Textured electronic states of the triangular lattice Hubbard model and Na$_x$CoO$_2$

TL;DR

This study explores the complex phase diagram of the triangular lattice Hubbard model, revealing novel spin-charge textures, phase transitions, and Fermi surface evolutions with doping, relevant to understanding cobaltate superconductivity.

Contribution

It uncovers new spin-charge ordered phases and Lifshitz transitions in the Hubbard model on a triangular lattice, expanding knowledge of correlated electron systems.

Findings

Identification of a novel spin-charge ordered insulator at x=1/3

Discovery of a Lifshitz transition between magnetic phases

Evolution of Fermi surface pockets with doping

Abstract

We show that geometric frustration and strong correlation in the triangular lattice Hubbard model lead a rich and novel phase structure of $\sqrt{3}\times\sqrt{3}$ spin-charge textured electronic states over a wide region of electron doping $0\le x \le 0.40$. In addition to the 120$^\circ$ N\'eel ordered insulator at half-filling, we found a novel spin-charge ordered insulator at $x=1/3$ with collinear antiferromagnetic (AF) order on the underlying unfrustrated honeycomb lattice. Separating the two insulating phases is a Lifshitz transition between a noncollinear AF ordered metal and one with coexisting charge order. We obtain the phase diagram and the evolution of the Fermi surface (FS). Remarkably, the correlated ground states near $x=1/3$ emerges as doping the "1/3 AF insulator" by excess carriers, leading to electron and hole FS pockets with important implications for the cobaltate superconducting state.