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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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...

Quasiparticle tunneling spectra of the electron-doped (n-type) infinite-layer cuprate Sr 0.9 La 0.1 CuO 2 reveal characteristics that counter a number of common phenomena in the hole-doped (p-type) cuprates. The optimally doped Sr 0.9 La 0.1 CuO 2 with T c 43 K exhibits a momentum-independent superconducting gap D 13.0 6 1.0 meV that substantially exceeds the BCS value, and the spectral characteristics indicate insignificant quasiparticle damping by spin fluctuations and the absence of pseudogap. The response to quantum impurities in the Cu sites also differs fundamentally from that of the p-type cuprates with d x 2 2y 2 -wave pairing symmetry. 74.50.+r, 74.62.Dh The predominantly d x 2 2y 2 pairing symmetry [1,2], the existence of spin fluctuations in the CuO 2 planes [3,4], and the pseudogap phenomena [3][4][5] [7,8], and it has been suggested that the pairing symmetry in the one-layer n-type cuprates may change from d x 2 2y 2 to s, depending on the electron doping level [9]. The nonuniversal pairing symmetries in cuprate superconductors imply that the symmetry is likely the result of competing orders rather than a sufficient condition for pairing. Nonetheless, an important consequence of either d x 2 2y 2 or ͑d x 2 2y 2 1 s͒-wave pairing is that the resulting nodal quasiparticles can interact strongly with the quantum impurities in the CuO 2 planes [10,11], such that a small concentration of impurities can give rise to strong suppression of superconductivity and modification of the collective Cu 21 spin excitations [6,[12][13][14][15][16][17]. In addition, Kondo effects could be induced by nonmagnetic impurities through breaking the nearestneighbor antiferromagnetic Cu 21 -Cu 21 interaction [18]. Such strong response to nonmagnetic impurities is in sharp contrast to conventional s-wave superconductivity [19,20]. Despite significant progress in the studies of cuprate superconductivity, the research on the simplest form of cuprates, the infinite-layer system Sr 12x L x CuO 2 (L La, Gd, Sm), has been limited [21][22][23] superconducting volume and a sharp superconducting transition temperature at T c 43 K, thus enabling reliable spectroscopic studies of the pairing symmetry and the effects of quantum impurities. These single-phased infinitelayer cuprates are n-type with P4͞mmm symmetry, which differ significantly from other cuprates in that no excess charge reservoir block exists between consecutive CuO 2 planes except a single layer of Sr(La), as illustrated in Fig. 1(a), suggesting stronger CuO 2 interplanar coupling. Furthermore, the c-axis superconducting coherence length ͑j c 0.53 nm͒ is found to be longer than the c-axis lattice constant ͑c 0 0.347 nm͒ [25], in stark contrast to other cuprate superconductors with j c ø c 0 . Hence, the superconducting properties of the infinite-layer system are expected to be more three-dimensional, as opposed to the quasi-two-dimensional nature of all other cuprates. In this Letter, we report experimental findings based on the scanning tunneling spectroscopy studies...

We present scanning tunneling spectroscopic and high-field thermodynamic studies of hole-and electron-doped (p-and n-type) cuprate superconductors. Our experimental results are consistent with the notion that the ground state of cuprates is in proximity to a quantum critical point (QCP) that separates a pure superconducting (SC) phase from a phase comprised of coexisting SC and a competing order, and the competing order is likely a spin-density wave (SDW). The effect of applied magnetic field, tunneling current, and disorder on the revelation of competing orders and on the low-energy excitations of the cuprates is discussed.