Topological invariant of multilayer Haldane models with irregular stackings

Abstract

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 for irregular stacking(except AA), and interlayer hoppings do not induce direct gap closing or phase transitions. However, if the next-to-nearest hopping is taken into account, phase transitions can occur.