Pairing fluctuations determine low energy electronic spectra in cuprate superconductors

Over the years, Angle Resolved Photo Emission Spectroscopy (ARPES) has uncovered a number of unusual spectral properties of near Fermi energy electrons with definite in-plane momenta in the hole doped cuprates. We describe here a minimal theory of tight binding electrons moving on the square planar Cu lattice of the cuprates, mixed quantum mechanically with pairs of them (Cooper pairs); superconductivity occurring at $T_c$ is their long range ($d$-wave symmetry) phase coherence. Fluctuations necessarily associated with incipient long range superconducting order have a generic large distance behavior near $T_c$. We calculate the spectral density of electrons coupled to such Cooper pair fluctuations and show that properties observed in ARPES above $T_c$ for different cuprates as a function of doping $x$ and temperature $T$ emerge inevitably; e.g. the `Fermi arcs' with $T$ dependent length and an antinodal pseudogap which fills up linearly as $T$ increases towards the pseudogap temperature $T^*$. Below $T_c$, the effects of nonzero superfluid density and thermal fluctuations are calculated and compared successfully with experiment.