A phase diagram of topological order (TO) of zigzag graphene nanoribbons (ZGNRs) is constructed based on numerical results of topological entanglement entropy. Topological order (TO) of zigzag graphene nanoribbons (ZGNRs) results from the interplay between on-site repulsion and disorder. However, the competition between them and doping concentration is detrimental to the TO. We explore that the suppression of TO is not trivial, i.e. forming crossover phases with distinguished properties.
Mutual information provides a quantitative measure for correlations. In this work, we conducted a throughout analysis of mutual information between carbon lines in zigzag graphene nanoribbons. Mutual information satisfies area law, yet exhibits distinguished characteristics across different phases. Through this analysis, it reveals topological phase transitions, and the behaviors of mutual information is elucidated via the concepts of mixed chiral states.
In-Hwan Lee, Hoang-Anh Le and S.-R. Eric Yang, Entropy 25 (10), 1449 (2023)