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We present a theory of the finite temperature thermo-electric responsefunctions of graphene, in the hydrodynamic regime induced by electron-electroncollisions. In moderate magnetic fields, the Dirac particles undergo acollective cyclotron motion with a temperature-dependent relativistic cyclotronfrequency proportional to the net charge density of the Dirac plasma. Incontrast to the undamped cyclotron pole in Galilean-invariant systems (Kohn'stheorem), here there is a finite damping induced by collisions between thecounter-propagating particles and holes. This cyclotron motion shows up as adamped pole in the frequency dependent conductivities, and should be readilydetectable in microwave measurements at room temperature. We also discuss thelarge Nernst effect to be expected in graphene.

Collective cyclotron motion of the relativistic plasma in graphene