Mottness in high-temperature copper-oxide superconductors

The standard theory of metals, Fermi liquid theory, hinges on the key assumption that although the electrons interact, the low-energy excitation spectrum stands in a one-to-one correspondence with that of a non-interacting system. In the normal state of the copper-oxide high-temperature superconductors, drastic deviations from the Fermi liquid picture are obtained, highlighted by a pseudogap, broad spectral features and T-linear resistivity. A successful theory in this context must confront the highly constraining scaling argument which establishes that all 4-Fermi interactions are irrelevant ( except for pairing) at a Fermi surface. This argument lays plain that new low-energy degrees of freedom are necessary. This paper focuses on the series of experiments on copper-oxide superconductors which reveal that the number of low-energy addition states per electron per spin exceeds unity, in direct violation of the key Fermi liquid tenet. These experiments point to new degrees of freedom, not made out of the elemental excitations, as the key mechanism by which Fermi liquid theory breaks down in the cuprates. A recent theoretical advance which permits an explicit integration of the high-energy scale in the standard model for the cuprates reveals the source of the new dynamical degrees of freedom at low energies, a charge 2e bosonic field which has nothing to do with pairing but rather represents the mixing with the high-energy scales. We demonstrate explicitly that at half-filling, this new degree of freedom provides a dynamical mechanism for the generation of the charge gap and antiferromagnetism in the insulating phase. At finite doping, many of the anomalies of the normal state of the cuprates including the pseudogap, T-linear resistivity and the mid-infrared band are reproduced. A possible route to superconductivity is explored.