Evidence for pairing above Tc from the electronic dispersion in the pseudogap phase of cuprates

In the BCS paradigm for the superconducting state, electrons close to the Fermi level $E_{F}$ form Cooper pairs which condense into a zero center of mass momentum state. This results in a gap in the electronic excitation spectrum which is symmetrically centered about $E_{F}$. Above $T_{c}$ where the condensate is lost, the pairs dissociate, the energy gap collapses, and the the normal state Fermi surface appears. On the other hand, in the underdoped high temperature superconductors, instead of a complete Fermi surface above $T_{c}$, only disconnected Fermi arcs appear, separated by regions that still exhibit an energy (pseudo)gap. We show that in this pseudogap phase, the energy-momentum relation of electronic excitations near $E_{F}$ behaves like the dispersion of a normal metal on the Fermi arcs, but like that of a superconductor in the gapped regions. We argue that this dichotomy in the dispersion is hard to reconcile with a competing order parameter, but is consistent with pairing without condensation. Below $T_{c}$ the pairs condense and the electronic excitations, that were short-lived above $T_{c}$, become long-lived and exhibit a d-wave energy gap.