Massive thermal fluctuation of massless graphene electrons

Whereas thermal current noise $\langle I^2 \rangle$ in typical conductors is proportional to temperature $T$, $\langle I^2 \rangle$ in graphene exhibits a nonlinear $T$ dependence due to the massless nature of individual electrons. This unique $\langle I^2 \rangle$ arising from individually massless electrons is intimately linked to the non-zero collective mass of graphene electrons; namely, $\langle I^2 \rangle$ is set by the equipartition theorem applied to the collective mass's kinetic energy, with the nonlinear $T$-dependence arising from the $T$-dependence of the collective mass. This link between thermal fluctuation and collective dynamics unifies $\langle I^2 \rangle$ in graphene and typical conductors, while elucidating the uniqueness of the former at the same time.

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