High temperature superconductivity emerges in the cuprate compounds upon
changing the electron density of an insulator in which the electron spins are
antiferromagnetically ordered. A key characteristic of the superconductor is
that electrons can be extracted from them at zero energy only if their momenta
take one of four specific values (the `nodal points'). A central enigma has
been the evolution of the zero energy electrons in the metallic state between
the antiferromagnet and the superconductor, and recent experiments yield
apparently contradictory results. The oscillation of the resistance in this
metal as a function of magnetic field indicate that the zero energy electrons
carry momenta which lie on elliptical `Fermi pockets', while ejection of
electrons by high intensity light indicates that the zero energy electrons have
momenta only along arc-like regions. We present a theory of new states of
matter, which we call `algebraic charge liquids', which arise naturally between
the antiferromagnet and the superconductor, and reconcile these observations.
Our theory also explains a puzzling dependence of the density of
superconducting electrons on the total electron density, and makes a number of
unique predictions for future experiments.Comment: 6+8 pages, 2 figures; (v2) Rewritten for broader accessibility; (v3)
corrected numerical error in Eq. (5