Three energy scales in the superconducting state of hole-doped cuprates detected by electronic Raman scattering

Abstract

We explore by electronic Raman scattering the superconducting state of the ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ (Bi-2212) crystal by performing a fine-tuned doping study. We find three distinct energy scales in ${A}_{1g}, {B}_{1g}$, and ${B}_{2g}$ symmetries which show three distinct doping dependencies. Above $p=0.22$, the three energies merge; below $p=0.12$, the ${A}_{1g}$ scale is no longer detectable, while the ${B}_{1g}$ and ${B}_{2g}$ scales become constant in energy. In between, the ${A}_{1g}$ and ${B}_{1g}$ scales increase monotonically with underdoping, while the ${B}_{2g}$ one exhibits a maximum at $p=0.16$. The three superconducting energy scales appear to be a universal feature of hole-doped cuprates. We propose that the nontrivial doping dependencies of the three scales originate from the Fermi-surface changes and reveal competing orders inside the superconducting dome.