Abstract
We provide an explicit model for a spin-1/2 quasi-particle, based on the superposition of plasmon excitations in a quantum plasmas with intrinsic orbital angular momentum. Such quasi-particle solutions can show remarkable similarities with single electrons moving in vacuum: they have spin-1/2, a finite rest mass, and a quantum dispersion. We also show that these quasi-particle solutions satisfy a criterium of energy minimum.
Highlights
We provide an explicit model for a spin-1/2 quasi-particle, based on the superposition of plasmon excitations in a quantum plasmas with intrinsic orbital angular momentum
The electric field associated with these quasi-particles is purely longitudinal and parallel to the direction of propagation. This means that, from their polarization, we can conclude that the simplest plasmon solutions have no intrinsic angular momentum, or no spin
It was recognized in recent years that electron plasma waves or plasmon solutions can exist with an integer intrinsic angular momentum
Summary
We provide an explicit model for a spin-1/2 quasi-particle, based on the superposition of plasmon excitations in a quantum plasmas with intrinsic orbital angular momentum. The electric field associated with these quasi-particles is purely longitudinal and parallel to the direction of propagation This means that, from their polarization, we can conclude that the simplest plasmon solutions (which are plane wave solutions) have no intrinsic angular momentum, or no spin. The situation changes when we consider a particular superposition of LG field solutions, with a total semi-integer topological charge This can be used to describe a plasmon quasi-particle with spin-1/2. We can see that the quantum plasma corrections, associated with the term in β2, shown in eq (7), introduce a small deviation from this interesting analogy with vacuum electrodynamics Such formal analogies and, in particular, the existence of an effective plasmon mass mf, had already been considered before for a classical plasma, when vF is replaced by the thermal velocity and the β2 corrections are absent[14]. Multiplying by ħ, and introducing the above definition of the plasmon effective mass, we can rewrite this in the standard form of a Schrödinger equation, as i ∂Φ ∂t
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