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

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.

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• Tunable valley filtering in dynamically strained $\alpha$-${\mathcal{T}}_3$ lattices
• Holstein polaron in a pseudospin-$1$ quantum spin Hall system: first and second order topological phase transitions
• One-dimensional flat bands and Dirac cones in narrow zigzag dice lattice ribbons
• Experimental realization of dice-lattice flat band at the Fermi level in layered electride YCl
• Generation of isolated flat bands with tunable numbers through Moiré engineering
• Zigzag dice lattice ribbons: Distinct edge morphologies and structure-spectrum correspondences
• Current distribution and group velocities for electronic states on $\alpha -{\mathcal{T}}_3$ lattice ribbons in a magnetic field