The Collective Cyclotron Motion of the Relativistic Plasma in Graphene: a Hydrodynamic Study

One of the main mysteries to contemporary physics is that of the behavior of many-body quantum systems which present a rich and complex ground for theoretical speculation. The many-body picture of graphene research promises insight into the behavior of many-body, relatively high-temperature systems which are more readily accessible than single-particle systems at cryogenic temperatures. Because of weak screening, vanishing density of states and a large coupling constant, graphene near its neutrality point provides an ideal testing ground for the theory of many-body systems. Particles in clean graphene have been found to behave as a relativistic electron-hole, many-body plasma with a certain universal, quantum critical behavior when the dominant parameter of the system is the rate of electron-electron scattering. The high scattering rate allows this plasma to be described through relativistic hydrodynamics. Plasma behavior is expected to occur at a relatively high temperature and small carrier density. The thermoelectric response functions of this system are expected to have a resonant frequency when subjected to small magnetic fields and an external AC electric field in the microwave frequency range. The magnetic field induces a collective cyclotron motion and the electric field establishes a longitudinal current across the sample. This system is expected to exhibit interesting quantum phase transitions from the Fermi liquid, disorder-dominated regime to the quantum-critical, hydrodynamic, relativistic regime. These transitions may be induced through changes in the carrier density, which is the critical tuning parameter of this system. At small or large values of the carrier density we expect Fermi liquid behavior and at a critical value, where the system is close to the particle-hole symmetric Dirac point, we expect relativistic plasma behavior. This text is an exploration of such a system and reflects both research in the literature and lab work, and culminates in an attempted experiment