Is Graphene's Current Capacity Really x1000 Times Higher Than Copper?

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Graphene is often claimed to have a current-carrying capacity up to 1000 times greater than copper, but this assertion lacks substantial evidence. While graphene exhibits high carrier mobilities, reaching up to 200,000 cm^2/Vs at room temperature, its low carrier density limits its specific conductivity compared to metals like silver and copper. The ability of a thin graphene sheet to carry significant current depends on effective heat dissipation, complicating quantification. Overall, the dramatic claims about graphene's superiority in current capacity may be overstated. The discussion highlights the need for more realistic assessments of graphene's electrical properties.
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Some articles would state that graphene(1 pure sheet) can carry x1000 the amount of current copper can. When I researched it, there isn't anything indicating so. Are those articles true? Or is it a lie?

I understand how graphene can be slightly better, but that is unrealistic... it is a wondrous material, yet that huge difference in current capacity and it's weight difference, it sounds too good to be true.
 
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Carrier mobilities in graphene are exceptionally high, up to 200, 000 cm^2/Vs at room temperature. But the number of carriers is low, so the specific conductivity is not that different from metals like silver or copper.
A thin sheet can carry a lot of current when heat is lead away, there is no simple way of putting a number on that.
 
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