Fluctuation-induced giant magnetoresistance in charge-neutral graphene

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.