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

TL;DR

This paper provides a comprehensive topological analysis of a bilayer Haldane system, establishing bulk-boundary correspondence, defining a robust Chern number, and proposing adiabatic pathways to connect different Chern phases.

Contribution

It introduces a complete topological characterization of bilayer Haldane models and demonstrates how to adiabatically connect different Chern phases through interlayer coupling.

Findings

Chern number accurately maps all phases of the bilayer system.

Adiabatic variation of interlayer coupling can connect different Chern phases.

The phase diagram guides adiabatic preparation of monolayer Chern insulators.

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 till 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, a 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.