$B_{\rm 1g}$ phonon anomaly driven by Fermi surface instability at intermediate temperature in YBa$_2$Cu$_3$O$_{7-\delta}$

We performed temperature- and doping-dependent high-resolution Raman spectroscopy experiments on YBa$_2$Cu$_3$O$_{7-\delta}$ to study $B$$_{\rm 1g}$ phonons. The temperature dependence of the real part of the phonon self-energy shows a distinct kink at $T=T_{\rm B1g}$ above $T$$_{\rm c}$ due to softening, in addition to the one due to the onset of the superconductivity. $T$$_{\rm B1g}$ is clearly different from the pseudogap temperature with a maximum in the underdoped region. The region between $T$$_{\rm B1g}$ and $T$$_{\rm c}$ resembles that of superconducting fluctuation or charge density wave order. While the true origin of the $B$$_{\rm 1g}$ phonon softening is not known, we can attribute it to a gap on the Fermi surface due to an electronic order. Our results may reveal the role of the $B$$_{\rm 1g}$ phonon not only in the superconducting state but also in the intertwined orders in multilayer copper oxide high-$T$$_{\rm c}$ superconductors.