Universal relationship between the energy scales of the pseudogap phase, the superconducting state and the charge density wave order in copper oxide superconductors

We report the hole doping dependencies of the pseudogap phase energy scale, $2{\mathrm{\Delta }}_{\mathrm{P}\mathrm{G}}$, the anti-nodal (nodal) superconducting energy scales $2{\mathrm{\Delta }}_{\mathrm{S}\mathrm{C}}^{AN}$ ($2{\mathrm{\Delta }}_{\mathrm{S}\mathrm{C}}^N$) and the charge density wave energy scale, $2{\mathrm{\Delta }}_{\mathrm{C}\mathrm{D}\mathrm{W}}$. They have been extracted from the electronic Raman responses of distinct copper oxide families. For all the cuprates studied, we reveal universal doping dependencies which suggest that $2{\mathrm{\Delta }}_{\mathrm{P}\mathrm{G}}$, $2{\mathrm{\Delta }}_{\mathrm{S}\mathrm{C}}^{AN}$ and $2{\mathrm{\Delta }}_{\mathrm{C}\mathrm{D}\mathrm{W}}$ are governed by common microscopic interactions and that these interactions become relevant well above the superconducting transition at $T_c$. In sharp contrast, $2{\mathrm{\Delta }}_{\mathrm{S}\mathrm{C}}^N$ tracks the doping dependence of $T_c$, appearing to be controlled by a different kind of interactions than the energy scales above.