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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.
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.
[1]: 161 The first one is the nearly free electron model, in which the electrons are assumed to move almost freely within the material. In this model, the electronic states resemble free electron plane waves, and are only slightly perturbed by the crystal lattice. This model explains the origin of the electronic dispersion relation, but the ...
The Dirac sea is a theoretical model of the electron vacuum as an infinite sea of electrons with negative energy, now called positrons. It was first postulated by the British physicist Paul Dirac in 1930 [ 1 ] to explain the anomalous negative-energy quantum states predicted by the relativistically-correct Dirac equation for electrons . [ 2 ]
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 ...
Free electron bands in a one dimensional lattice The periodic potential of the lattice in this free electron model must be weak because otherwise the electrons wouldn't be free. The strength of the scattering mainly depends on the geometry and topology of the system.
Under the free electron model, the electrons in a metal can be considered to form a uniform Fermi gas. The number density N / V {\displaystyle N/V} of conduction electrons in metals ranges between approximately 10 28 and 10 29 electrons per m 3 , which is also the typical density of atoms in ordinary solid matter.
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]