Surface Contribution to Raman Scattering from Layered Superconductors

TL;DR

This paper calculates how surface effects influence Raman scattering in layered superconductors, revealing significant modifications to the spectrum and potential surface plasmon modes, with implications for experimental detection.

Contribution

It extends the formalism of Raman scattering in superlattices to include surface contributions, showing their impact on the spectrum and identifying conditions where surface modes may be observed.

Findings

Surface contributions significantly modify the Raman spectrum below 2Δ.

Additional surface plasmon modes may appear above 2Δ.

Out-of-phase Cooper pair tunneling modes are unaffected by surface effects.

Abstract

Generalizing recent work, the Raman scattering intensity from a semi-infinite superconducting superlattice is calculated taking into account the surface contribution to the density response functions. Our work makes use of the formalism of Jain and Allen developed for normal superlattices. The surface contributions are shown to strongly modify the bulk contribution to the Raman-spectrum line shape below $2\Delta$, and also may give rise to additional surface plasmon modes above $2\Delta$. The interplay between the bulk and surface contribution is strongly dependent on the momentum transfer $q_\parallel$ parallel to layers. However, we argue that the scattering cross-section for the out-of-phase phase modes (which arise from interlayer Cooper pair tunneling) will not be affected and thus should be the only structure exhibited in the Raman spectrum below $2\Delta$ for relatively large $q_\parallel\sim 0.1\Delta/v_F$. The intensity is small but perhaps observable.