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I've read that electrons in graphene can travel masslessly, due to the effect of the graphene crystal around them. I'd also read that the application of an electric field can change this behavior and cause the electrons to travel in a non-massless way. So I'd like to ask if changing from one mode of electron behavior to the other (or vice-versa) actually affects the overall mass of the graphene. I'd also like to ask: if the graphene were to be mechanically oscillated like a vibrating drum-skin, and the electric field was selectively applied or switched off depending on the direction of motion by the graphene during its oscillation cycle, then could this result in a net acceleration on the overall system due to an imbalance/asymmetry in the action-reaction forces produced across the oscillation cycle?

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