Mottness

We review several of the normal state properties of the cuprates in an attempt to establish an organizing principle from which pseudogap phenomena, broad spectral features, T-linear resistivity, and spectral weight transfer emerge. We first show that standard field theories with a single critical length scale cannot capture the T-linear resistivity as long as the charge carriers are critical. What seems to be missing is an additional length scale, which may or may not be critical. Second, we prove a generalised version of Luttinger’s theorem for a Mott insulator. In particular, we show that for Mott insulators, regardless of the spatial dimension, the Fermi surface of the non-interacting system is converted into a surface of zeros of the single-particle Green function when the underlying band structure has particle-hole symmetry. Only in the presence of particle-hole symmetry does the volume of the surface of zeros equal the particle density. The surface of zeros persists at finite doping and is shown to provide a framework from which pseudogaps, broad spectral features, spectral weight transfer on the Mott gap scale, and the additional length scale required to capture T-linear resistivity can be understood.