Resonant Raman scattering in mercurate single crystals

We report resonant electronic Raman scattering in optimally doped single layer HgBa${}_2$CuO${}_{4+\delta }$ (Hg-1201) and trilayer HgBa${}_2$Ca${}_2$Cu${}_3$O${}_{8+\delta }$ (Hg-1223) single crystals. Analysis of the $B_{1g}$ and B${}_{2g}$ channels in the superconducting state of Hg-1201 advocates for a gap having d-wave symmetry. In addition a resonant study $B_{1g}$ pair-breaking peak and the $A_{1g}$ peak suggests that the $A_{1g}$ peak is not directly related to the d-wave superconducting gap amplitude. Comparison with trilayer Hg-1223 demonstrates the universal behavior of this two energy scales in optimally doped cuprates.