Mottness

TL;DR

This paper reviews the normal state properties of cuprates, proposing a new framework involving a surface of zeros in the Green function to explain pseudogaps, spectral features, and resistivity behaviors.

Contribution

It introduces a generalized Luttinger's theorem for Mott insulators and highlights the importance of an additional length scale for understanding $T$-linear resistivity.

Findings

Surface of zeros of Green function persists at finite doping

Generalized Luttinger's theorem applies to Mott insulators with particle-hole symmetry

Surface of zeros explains pseudogap phenomena and spectral weight transfer

Abstract

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. Namely, 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 Mott insulator posesses 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 can be understood.