Such a feedback has a sign-reversed eigenenergy, , and is expressed by , where Θ(t), Δ k , γ k and Γ k denote the step function, the particle-hole off-diagonal element, and the scattering rates of the

intermediate and bare-particle states, respectively. The Fourier transform of Σ k (t) gives the frequency representation of the self-energy of the BQPs, (3) Figure 1 shows the ARPES spectra of BQPs for underdoped and overdoped Bi2212 samples with T c = 66 and 80 K (UD66 and OD80, respectively) [8]. As shown in Figure 1b,c, an energy distribution curve was extracted from the minimum PI3K Inhibitor Library gap locus for each off-node angle θ and symmetrized with respect to the Fermi energy ω = 0. These spectra were well fitted with a phenomenological function, (4) except for a featureless background. Equation 4 is deduced from Equation

3 and , neglecting γ k after Norman et al. [11]. Figure 1b,c exemplifies that the superconducting gap energy Δ at each θ is definitely determined by sharp spectral peaks. In Figure 1d,e, the obtained gap energies (small yellow circles) are plotted over the image of spectral intensity as a Mocetinostat research buy function of sin 2θ, so that the deviation from a d-wave gap is readily seen with reference to a straight line. While the superconducting gap of the overdoped sample almost follows the d-wave line, that of the underdoped PXD101 sample is deeply curved against sin 2θ. Furthermore, Figure 1d indicates that the deviation from the d-wave gap penetrates into the close vicinity of the node and that it is difficult to define the pure d-wave region near the node. Therefore, the next-order harmonic term, sin 6θ, has been introduced, so that the smooth experimental gap profile is properly parametrized [12–14]. The next-order high-harmonic function is also expressed as Δ(θ) = ΔN sin 2θ + (Δ∗-ΔN)(3 sin 2θ- sin 6θ)/4, where the antinodal and nodal gap energies are defined as Δ∗ = Δ(θ)| θ=45° and , respectively, so that ΔN/Δ∗ = 1 is satisfied for a pure d-wave gap. Figure 1 Superconducting

gap manifested in BQP spectra. The data are for underdoped and overdoped Bi2212 samples with T c = 66 and 80 K (UD66 and OD80, respectively) [8]. (a) Momentum-space diagram for an off-node Vildagliptin angle, θ, and a bonding-band (BB) Fermi surface along which the ARPES spectra were taken. (b, c) Symmetrized energy distribution curves (colored circles) and their fits (black curves). (d, e) ARPES spectral images as a function of energy ω and sin 2θ. Superimposed are the gap energies (yellow circles) and high-harmonic fit (yellow curve) as functions of sin 2θ. The doping dependences of the superconducting gap parameters are summarized in Figure 2. One can see from Figure 2a that as hole concentration decreases with underdoping, the nodal gap energy 2ΔN closely follows the downward curve of 8.5k B T c in contrast to the monotonic increase in the antinodal gap energy 2Δ∗.