5.4 Discussion
5.4.2 The origin of the pseudogap and subgap energies in vortex cores of hole-type cuprateshole-type cuprates
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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.
5.4.2 The origin of the pseudogap and subgap energies in vortex cores of
indicate the pseudogap is due to disordered pairing above TC. The data in Y-123 for supporting this argument are in fact only one doping level at optimal doping [150], and the analysis in Ref. [150]
suggests that a single superconducting gap, which does not change in energy, may be used to account for the observed quasiparticle tunneling spectra up to TC in Y-123. This point is made because the gap width does not appear to change much in Y-123 until above TC, when the gapped quasiparticle spectra disappears. We observe this same behavior in our Y-123 data as shown in Fig. 5.2; however, our model of coexisting superconductivity and competing orders (SC/CO) can quantitatively account for the observed behavior as temperature increases in Y-123, such that the observed gap does not appear to change much with increasing temperature because of the presence of a larger competing energy gap above TC. In addtion, our SC/CO model accounts for the observed satellite features in Y-123 for T TC, while the hand-waving assertion of one superconducting gap [150] fails to account for either the presence of the satellite features or the quantitative temperature-dependent evolution of both the coherence peaks and the satellite features.
Furthermore, conclusions made regarding the scaling between the pseudogap for T > TC and the peak-to-peak gap, ∆pk−pk for T TC in Bi-2212 and Bi-2201 must be brought to question because, unlike Y-123, ∆pk−pkis highly inhomogeneous in Bi-2212 and is not necessarily associated with the superconducting gap, as is shown more fully in Chapter 7. Additionally, the ∆pk−pk gap maps in Bi-2212 [99] and (Bi1−yPby)2Sr2CuO6+x[(BiPb)-2201] [4] show nanoscale variations on the order of 10meV or greater. The large variations are generally associated with rounded pseudogap like features, in sharp contrast to the highly homogeneous coherence peaks observed in Y-123, as illustrated in Fig. 5.3. The issue of questionable identification of the superconducting gap simply
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Figure 5.13: Energy dispersion relations of energy dependent diffraction modes in Y-123. (a) The energy dispersion relations and uncertainties of|q1|,|q2|, |q3|,|q6|, and|q7|obtained in Y-123 are shown. We use the notation convention from Ref. [99]. (b) Visual representation of the notation from Ref. [99]. [Figure in (b) reproduced from Ref. [99].]
by the peak-to-peak features in Bi-2212 is further corroborated by recent studies of the (BiPb)- 2201 spectra [4]. In (BiPb)-2201, the authors of Ref. [4] showed that the average ∆pk−pk'16meV observed in (BiPb)-2201 for T TC evolved into the pseudogap spectra, with gap of ∼16meV above TC. However, further analysis revealed a spectrum with coherence peaks at a smaller energy
∆N '6.7meV well below TC by normalizing away the pseudogap background spectra found above TC. It was further found that with increasing temperature, the smaller energy gap in the normalized spectra did close at TC. In agreement with these findings, our analysis from Chapter 7 indicates that the average quasiparticle spectra for T TC in Bi-2212 may be modeled using coexisting SC/CO such that the rounded pseudogap-like features are in fact associated with the effective gap
∆ef f = ∆pk−pkfor TTC, and are due to contributions from both superconductivity and disorder- pinned competing orders. Our model assumes that the competing order persists above TC to T*, that the competing order energy, VCO, exceeds ∆SC, and that disorder in Bi-2212 contributes to an increase in spectral weight for the effective gap features. For heavily underdoped Bi-2212, VCO
∆SC leading to ∆ef f ∼VCO, which naturally leads to an empirical observation of a linear relationship between ∆ef f = ∆pk−pk and the pseudogap as a function of doping because the competing order energy, VCO, is the cause of the pseudogap.
The second argument that the pseudogap arises from a ground state of superconductivity alone
intra-vortex spectra, as shown in Figs. 5.3 and 5.5, respectively, and indicateVP G>∆SC = ∆pk−pk. In contrast, we observe intra-vortex pseudogap energies VP Gthat obey VP G <∆ef f = ∆pk−pk in La-112. In fact, we find in Chapter 7 that the differences in La-112 and Y-123 can be accounted for by using a coexisting SC/CO model if VCO >∆SC in Y-123 and VCO <∆SC in La-112, but there is no natural explanation for the differences in the shift of the quasiparticle energies in La-112 and Y-123 based on a ground state of pure superconductivity alone. In fact, we find the empirical value VP G'32meV in vortex cores in Y-123 agrees with the competing order energy VCO = 32meV derived from our SC/CO fitting of the satellite features in the T=6K zero field quasiparticle spectra of Fig. 5.2. Specifically, the fitting yields a competing order of a CDW with VCO=32meV and
|Q|CO=(0.25±0.03)πalong the Cu-O bonding direction, and the competing order wavevector is in further agreement with the QCDW value observed in the FT-LDOS.
Finally, the subgap energy observed in the vortex cores of hole-type cuprates has also been attributed to arising from superconductivity alone in a phenomenological model [32] to explain the apparent linear relationship between ∆0 and ∆pk−pk observed in Bi-2212 and in one measurement on optimally doped Y-123 [19, 3]. While the subgap energy can essentially arise from disordered pairs, possibly in the form of a PDW, we find that the assumed equivalence between VP Gand ∆SC is not consistent with our histograms of spatially resolved ∆pk−pkvalues in Y-123. As we have seen from our ∆pk−pk histograms as a function of magnetic field, the energy scales of VP G and ∆SC differ by∼7−12meV in Y-123, and this “one-gap” model cannot account for the presence of these two distinctly different energy scales at T TC. Furthermore, the linear relationship between
∆0 and ∆pk−pk observed in Bi-2212 may imply that the ∆0 and VP G have a similar origin since
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Figure 5.14: Low energy summed FT-LDOS at H = 3T in Y-123. The FT-LDOS,|F(k,ω,H=3T)|, shown in Y-123 is summed from ω=-1meV to ω=-30meV. The energy independent spots QP DW, QCDW, andQSDW at H = 3T in Y-123 are indicated by circles in the figure.
∆ef f = ∆pk−pk ∼VP G for underdoped Bi-2212, as pointed out in the discussion above. However, the assertion of the “one-gap” model that both features can be explained by superconductivity alone does not seem applicable to Y-123 based on our analysis of the energy scales of ∆SC, ∆ef f, ∆0, and VP G.