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Microwave conductivity experiments can directly measure the quasiparticlescattering rate in the superconducting state. We show that this, combined withknowledge of the Fermi surface geometry, allows one to distinguish betweenclosely related superconducting order parameters, e.g., d$_{x^2-y^2}$ andd$_{xy}$ superconductivity. We benchmark this method onYBa$_2$Cu$_3$O$_{7-\delta}$ and, unsurprisingly, confirm that this is ad$_{x^2-y^2}$ superconductor. We then apply our method to$\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br, which we discover is a d$_{xy}$superconductor.

Microwave Conductivity Distinguishes Between Different d-wave States: Umklapp Scattering in Unconventional Superconductors