Algebraic charge liquids

Understand

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.