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Determining of bosons (phonon or magnetic modes) which play an important role in the electron-boson interaction (EBI) and making pairs in HTSCs has been complicated, because different aspects of experimental evidences such as ARPES and optical spectroscopy could be interpreted by one of these bosons. Recently atomic-resolution STM study of Bi-2212 has been done by a group of scientists from the USA and Japan indicates phonon is the boson. They have studied the dI/dV and d²I/dV² spectra for Bi2212 in different doping value (0.12-0.24 of hole concentration) which give information about the superconducting gap ∆ and boson energy Ω. Because ∆ is inhomogeneous in atomic scale, the atomic scale information of Ω and their correlation also give valuable information.

Their most important results could be summarized as:

•  Ω(r)=Π(r)-∆(r) [Π(r) is the position of peak in  the d²I/dV² and r is the position on the surface] is heterogeneous at ~2nm scale in the range of 40-65 meV (Fig. 1a&b). The mean value of Ω(r) is < Ω(r)>=52 meV with a statistical spread of ±8 meV in consistent with the value for antinodal EBI in ARPES.  

• There is no spatially periodic structure in unprocessed d²I/dV², but this is maybe due to the strong special disorder of ∆(r). However the Γ(r)=∑_ω=40 ⁶⁵ d²I/dV²(r,ω) [ω(r)= E-∆(r) and integrated is because of enhancing the their spatial contrast] shows modulations parallel to the Cu-O bond direction with wavelength ~5a and correlation length of ~50 Å (Fig. 2). The Fourier transform Γ(q) determines the modulation wavevector as P₁≈2π/a[(0.2,0);(0,0.2)]±0.15.

• The modulation of d²I/dV² can be calculated by considering scattering of electronic states due to atomic-scale variations in the pair potential and considering phonons for bosons, which is consistent with the experimental data.     

• Although both <Π(r)> and <∆(r)> change rapidly with doping, the <Ω(r)>=52±1 meV is almost constant with doping (Fig. 4). Changes occur in spatial correlation of Ω(r), but both of the Γ(r) modulation and <Ω(r)> are independent of hole doping.

• Completely substituted of ¹⁶O by ¹⁸O in some different samples indicate that the histogram of Ω(r)-∆(r) shifted downward by several meV (Fig. 5a). Quantitative analysis indicates that this value is -3.7±0.8 meV (~6 % of <Ω(r)&gt which is near the value expected for lattice vibrational modes involving the O atom (1-√16/18). This effect happens for both filled E=-(∆+Ω) and empty E=(∆+Ω) states, as expected from strongly coupling theory of superconductivity.

• Whereas the zero-displacement correlation O(r):∆(r)≈+0.35 [O(r) is the dopant atom location] and Ω(r):∆(r)≈-0.30 (Fig. 3), Ω(r) and O(r) are uncorrelated (Fig. 5c). Therefore correlation between Ω(r) and ∆(r) cannot be occurring trivially, through a similar effect of dopant disorder on both.