Flat-band engineering in tight-binding models: Beyond the nearest-neighbor hopping

TL;DR

This paper introduces a method to tune flat-band energies in tight-binding models by adding farther-neighbor hoppings that depend solely on Manhattan distance, enabling precise energy control without losing flatness.

Contribution

The authors propose a novel approach to adjust flat-band energies in tight-binding models through Manhattan-distance-dependent hoppings, extending flat-band engineering beyond nearest-neighbor models.

Findings

Method successfully tunes flat-band energies in various lattice models.

Applicable to 2D kagome and 3D pyrochlore lattices and their variants.

Potential to enhance superconducting transition temperatures and realize topological phases.

Abstract

In typical flat-band models, defined as nearest-neighbor tight-binding models, flat bands are usually pinned to the special energies, such as top or bottom of dispersive bands, or band-crossing points. In this paper, we propose a simple method to tune the energy of flat bands without losing the exact flatness of the bands. The main idea is to add farther-neighbor hoppings to the original nearest-neighbor models, in such a way that the transfer integral depends only on the Manhattan distance. We apply this method to several lattice models including the two-dimensional kagome lattice and the three-dimensional pyrochlore lattice, as well as their breathing lattices and non-line graphs. The proposed method will be useful for engineering flat bands to generate desirable properties, such as enhancement of $T_c$ of superconductors and nontrivial topological orders.