Topological invariant of multilayer Haldane models with irregular stackings

TL;DR

This paper proves that in multilayer Haldane models with irregular stacking, the topological invariant scales linearly with the number of layers and remains unaffected by stacking irregularities or interlayer hoppings.

Contribution

It establishes that the topological invariant in multilayer Haldane models is proportional to the number of layers and is robust against stacking irregularities and interlayer couplings.

Findings

Topological invariant equals number of layers times monolayer invariant

Interlayer hoppings do not cause gap closing or phase transitions

Stacking irregularities do not affect the topological invariant

Abstract

We study multilayer Haldane models with irregular type of stacking, considering the nearest interlayer hopping. We prove that the value of the topological invariant is equal to the number of layers times the value of the topological invariant of monolayer Haldane model, regardless of stacking type, and interlayer hoppings do not induce gap closing and phase transitions.