Method for measuring the momentum-dependent relative phase of the superconducting gap of high-temperature superconductors

The phase variation of the superconducting gap over the (normal) Fermi surface of the high-temperature superconductors remains a significant unresolved question. Is the phase of the gap constant, does it change sign, or is it perhaps complex? A detailed answer to this question would provide important constraints on various pairing mechanisms. Here we propose a new method for measuring the relative gap phase on the Fermi surface which is direct, is angle-resolved, and probes the bulk. The required experiments involve measuring phonon linewidths in the normal and superconducting state, with resolution available in current facilities. We primarily address ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$ ${\mathrm{CuO}}_4$ material, but also propose a more detailed study of a specific phonon in ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$.