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

TL;DR

This paper models high-energy boson features in cuprate superconductor spectra using a weak-coupling approach, enabling extraction of boson properties and assessing its role in superconductivity.

Contribution

It introduces an analytic fitting form for boson features in STM spectra, allowing estimation of boson frequency and coupling strength, and evaluates the boson's limited role in superconductivity.

Findings

Boson mode's frequency estimated from spectra.

Electron-boson coupling strength found to be weak.

Boson contributes less than 20% to the observed gap.

Abstract

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.