Equilibrium statistical mechanics of a nearly classical one-component plasma in a magnetic field, in three or two dimensions1–3)

The behaviour of a nearly classical one-component plasma in a magnetic field is studied. The Wigner distribution function obeys a Bloch equation which can be cast into an explicitly gauge-invariant form. If the de Broglie wavelength λ is small compared to all other characteristics length, Planck's constant ħ is a small parameter, and a straight Wigner-Kirkwood expansion in powers of ħ2 can be used. In a strong field, the Landau radius l becomes smaller than λ, and a modified expansion must be devised. Exchange effects give only exponentially small corrections. The leading term of the induced magnetization is independent of the interactions between the particles; the next term is structure-independent for the three-dimensional case. A strong magnetic field quenches the position quantum fluctuations transverse to it. In two dimensions, in the strong field limit, the plasma is a system of point-like Landau orbits, which behave like classical particles; as a consequence, a classical Wigner crystallization can be induced by the magnetic field. The model can be used for describing electron layers at the surface of liquid helium or in a metal-oxide-semiconductor sandwich (MOS).