Boson features in STM spectra of cuprate superconductors: Weak-coupling phenomenology

We derive the shape of the high-energy features due to a weakly coupled boson in cuprate superconductors, as seen experimentally in Bi_2 Sr_2 Ca_1 Cu_2 O_8+x (BSCCO) by Lee et al. [Nature (London) 442, 546 (2006)]. A simplified model is used of d-wave Bogoliubov quasiparticles coupled to Einstein oscillators with a momentum-independent electron-boson coupling and an analytic fitting form is derived, which allows us (a) to extract the boson mode's frequency and (b) to estimate the electron-boson coupling strength. We further calculate the maximum possible superconducting gap due to an Einstein oscillator with the extracted electron-boson coupling strength, which is found to be less than 0.2 times of the observed gap indicating at the observed boson's non-dominant role in the superconductivity's mechanism. The extracted momentum-independent electron-boson coupling parameter (that we show a posteriori to indeed be in the weak-coupling regime) is then to be interpreted as an (band-structure detail dependent weighted) average over the Brillouin zone of the actual momentum-dependent electron-boson coupling in BSCCO.