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In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, [1] principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.
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The dispersion relations show conics of the free-electron energy dispersion parabolas for all possible reciprocal lattice vectors. This results in a very complicated set intersecting of curves when the dispersion relations are calculated because there is a large number of possible angles between evaluation trajectories, first and higher order ...
The free-electron picture has, nevertheless, remained a dominant one in introductory courses on metallurgy. The electronic band structure model became a major focus for the study of metals and even more of semiconductors. Together with the electronic states, the vibrational states were also shown to form bands.
Jellium, also known as the uniform electron gas (UEG) or homogeneous electron gas (HEG), is a quantum mechanical model of interacting electrons in a solid where the positive charges (i.e. atomic nuclei) are assumed to be uniformly distributed in space; the electron density is a uniform quantity as well in space.
The fan diagram of the composite fermion Landau levels has been determined by transport, and shows both spin-up and spin-down composite fermion Landau levels. [24] The fractional quantum Hall states as well as composite fermion Fermi sea are also partially spin polarized for relatively low magnetic fields. [24] [25] [26]
Valence electron, as an outer shell electron that is associated with an atom; Valence and conduction bands, as a conduction band electron relative to the electronic band structure of a solid; Fermi gas, as a particle of a non-interacting electron gas; Free electron model, as a particle in the Drude-Sommerfeld model of metals; Free-electron ...