2017/03/24 by Saurabh Maiti, Andrey Chubukov, P. J. Hirschfeld
Physics and Astronomy · #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.96.014503
published as Phys. Rev. B 96, 014503 (2017) · 19pp; 8figs; References to more old work added
arxiv created 2017/03/24 · arxiv updated 2017/07/12
We present a microscopic theory for the Raman response of a clean multiband superconductor accounting for the effects of vertex corrections and long-range Coulomb interaction. The measured Raman intensity, R(Ω), is proportional to the imaginary part of the fully renormalized particle-hole correlator with Raman form-factors γ( k). In a BCS superconductor, a bare Raman bubble is non-zero for any γ( k) and diverges at Ω= 2Δ+0, where Δ is the largest gap along the Fermi surface. However, for γ( k) = const, the full R(Ω) is expected to vanish due to particle number conservation. It was long thought that this vanishing is due to the singular screening by long-range Coulomb interaction. We argue that this vanishing actually holds due to vertex corrections from the same short-range interaction that gives rise to superconductivity. We further argue that long-range Coulomb interaction does not affect the Raman signal for any γ( k). We argue that vertex corrections eliminate the divergence at 2Δ and replace it with a maximum at a somewhat larger frequency. We also argue that vertex corrections give rise to sharp peaks in R(Ω) at Ω< 2Δ, when Ω coincides with the frequency of one of collective modes in a superconductor, e.g, Leggett mode, Bardasis-Schrieffer mode, or an excitonic mode.