Electronic Raman scattering in superconductors as a probe of anisotropic electron pairing

Abstract

A gauge invariant theory for electronic Raman scattering for superconductors with anisotropic pairing symmetry is analyzed in detail. It is shown that Raman scattering in anisotropic superconductors provides a wealth of polarization-dependent information which probes the detailed angular dependence of the superconducting ground state order parameter. The Raman spectra shows a unique polarization dependence for various anisotropic pair- state symmetries which affects the peak position of the spectra and generates symmetry dependent low frequency and temperature power-laws which can be used to uniquely identify the magnitude and symmetry of the energy gap. In particular, we calculate the collective modes and the subsequent symmetry--dependent Raman spectra for a $d_{x^2-y^2}$ superconductor and compare our results to the relevant data on the cuprate systems as well as theoretical predictions for $s$--wave, anisotropic $s$--wave and $s+id$ energy gaps. Favorable agreement is shown with the predictions for $d_{x^2-y^2}$ pairing and the experimental data on YBa${}_2$Cu${}_3$O${}_7$, Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$ and Tl${}_2$Ba${}_2$CuO${}_6$.

53 pages, Revtex, t.p.d

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