Algebraic Fermi Liquid from Phase Fluctuations: “Topological” Fermions, Vortex “Berryons,” andQED3Theory of Cuprate Superconductors

Within the phase fluctuation model for the pseudogap state of cuprate superconductors we identify a novel statistical “Berry phase” interaction between the nodal quasiparticles and fluctuating vortex-antivortex excitations. The effective action describing this model assumes the form of an anisotropic Euclidean quantum electrodynamics in $(2+1)$ dimensions $\left(\mathrm{QED}{}_3\right)$ and naturally generates non-Fermi liquid behavior for its fermionic excitations. The doping axis in the $x-T$ phase diagram emerges as a quantum critical line which regulates the low energy fermiology.