Mottness on a triangular lattice

TL;DR

This paper investigates the Hubbard model on a triangular lattice using CDMFT and NCA, revealing a non-Fermi liquid quasi-dispersionless band, a doping-dependent metal-insulator transition, and proposing a new pseudogap framework.

Contribution

It introduces a novel framework for understanding pseudogap phenomena based on momentum-dependent low-energy physics without long-range order.

Findings

Discovery of a quasi-dispersionless band at low doping.

Identification of a weakly doping-dependent metal-insulator transition at Uc.

Prediction of pseudogap existence in weakly hole-doped regimes.

Abstract

We study the physics on the paramagnetic side of the phase diagram of the cobaltates, $Na_{x}CoO_{2}$, with an implementation of cellular dynamical mean field theory (CDMFT) with the non-crossing approximation (NCA) for the one-band Hubbard model on a triangular lattice. At low doping we find that the low energy physics is dominated by a quasi-dispersionless band. At half-filling, we find a metal-insulator transition at $U_{c}=5.6\pm0.15t$ which depends weakly on the cluster size. The onset of the metallic state occurs through the growth of a coherence peak at the chemical potential. Away from half filling, in the electron-doped regime, the system is metallic with a large, continuous Fermi surface as seen experimentally. Upon hole doping, a quasi non-dispersing band emerges at the top of the lower Hubbard band and controls the low-energy physics. This band is a clear signature of non-Fermi liquid behavior and cannot be captured by any weakly coupled approach. This quasi non-dispersive band, which persists in a certain range of dopings, has been observed experimentally. We also investigate the pseudogap phenomenon in the context of a triangular lattice and we propose a new framework for discussing the pseudogap phenomena in general. This framework involves a momentum-dependent characterization of the low-energy physics and links the appearance of the pseudogap to a reconstruction of the Fermi surface without invoking any long range order or symmetry breaking. Within this framework we predict the existence of a pseudogap for the two dimensional Hubbard model on a triangular lattice in the weakly hole-doped regime.