Distant-Neighbor Hopping in Graphene and Haldane Models

TL;DR

This paper explores how long-distance hopping in graphene and Haldane models enables the realization of large Chern number phases by manipulating Dirac points and band touchings, expanding the topological phase space.

Contribution

It introduces the concept of distant-neighbor hopping to control Dirac point multiplicity and topological phases in graphene-based models.

Findings

Long-distance hopping leads to supermerging band touchings.

Distant-neighbor hoppings enable large Chern number phases.

Energy dispersion often exceeds the topological charge.

Abstract

Large Chern number phases in a Haldane model become possible if there is a multiplication of Dirac points in the underlying graphene model. This is realized by considering long-distance hopping integrals. Through variation of these integrals, it is possible to arrive at supermerging band touchings, which up to N7 graphene are unique in parameter space. They result from the synchronized motion of all supplementary Dirac points into the regular +/-K points of graphene. The energy dispersion power law is usually larger than the topological charge associated with them. Moreover, adding distant-neighbor hoppings in the Haldane mass allows one to sweep large Chern number phases in the topological insulator.