Quasiparticle dispersion in the cuprate superconductors and the two-dimensional Hubbard model

Characteristics of the Mott transition and electronic states of high-temperature cuprate superconductors from the perspective of the Hubbard model

A fundamental issue of the Mott transition is how electrons behaving as single particles carrying spin and charge in a metal change into those exhibiting separated spin and charge excitations (low-energy spin excitation and high-energy charge excitation) in a Mott insulator. This issue has attracted considerable attention particularly in relation to high-temperature cuprate superconductors, which exhibit electronic states near the Mott transition that are difficult to explain in conventional pictures. Here, from a new viewpoint of the Mott transition based on analyses of the Hubbard model, we review anomalous features observed in high-temperature cuprate superconductors near the Mott transition.

Mott transition in the two-dimensional Hubbard model

Spectral properties of the two-dimensional Hubbard model near the Mott transition are investigated by using cluster perturbation theory. The Mott transition is characterized by freezing of the charge degrees of freedom in a single-particle excitation that leads continuously to the magnetic excitation of the Mott insulator. Various anomalous spectral features observed in cuprate high-temperature superconductors are explained in a unified manner as properties near the Mott transition.

Marginal fermi liquid theory in the Hubbard model

We find marginal-Fermi-liquid- (MFL) like behavior in the Hubbard model on a square lattice for a range of hole doping and on-site interaction parameter U. Thereby we use a self-consistent projection operator method. It enables us to compute the momentum and frequency dependence of the single-particle excitations with high resolution. The Fermi surface is found to be holelike in the underdoped regime and electronlike in the overdoped regime. Our calculations concern normal state properties of the system. When a comparison is possible, we find consistency with finite temperature quantum Monte Carlo results. We also find a discontinuous change with doping concentration from a MFL to a Fermi-liquid behavior resulting from a collapse of the lower Hubbard band. This renders Luttinger's theorem inapplicable in the underdoped regime.

Single-particle spectrum in the electron-doped cuprates

We study the evolution of the single-particle spectrum with electron doping in a scheme which adds multiple exchange of transverse spin excitations to the mean-field antiferromagnetic insulator. Away from half-filling small Fermi surface pockets appear first around the X points, and simultaneously new spectral weight grows in the insulating gap. With further doping the in-gap states develop the character of a renormalized quasiparticle band near the chemical potential. The essential features in momentum-energy space agree well with recent studies using angle-resolved photoemission spectroscopy on electron-doped cuprates. We interpret the origins and the nature of the in-gap states using a simple variational wave function.

Superconductivity from flat dispersion designed in doped mott insulators

Routes to enhance superconducting instability are explored for doped Mott insulators. With the help of insight for criticalities of metal-insulator transitions, geometrical design of lattice structure is proposed to control the instability. A guideline is to explicitly make flat band dispersions near the Fermi level without suppressing two-particle channels. In a one-dimensional model, numerical studies show that our prescription with finite-ranged hoppings realizes large enhancement of spin-gap and pairing dominant regions. We also propose several multiband systems, where the pairing is driven by intersite Coulomb repulsion.