Flat Bands and Ferrimagnetic Order in Electronically Correlated Dice-Lattice Ribbons

TL;DR

This paper investigates dice-lattice ribbons, revealing flat bands, topological edge states, and ferrimagnetic order induced by electron correlations, demonstrating their potential for exploring topology and correlation effects in quantum materials.

Contribution

It provides a comprehensive analysis of topological properties and correlation effects in dice-lattice ribbons, including flat bands, edge states, and magnetic order, extending understanding from 2D to quasi-1D systems.

Findings

Flat bands persist in dice ladders with few legs.

Hubbard U induces flat band splitting and ferrimagnetic order.

Dice ladders exhibit topological edge states and nonzero Hall conductance.

Abstract

We study ribbons of the dice two-dimensional lattice (that we call ``dice ladders'') known to have nontrivial topological properties, such as Chern numbers 2 [Wang and Y. Ran, Phys. Rev. B {\bf 84}, 241103 (2011)]. Our main results are two folded: (1) Analyzing the tight-binding model in the presence of Rashba spin-orbit coupling and an external magnetic field, we observed that dice ladders qualitatively display properties similar to their two-dimensional counterpart all the way to the limit of only two legs in the short direction. This includes flat bands near the Fermi level, edge currents and edge charge localization near zero energy when open boundary conditions are used, two chiral edge modes, and a nonzero Hall conductance. (2) We studied the effect of Hubbard correlation $U$ in the two-leg dice ladder using Lanczos and density matrix renormalization group techniques. We show that increasing $U$ the flat bands split without the need of introducing external fields. Moreover, robust ferrimagnetic order develops. Overall, our work establishes dice ladders as a promising playground to study the combined effect of topology and correlation effects, one of the frontiers in Quantum Materials.