Instability in the Quantum Helicon Dispersion Relation

Publisher Website
Google Scholar
Abstract
The classical stability theorem for the conventional thermal equilibrium state of an electron gas in a uniform magnetic field is generalized to (a) the semiclassical case, (b) the quantum case when there is no magnetic field, and (c) the quantum case in the presence of a magnetic field, provided that only Coulomb interactions, are retained. However, when the quantum gas in a magnetic field is treated with all electromagnetic interactions, at very low temperatures it becomes unstable against transverse excitations propagating in the direction of the field. This instability appears as a root of the quantum helicon dispersion relation in the upper half frequency plane. It is shown that the instability is due to the failure of the conventional Hartreeground state (in which the one-electron states are the ordinary Landau ones) to minimize the ground-state energy, when magnetic current-current interactions are retained along with Coulomb interactions. We have found a state giving a lower energy than the conventional one, in which transverse volume currents exist perpendicular to the magnetic field. Because, however, the magnetic coupling is very weak, the reduction in energy is unobservably small at any realistic field strengths or electronic densities. We conclude that the instability does not lead to any measurable effects, and that for all practical purposes the conventional thermal equilibrium state can be regarded as stable.

This publication has 7 references indexed in Scilit: