Topological insulators and fractional quantum Hall effect on the ruby lattice

TL;DR

This paper investigates a tight-binding model on the ruby lattice, revealing topological insulator phases and flat bands with high Chern numbers, which could facilitate fractional quantum Hall effects and other exotic states.

Contribution

It introduces a detailed phase diagram of the ruby lattice model, highlighting flat bands with finite Chern numbers suitable for fractional quantum Hall states.

Findings

Presence of topological insulating phases driven by spin-orbit interactions.

Discovery of flat bands with high Chern numbers (~70 ratio of gap to width).

Potential realization of fractional quantum Hall effect in engineered ruby lattice systems.

Abstract

We study a tight-binding model on the two-dimensional ruby lattice. This lattice supports several types of first and second neighbor spin-dependent hopping parameters in an $s$-band model that preserves time-reversal symmetry. We discuss the phase diagram of this model for various values of the hopping parameters and filling fractions, and note an interesting competition between spin-orbit terms that individually would drive the system to a $Z_2$ topological insulating phase. We also discuss a closely related spin-polarized model with only first and second neighbor hoppings and show that extremely flat bands with finite Chern numbers result, with a ratio of the band gap to the band width approximately 70. Such flat bands are an ideal platform to realize a fractional quantum Hall effect at appropriate filling fractions. The ruby lattice can be possibly engineered in optical lattices, and may open the door to studies of transitions between quantum spin liquids, topological insulators, and integer and fractional quantum Hall states.