copper oxide superconductors.

Electronic Origin of the Inhomogeneous Pairing Interaction in the High-Tc Superconductor Bi2Sr2CaCu2O8+δ

Identifying the mechanism of superconductivity in the high-temperature cuprate superconductors is one of the major outstanding problems in physics. We report local measurements of the onset of superconducting pairing in the high–transition temperature (Tc) superconductor Bi2Sr2CaCu2O8+δ using a lattice-tracking spectroscopy technique with a scanning tunneling microscope. We can determine the temperature dependence of the pairing energy gaps, the electronic excitations in the absence of pairing, and the effect of the local coupling of electrons to bosonic excitations. Our measurements reveal that the strength of pairing is determined by the unusual electronic excitations of the normal state, suggesting that strong electron-electron interactions rather than low-energy (<0.1 volts) electron-boson interactions are responsible for superconductivity in the cuprates.

Extending Universal Nodal Excitations Optimizes Superconductivity in Bi2Sr2CaCu2O8+δ

Cuprate Analysis Despite more than 20 years of intensive effort, the mechanism providing superconductivity in the cuprates remains elusive and contentious, partly because the cuprates are inhomogeneous. Scanning tunneling spectroscopy (STS) and high-resolution, angle-resolved photoemission spectroscopy provide energy and momentum information about the excitations in the high-temperature cuprate superconductors. Pushp et al. (p. 1689, published online 4 June) provide a STS study of the cuprate Bi2Sr2CaCu2O8+δ over a range of doping levels and temperatures. This methodology for analyzing the spectra takes into account the inhomogeneity and may provide insight into how a superconducting pairing mechanism evolves from the parent insulating state. Scanning tunneling spectroscopy reveals strong electronic correlations in the insulating state of a cuprate superconductor. Understanding the mechanism by which d wave superconductivity in the cuprates emerges and is optimized by doping the Mott insulator is one of the major outstanding problems in condensed-matter physics. Our high-resolution scanning tunneling microscopy measurements of the high–transition temperature (Tc) superconductor Bi2Sr2CaCu2O8+δ show that samples with different Tc values in the low doping regime follow a remarkably universal d wave low-energy excitation spectrum, indicating a doping-independent nodal gap. We demonstrate that Tc instead correlates with the fraction of the Fermi surface over which the samples exhibit the universal spectrum. Optimal Tc is achieved when all parts of the Fermi surface follow this universal behavior. Increasing the temperature above Tc turns the universal spectrum into an arc of gapless excitations, whereas overdoping breaks down the universal nodal behavior.

Momentum dependence of superconducting gap, strong-coupling dispersion kink, and tightly bound Cooper pairs in the high- Tc (Sr,Ba) 1-x(K,Na)xFe2As2 superconductors

We present a systematic angle-resolved photoemission spectroscopic study of the high-Tc superconductor class (Sr/Ba)_(1−x)K_xFe_2As_2. By utilizing a photon-energy-modulation contrast and scattering geometry we report the Fermi surface and the momentum dependence of the superconducting gap, Δ(k ). A prominent quasiparticle dispersion kink reflecting strong scattering processes is observed in a binding-energy range of 25–55 meV in the superconducting state, and the coherence length or the extent of the Cooper pair wave function is found to be about 20 A, which is uncharacteristic of a superconducting phase realized by the BCS-phonon-retardation mechanism. The observed 40±15 meV kink likely reflects contributions from the frustrated spin excitations in a J_1-J_2 magnetic background and scattering from the soft phonons. Results taken collectively provide direct clues to the nature of the pairing potential including an internal phase-shift factor in the superconducting order parameter which leads to a Brillouin zone node in a strong-coupling setting.L. Wray, D. Qian, D. Hsieh, Y. Xia, L. Li, J.G. Checkelsky, A. Pasupathy, K.K. Gomes, A.V. Fedorov, G.F. Chen, J.L. Luo, A. Yazdani, N.P. Ong, N.L. Wang, and M.Z. Hasan 4, ∗ Joseph Henry Laboratories of Physics, Department of Physics, Princeton University, Princeton, NJ 08544, USA Lawrence Berkeley National Laboratory, Advanced Light Source, Berkeley, CA 94305, USA Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, P.R. China Princeton Center for Complex Materials, Princeton University, Princeton, NJ 08544, USA (Dated: 14 August, 2008)

Nanoscale Proximity Effect in the High-Temperature Superconductor Bi2Sr2CaCu2O8+δ Using a Scanning Tunneling Microscope

High temperature cuprate superconductors exhibit extremely local nanoscale phenomena and strong sensitivity to doping. While other experiments have looked at nanoscale interfaces between layers of different dopings, we focus on the interplay between naturally inhomogeneous nanoscale regions. Using scanning tunneling microscopy to carefully track the same region of the sample as a function of temperature, we show that regions with weak superconductivity can persist to elevated temperatures if bordered by regions of strong superconductivity. This suggests that it may be possible to increase the maximum possible transition temperature by controlling the distribution of dopants. PACS numbers: 74.72.Gh, 74.55.+v, 74.62.En

Imaging quasiperiodic electronic states in a synthetic Penrose tiling

Quasicrystals possess long-range order but lack the translational symmetry of crystalline solids. In solid state physics, periodicity is one of the fundamental properties that prescribes the electronic band structure in crystals. In the absence of periodicity and the presence of quasicrystalline order, the ways that electronic states change remain a mystery. Scanning tunnelling microscopy and atomic manipulation can be used to assemble a two-dimensional quasicrystalline structure mapped upon the Penrose tiling. Here, carbon monoxide molecules are arranged on the surface of Cu(111) one at a time to form the potential landscape that mimics the ionic potential of atoms in natural materials by constraining the electrons in the two-dimensional surface state of Cu(111). The real-space images reveal the presence of the quasiperiodic order in the electronic wave functions and the Fourier analysis of our results links the energy of the resonant states to the local vertex structure of the quasicrystal.