Determine the physical origin of apparent gap closings at small twist angles

Determine whether apparently vanishing gaps between narrow and remote bands at small twist angles in the continuum model of twisted bilayer–trilayer graphene represent genuine physical gap closings or numerical artifacts.

Background

The paper analyzes topological transitions in AB–ABC, BA–ABC, AB–ABA, and BA–ABA twisted bilayer–trilayer graphene by tracking the Chern numbers of the conduction and valence narrow bands together with the gaps separating these bands from one another and from remote bands. At sufficiently small twist angles, the narrow and remote bands become compressed into a very narrow energy window, making numerical identification of isolated bands and topological transitions challenging.

Resolving whether the apparent gap closings are physical is important because the Chern-number sum rules derived in the chiral limit apply only while the two narrow bands remain isolated from remote bands. A genuine gap closing can signal a topological transition and Chern-number transfer, whereas a numerically induced apparent closing should not be interpreted as a physical phase boundary.