Paper detail

Bright and dark modes induced by graphene bubbles

Through a lattice dynamics analysis, it is revealed that the bubble plays a role of energy shield in the graphene, which helps to split the normal modes into two categories of distinct topological nature, namely the bright and dark modes. The topological invariants, Euler characteristic, of the bright and dark modes are 1 and 0, respectively. For bright modes, the energy is confined inside the bubble, so this type of modes are sensitive to the shape of the bubble; while opposite phenomenon is observed for the dark modes. The different behavior from these two types of normal modes is examined and verified in the process of phonon thermal transport. The bright and dark modes are expected to be distinguished in experiment with existing scanning force microscope techniques, and they should play significant roles in many other physical processes.