Eigenmodes and resonance vibrations of graphene nanomembranes

Natural and resonant oscillations of suspended circular graphene membranes (single-layer sheets lying on a flat substrate having a circular hole of radius R) have been simulated using full-atomic models. Substrates formed by flat surfaces of graphite and hexagonal boron nitride (h-BN) crystal, hexagonal ice, silicon carbide 6H-SiC, and nickel (111) surface have been used. The presence of the substrate leads to the forming of a gap at the bottom of the frequency spectrum of transversal vibrations of the sheet. The frequencies of natural oscillations of the membrane (oscillations localized on the suspended section of the sheet) always lie in this gap, and the frequencies of oscillations decrease by increasing radius of the membrane as (R + R-i)(-2) with nonzero effective increase of radius R-i > 0. The modeling of the sheet dynamics has shown that small periodic transversal displacements of the substrate lead to resonant vibrations of the membranes at frequencies close to eigenfrequencies of nodeless vibrations of membranes with a circular symmetry. The energy distribution of resonant vibrations of the membrane has a circular symmetry and several nodal circles, whose number i coincides with the number of the resonant frequency. The resonant frequencies decrease with increasing the membrane radius as (R + R-i)(-alpha i) with the exponent alpha(i) < 2. The lower rate of resonance frequency decrease is caused by the hard anharmonicity of membrane vibrations.

Automated summary

In this study, natural and resonant oscillations of suspended circular graphene membranes were simulated using full-atomic models. The presence of various substrates was found to affect the frequency distribution of membrane vibrations and the pattern of resonant frequencies changing with radius.