Collective cyclotron motion of the relativistic plasma in graphene

TL;DR

The paper develops a finite-temperature hydrodynamic theory for graphene's thermo-electric response in the collision-dominated regime, revealing a collective relativistic cyclotron resonance whose frequency $\omega_c$ scales with net charge density and whose damping $\gamma$ arises from electron-electron collisions. It derives a relativistic fluid framework with instantaneous Coulomb interactions, provides scaling functions for thermodynamics, and computes the full linear thermo-electric response in weak magnetic fields, yielding explicit expressions for $\sigma_{xx}$, $\sigma_{xy}$, and the Nernst signal $e_N$. The work predicts a damped cyclotron pole observable in room-temperature microwave experiments and highlights a large Nernst effect near charge neutrality, offering insights into quantum-critical transport in graphene. Overall, this study connects relativistic hydrodynamics, Coulomb interactions, and magneto-thermoelectric phenomena in graphene, with clear experimental signatures and implications for Dirac plasmas.

Abstract

We present a theory of the finite temperature thermo-electric response functions of graphene, in the hydrodynamic regime induced by electron-electron collisions. 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 discuss the large Nernst effect to be expected in graphene.

Figures (2)

• Figure 1: The dimensionless function $\Phi_{\varepsilon+P}$ of the density $\rho/\rho_{\rm th}$ for non-interacting Dirac fermions.
• Figure 2: The real imaginary and imaginary parts of $\sigma_{xx}$, in units of $\sigma_Q$, for $\gamma/\omega_c = 0.3$ and $\omega_c \tau = 3$.