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Mutual Information and Correlations across Topological Phase Transitions in Topologically Ordered Graphene Zigzag Nanoribbons

Graphene zigzag nanoribbons, initially in a topologically ordered state, undergo a topological phase transition into crossover phases distinguished by quasi-topological order. We computed mutual information for both the topologically ordered phase and its crossover phases, revealing the following re...

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Detalles Bibliográficos
Autores principales: Lee, In-Hwan, Le, Hoang-Anh, Yang, S.-R. Eric
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10606814/
https://www.ncbi.nlm.nih.gov/pubmed/37895570
http://dx.doi.org/10.3390/e25101449
Descripción
Sumario:Graphene zigzag nanoribbons, initially in a topologically ordered state, undergo a topological phase transition into crossover phases distinguished by quasi-topological order. We computed mutual information for both the topologically ordered phase and its crossover phases, revealing the following results: (i) In the topologically ordered phase, A-chirality carbon lines strongly entangle with B-chirality carbon lines on the opposite side of the zigzag ribbon. This entanglement persists but weakens in crossover phases. (ii) The upper zigzag edge entangles with non-edge lines of different chirality on the opposite side of the ribbon. (iii) Entanglement increases as more carbon lines are grouped together, regardless of the lines’ chirality. No long-range entanglement was found in the symmetry-protected phase in the absence of disorder.