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

Résumé

We report the hole doping dependencies of the pseudogap phase energy scale $2\Delta_{PG}$, the antinodal (nodal) superconducting energy scales $2\Delta^{AN}{SC}$ ($2\Delta^{N}{SC}$), and the charge-density-wave energy scale $2\Delta_{CDW}$ extracted from the electronic Raman responses of several copper oxide families. We show for all the cuprates studied that the three energy scales $2\Delta_{PG}$, $2\Delta^{AN}{SC}$, and $2\Delta{CDW}$ display the same decreasing monotonic behavior with doping. In particular, $2\Delta^{AN}{SC}$ and $2\Delta{CDW}$ have nearly equal values. This suggests a universal scenario in which $2\Delta_{PG}$, $2\Delta^{AN}{SC}$, and $2\Delta{CDW}$ are governed by common microscopic interactions that become relevant well above the superconducting transition at Tc. This is to be contrasted with the behavior of the nodal superconducting energy scale $2\Delta^{N}_{SC}$, which tracks the doping dependence of Tc and, hence, seems to be controlled by different interactions.