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Through a lattice dynamics analysis, it is revealed that the bubble plays arole of energy shield in the graphene, which helps to split the normal modesinto two categories of distinct topological nature, namely the bright and darkmodes. The topological invariants, Euler characteristic, of the bright and darkmodes are 1 and 0, respectively. For bright modes, the energy is confinedinside the bubble, so this type of modes are sensitive to the shape of thebubble; while opposite phenomenon is observed for the dark modes. The differentbehavior from these two types of normal modes is examined and verified in theprocess of phonon thermal transport. The bright and dark modes are expected tobe distinguished in experiment with existing scanning force microscopetechniques, and they should play significant roles in many other physicalprocesses.

Bright and dark modes induced by graphene bubbles