The electronic phase diagram of high temperature copper oxide superconductors

In order to understand the origin of high temperature superconductivity in copper oxides, we must understand the normal state from which it emerges. In this talk, we examine the evolution of the normal state electronic excitations with temperature and carrier concentration in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ using angle resolved photoemission (ARPES). In contrast to conventional superconductors, where there is a single temperature scale $T_c$ separating the normal from the su- perconducting state, the high temperature superconductors exhibit two additional temperature scales.  One is the pseudogap scale $T^*$, below which electronic excitations exhibit an energy gap. The second is the coherence scale $T_{coh}$, below which sharp spectral features appear due to increased lifetime of the excitations. We find that $T^*$ and $T_{coh}$ are strongly doping dependent, and cross each other near optimal doping. Thus the highest superconducting $T_c$

emerges from an unusual normal state that is characterized by coherent excitations with an energy gap.