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This lab curiousity only needs to be millions of times to power tiny low voltage computer chips.
If millions of these tiny circuits could be built on a 1-millimeter by 1-millimeter chip, they could serve as a low-power battery replacement. The system seems to be energy harvesting from Brownian motion. The amount of graphene and processing needed to achieve this energy harvesting is system is something that can make sense for certain niches powering circuits but this is not something that would be practical for any large-scale energy generation. The "limitless" power refers to tiny, tiny constant trickles of power.
"An energy-harvesting circuit based on graphene could be incorporated into a chip to provide clean, limitless, low-voltage power for small devices or sensors," said Paul Thibado, professor of physics and lead researcher in the discovery.
Fluctuation-induced current from freestanding graphene P. M. Thibado, P. Kumar, Surendra Singh, M. Ruiz-Garcia, A. Lasanta, and L. L. Bonilla Phys. Rev. E 102, 042101 – Published 2 October 2020