5.4 Discussion
5.4.1 Relevant low-energy excitations in Y-123
An important objective of the work considered here was to distinguish between the “one-gap” and
“two-gap” models of the origin of the pseudogap and the unconventional quasiparticle excitations in hole-type cuprates. The STS results of Y-123 presented here indicate that the quasiparticle excitations in Y-123 are complex and appear to involve a ground state that displays excitation phenomena of both fermionic quasiparticle excitations and bosonic collective modes. Specifically, the “one-gap” model asserting simple Bogoliubov quasiparticle excitations cannot account for all phenomena, such as the energy-independent collective modes and additional energy scales besides
∆SC. Hence, multiple orders are needed, which is consistent with the spirit of the “two-gap”
model. Interestingly, we note that a PDW alone may be reconciled with the “one-gap” model
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Figure 5.10: FT-LDOS maps at H = 0,5T in Y-123. Left panel: FT-LDOS in Y-123 for H = 0 at ω=-12meV with QP DW, QCDW,QSDW indicated by circles. Additionally, the lattice constant diffraction modes are circled in white, as well as diffraction modes that appear at (π,π). The scan direction of the STM tube scanner is indicated by a yellow arrow. Right panel: FT-LDOS in Y-123 for H = 5T at ω=-12meV withQP DW,QCDW, andQSDW indicated by circles. Additionally, the lattice constant diffraction spots are circled in white, as well as diffraction modes that appear at (π, π). The scan direction of the STM tube scanner is indicated by a yellow arrow.
because it supposes that Cooper pairs exist in the PDW mode but they no longer acquire a global superconducting phase [84]. Instead of a global phase, the disordered Cooper pairs in the PDW mode exhibit a spatially varying phase characterized by an ordering wavevectorQP DW. In contrast, the presence of either CDW or SDW collective excitations is a manifestation of the “two-gap” model because both modes are particle-hole collective excitations that exhibit energy scales differing from the superconducting gap (VCO and/or ∆0) and ordering wavevectors, given byQCDW andQSDW. As further evidence of the complexity of the excitations in Y-123, the data in Figs. 5.15 and 5.16 show significant contributions to FT-LDOS that may be attributed to PDW, CDW, and SDW, but the relative symmetric and anti-symmetric amplitudes vary as functions of energy and magnetic field. The symmetric components of QP DW,QCDW, andQSDW appear to increase with magnetic field.
Additionally, while the PDW, CDW, and SDW cannot be explained by conventional supercon- ductivity, the quasiparticle excitations energies and spectral shifts among the PDW, SDW, and CDW excitations as a function of energy and magnetic field further indicate a complex ground state in Y-123. Close inspection of Figs. 5.11 and 5.12 reveal that all modes exhibit significant spectral
Figure 5.11: Intensity plots of FT-LDOS-vs.-kalong the bonding direction in Y-123 at H = 0, 5T.
Left panel: Intensity plot of FT-LDOS-vs.-k along the bonding direction for H = 0 in Y-123. The energy-independent diffraction modes, QP DW and QCDW, are indicated by thick dashed lines. A dispersive energy-dependent mode is shown as a thin dotted line. Right panel: Intensity plot of FT- LDOS-vs.-kalong the bonding direction for H = 5T in Y-123. The energy-independent diffraction modes, QP DW and QCDW, are indicated by thick dashed lines. A dispersive energy-dependent diffraction spot is shown as a thin dotted line.
intensity around ∆SC, ∆0 and VP G at H = 0, but the spectral intensity also varies with energy as magnetic field increases to H = 5T. For H = 5T, the QP DW mode loses its intensity above
∆SC, which could be attributed to the fact that superconducting pairing is absent above ∆SC. In addition, longitudinal optical phonon modes associated with the Cu-O bond can also contribute to overdamping of the collective modes along the (π,0)/(0, π) direction at higher energies due to inelastic scattering of the collective modes. Specifically, longitudinal optical phonon modes arise in the energy range between 45–55meV in cuprates [149] and can be expected to damp the QP DW andQCDW collective excitations along the Cu-O bonding direction. Empirically, for|ω|>40meV, the mode with ordering wavevector of QSDW maintain its intensity over the entire energy range, whereas the intensity of QP DW andQCDW fades for|ω|>40meV. This observation lends credence to the interplay of phonons and the collective excitations. Therefore, it appears that PDWs, CDWs, SDWs, and phonons all contribute to the low-energy excitations in hole-type Y-123.
Based on the fact that we observe diffraction modes atQP DW,QCDW, andQSDW in Y-123, the
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Figure 5.12: Intensity plots of FT-LDOS-vs.-k along the nodal direction in Y-123 at H = 0, 5T.
Left panel: Intensity plot of FT-LDOS-vs.-k along the nodal direction for H = 0 in Y-123. The energy-independent diffraction spot,QSDW, is indicated by a thick dashed line. Energy-dependent modes are shown as a thin dotted lines, while the dispersive energy-dependent modes modulated by reciprocal lattice vectors are shown as thinner dotted lines. The fact that we observe the energy- dependent diffraction patterns modulated by the reciprocal lattice vectors indicates that our sample surface is clean and kis a good quantum number. Right panel: Intensity plot of FT-LDOS-vs.-k along the nodal direction for H = 5T in Y-123. The energy-independent mode,QSDW, is indicated by a thick dashed line. Energy-dependent patterns are shown as a thin dotted lines, while the dispersive energy-dependent diffraction modes modulated by reciprocal lattice vectors are shown as thinner dotted lines.
ground state of Y-123 appears inconsistent with notion that “one-gap”, due to superconductivity alone, can account for all the excitations observed. In fact, we observe both disordered pairs, in the form of PDWs, and competing orders, in the form of CDWs and SDWs, as relevant excitations of the ground state of Y-123.