Multistability of graphene nanobubbles

Using He, Ne, Ar, Kr, and Xe atoms as a model system, it is demonstrated that graphene nanobubbles on flat substrates are multistable systems. A nanobubble can adopt multiple stable stationary states, each characterized by the number of layers l within the cluster of encapsulated atoms. The layers are circular, concentrically stacked, and form an l-stepped pyramid with a flat top. Encapsulation of this pyramid by the graphene sheet is achieved through local stretching of the membrane: the valence bonds elongate only directly above the confined atoms. Outside this coverage zone, the sheet remains undeformed and lies flush against the substrate. The maximum number of possible layers, l_m, increases monotonically with the number of encapsulated atoms N, reaching l_m = 6 for N = 4000. The graphene membrane, through van der Waals interaction with the substrate, compresses the internal atomic cluster, generating internal pressures on the order of P_in ∼ 1 GPa. Numerical simulations of thermal vibrations reveal that among all l-layer configurations, one ground state always exists. Upon heating, this state smoothly transitions into a layerless liquid configuration. All other stationary states transform into this ground state once a characteristic temperature T_l is reached. For N = 4000, the ground state corresponds to the four-layer packing (l = 4). The coexistence of multiple stable states with distinct layer numbers at low temperatures leads to the absence of a universal shape for the nanobubbles. In this scenario, the height-to-radius ratio, H/R, is not constant and can vary from 0 to 0.28, depending on the number of layers. The commonly reported universal aspect ratio H/R ∼ 0.2 holds only for the ground states of the system. External hydrostatic pressure P does not lead to a change in the multistability of the nanobubbles. An increase in pressure can lead to crystallization of the system of encapsulated atoms, which results in a change in the shape of the nanobubble (a decrease in the H/R ratio). In the absence of crystallization under pressure, uniform compression of the nanobubble occurs, in which the H/R ratio does not change.