In two-dimensional systems with space-time inversion symmetry, Dirac nodes (DNs) carry non-Abelian topological charges, which induce an intriguing momentum space braiding phenomenon. Although the original idea was proposed in condensed matter setup, the experimental verification of non-Abelian charge conversion has been limited to artificial metamaterials because of the difficulty in identifying suitable materials in which controlled tuning of DN positions is possible. In this work, we propose bilayer binary honeycomb lattices (BBHLs) as a material platform to study the non-Abelian charge conversion phenomenon in which DN positions in momentum space can be manipulated. More explicitly, we demonstrate that layer sliding and vertical pressure serve as tunable braiding parameters controlling the non-Abelian charge conversion process, which is crucial to understand the stacking-dependent electronic properties of BBHL systems. We show that the BBHL systems are a promising candidate for the experimental realization of non-Abelian phenomena of DNs in condensed matter.

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• Dirac fermions
• Edge states
• Topological phases of matter
• Bilayer graphene
• Dirac semimetal
• Density functional calculations
• Tight-binding model