The Johnson-Nyquist noise associated with the intrinsic conductivity of the electron liquid induces fluctuations of the electron density in charge-neutral graphene devices. In the presence of external electric and magnetic fields, the fluctuations of charge density and electric current induce a fluctuating hydrodynamic flow. We show that the resulting advection of charge produces a fluctuation contribution to the macroscopic conductivity of the system, ${\sigma }_{\mathrm{fl}}$, and develop a quantitative theory of ${\sigma }_{\mathrm{fl}}$. At zero magnetic field, ${\sigma }_{\mathrm{fl}}$ diverges logarithmically with the system size and becomes rapidly suppressed at relatively small fields. This results in giant magnetoresistance of the system.

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• Electrical conductivity
• Magnetotransport
• Graphene
• Two-dimensional electron system
• Hydrodynamic models
• Methods in transport