Bilayer Haldane system: Topological characterization and adiabatic passages connecting Chern phases

Abstract

We present a complete topological characterization of a bilayer composite of two Chern insulators (specifically, Haldane models) and explicitly establish the bulk-boundary correspondences. We show that an appropriately defined Chern number accurately maps out all the possible phases of the system and remains well defined even in the presence of degeneracies in the occupied bands. Importantly, our result paves the way for realizing adiabatic preparation of monolayer Chern insulators. This has been a major challenge to date, given the impossibility of unitarily connecting inequivalent topological phases. We show that this difficulty can be circumvented by adiabatically varying the interlayer coupling in such a way that the system remains gapped at all times. In particular, complete knowledge of the phase diagram of the bilayer composite immediately allows one to identify all such adiabatic passages which may connect the different Chern inequivalent phases of the individual monolayers.

Engineering Gapless Edge States from Antiferromagnetic Chern Homobilayer

“…We perceive that Haldane model is the first to put forward a model that can accomplish the QAHE . When two layers of the Haldane model are stacked, the aggregate Chern number of the bilayer equals the summation of Chern numbers for each layer. − If the chiralities of the two layers are opposite, resulting from oppositely broken time-reversal symmetry, scriptC = 0 can be achieved, i.e., leading to a vanishing Chern number . The Kane–Mele model discloses that the layer index can be replaced by the spin projection in nonmagnetic systems, and a nontrivial TI consisting of a pair of CIs with opposite chiralities is established .…”

“…56−58 If the chiralities of the two layers are opposite, resulting from oppositely broken time-reversal symmetry, = 0 can be achieved, i.e., leading to a vanishing Chern number. 57 The Kane−Mele model discloses that the layer index can be replaced by the spin projection in nonmagnetic systems, and a nontrivial TI consisting of a pair of CIs with opposite chiralities is established. 59 Accordingly, we argue that if the layer index and spin projection are coupled, that is, one layer has the majority of spin-up manifolds and the other layer has the equivalent spin-down manifolds, an AFM insulator can be obtained as illustrated in Figure 1(a); remarkably, topologically nontrivial characteristics of 2D stacked CIs are evidenced by the occurrence of helical edge states.…”

Stacking-induced Chern insulator

“…17 for the AA bilayer [18]. In particular, a vanishing Chern number C = 0 is expected if the layers have opposite chiralities resulting from oppositely broken TRS [17,18]. This expectation is at the heart of the Kane and Mele [19] idea, where the layer index is replaced by the spin projection and the two opposite TRS copies of the spin polorized HM give rise to a vanishing (Z) Chern number.…”