Collective cyclotron motion of the relativistic plasma in graphene

We present a theory of the finite temperature thermoelectric response functions of graphene in the hydrodynamic regime where electron-electron collisions dominate the scattering. In moderate magnetic fields, the Dirac particles undergo a collective cyclotron motion with a temperature-dependent relativistic cyclotron frequency proportional to the net charge density of the Dirac plasma. In contrast to the undamped cyclotron pole in Galilean-invariant systems (Kohn's theorem), here there is a finite damping induced by collisions between the counter-propagating particles and holes. This cyclotron motion shows up as a damped pole in the frequency-dependent conductivities and should be readily detectable in microwave measurements at room temperature. We also compute the large Nernst signal in the hydrodynamic regime, which is significantly bigger than that in ordinary metals.