2 Boeing Phantom Works, Seattle, Washington 98124 the generalized BTK theory, with b as the tunnel-cone width, Z the barrier strength, D 0 the d-wave gap maximum, and 2D 0 ͞k B T c the reduced-gap ratio.

We report a direct observation of surface dominated conduction in an intrinsic Bi(2)Se(3) thin film with a thickness of six quintuple layers grown on lattice-matched CdS (0001) substrates by molecular beam epitaxy. Shubnikov-de Haas oscillations from the topological surface states suggest that the Fermi level falls inside the bulk band gap and is 53 ± 5 meV above the Dirac point, which is in agreement with 70 ± 20 meV obtained from scanning tunneling spectroscopies. Our results demonstrate a great potential of producing genuine topological insulator devices using Dirac Fermions of the surface states, when the film thickness is pushed to nanometer range.

We demonstrate evidence of a surface gap opening in topological insulator (TI) thin films of (Bi0.57Sb0.43)2Te3 below six quintuple layers through transport and scanning tunneling spectroscopy measurements. By effective tuning the Fermi level via gate-voltage control, we unveil a striking competition between weak localization and weak antilocalization at low magnetic fields in nonmagnetic ultrathin films, possibly owing to the change of the net Berry phase. Furthermore, when the Fermi level is swept into the surface gap of ultrathin samples, the overall unitary behaviors are revealed at higher magnetic fields, which are in contrast to the pure WAL signals obtained in thicker films. Our findings show an exotic phenomenon characterizing the gapped TI surface states and point to the future realization of quantum spin Hall effect and dissipationless TI-based applications.

We investigate the low-energy quasiparticle excitation spectra of cuprate superconductors by incorporating both superconductivity (SC) and competing orders (CO) in the bare Green's function and quantum phase fluctuations in the proper self-energy. Our approach provides consistent explanations for various empirical observations, including the excess subgap quasiparticle density of states, "dichotomy" in the momentum-dependent quasiparticle coherence and the temperature-dependent gap evolution, and the presence (absence) of the low-energy pseudogap in hole-(electron-) type cuprates depending on the relative scale of the CO and SC energy gaps. 74.25.Jb, 74.50.+r Keywords: Quasiparticle spectra; pseudogap; competing orders; cuprate superconductors Cuprate superconductors differ fundamentally from conventional superconductors in that they are doped Mott insulators with strong electronic correlation that leads to possibilities of different competing orders (CO) in the ground state besides superconductivity (SC) [1][2][3][4][5][6][7][8]. The existence of competing orders and the proximity to quantum criticality [2,3,7,8] gives rise to unconventional low-energy excitations of the cuprates, manifested as weakened superconducting phase stiffness [6], occurrence of excess subgap quasiparticle density of states (DOS) [9], spatial modulations in the lowtemperature quasiparticle spectra that are unaccounted for by Bogoliubov quasiparticles alone [10][11][12], "dichotomy" in the momentum-dependent quasiparticle coherence [13] and temperature-dependent gap evolution [14], and the presence (absence) of the low-energy pseudogap (PG) [9,15,16] and Nernst effect [17] in the hole (electron)-type cuprates above the SC transition. Microscopically, the existence of CO is likely responsible for various non-universal phenomena among different cuprates [8,9,18,19]. Macroscopically, the weakened superconducting phase stiffness and proximity to CO can give rise to strong fluctuations that lead to the extreme type-II nature and rich vortex dynamics [8,20,21].To date there are two typical theoretical approaches to describing the quasiparticle excitation spectra of the cuprates. One approach takes the BCS-like Hamiltonian as the unperturbed mean-field state and a competing order, pinned by disorder, as the perturbation that gives rise to a weak scattering potential for the Bogoliubov quasiparticles [11,[22][23][24]. The other approach begins with the BCS-like Hamiltonian and includes superconducting phase fluctuations in the proper self-energy correction [25,26]. However, no quantitative calculations have been made by incorporating both CO and quantum phase fluctuations in the SC state. The objective of this work is to consider the latter scenario and compute the corresponding low-energy excitation spectra with realistic physical parameters for comparison with experiments. We find that the low-energy excitations thus derived differ from typical Bogoliubov quasiparticles and can account for various puzzling phenomena aforementioned....

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We report phenomena manifesting nonequilibrium superconductivity induced by spin-polarized quasiparticles in perovskite ferromagnet-insulator-superconductor ͑F-I-S͒ heterostructures. Measurements of the critical current J c , using a pulsed current technique to minimize Joule heating, reveal a monotonic increase with increasing insulator thickness; and for F-IS with thin insulating barriers, a slight increase in J c is observed under small injection currents I m from the ferromagnet, followed by a strong suppression of J c under large I m. In contrast, no effect of injection on J c can be detected in the N-IS control sample ͑N: nonmagnetic metal͒. The spin diffusion time and length in cuprate superconductors are also estimated and compared with our experimental results. ͓S0163-1829͑99͒05638-6͔

Scanning tunneling spectroscopy studies reveal long-range spatial homogeneity and predominantly d x 2 2y 2 -pairing spectral characteristics in under-and optimally doped YBa 2 Cu 3 O 72d superconductors, whereas STS on YBa 2 ͑Cu 0.9934 Zn 0.0026 Mg 0.004 ͒ 3 O 6.9 exhibits microscopic spatial modulations and strong scattering near the Zn or Mg impurity sites, together with global suppression of the pairing potential. In contrast, in overdoped ͑Y 0.7 Ca 0.3 ͒Ba 2 Cu 3 O 72d , ͑d x 2 2y 2 1 s͒-pairing symmetry is found, suggesting significant changes in the superconducting ground state at a critical doping value. A possible consequence of a QCP is the dopingdependent pseudogap phenomenon [13], which may represent a precursor for superconductivity in the cuprates [13]. Early experiments on the Bi-2212 system reported a measured energy gap D ‫ء‬ ͑p͒ that increased monotonically with decreasing p and was nearly independent of temperature [14][15][16][17][18][19]. However, the low-temperature spectra of the optimally doped and underdoped Bi-2212 appeared to consist of a sharp peak feature on top of a broad "hump." Recent bulk measurements on Bi-2212 mesas [20] demonstrated strong temperature dependence associated with the sharp peak, which vanished at the superconducting transition temperature T c , while the hump feature persisted well above T c . The coexistence of these two gaplike features in the superconducting state has been attributed to a different physical origin associated with each gap [20,21].In this work, we address some of these issues via studies of the directional and spatially resolved quasiparticle tunneling spectra on the YBa 2 Cu 3 O 72d (YBCO) with a range of doping levels. The doping dependence of the pairing symmetry, pairing potential, and spatial homogeneity is derived from these studies.The samples used in this investigation included three optimally doped YBCO single crystals with T c 92.9 6 0.1 K, three underdoped YBCO single crystals with T c 60.0 6 1.5 K, one underdoped YBCO c-axis film with T c 85.0 6 1.0 K, two overdoped ͑Y 0.7 Ca 0.3 ͒Ba 2 Cu 3 O 72d (Ca-YBCO) c-axis films [22] with T c 78.0 6 2.0 K, and one optimally doped single crystal containing small concentrations of nonmagnetic impurities, YBa 2 ͑Cu 0.9934 Zn 0.0026 Mg 0.004 ͒ 3 O 6.9 [(Zn,Mg)-YBCO], with T c 82.0 6 1.5 K [8,22]. The spectra of YBCO single crystals were taken primarily with the quasiparticles tunneling along three axes: the antinode axes ͕100͖ or ͕010͖, the nodal axis ͕110͖, and the c axis ͕001͖; while those of the pure and Ca-YBCO films were taken along the c axis. All samples except (Zn,Mg)-YBCO are twinned. The surface was prepared by chemical etching [23,24], and samples were kept either in high-purity helium gas or under high vacuum at all times. Our surface preparation has the advantage of terminating the YBCO top surface at the CuO 2 plane by chemically passivating the layer while retaining the bulk properties of the constituent elements [23,24], thus yielding reproducible spectra for samples of the same 0...

We present the first demonstration of vortices in an electron-type cuprate superconductor, the highest Tc (= 43 K) electron-type cuprate Sr0.9La0.1CuO2. Our spatially resolved quasiparticle tunneling spectra reveal a hidden low-energy pseudogap inside the vortex core and unconventional spectral evolution with temperature and magnetic field. These results cannot be easily explained by the scenario of pure superconductivity in the ground state of high-Tc superconductivity.