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A Fermi sea consists of those fermions filling the lowest-energy quantum states allowed by a quantum system. The quantum system can be any quantum-scale (particle-scale) region of fermions (e.g., electrons), such as within atoms (especially, with significant atomic numbers), collections of atoms, or degenerate matter, and the term Fermi sea is used because of the particular behavior of fermions within such a system. The maximally energetic of these (low energy) fermions constitute the Fermi surface and their energy level is termed the Fermi level (or Fermi energy). The word sea is in analogy to a body of water, which fills the space with the lowest gravitational potential energy, forming a surface at some altitude. The term Fermi sea is commonly used in regards to electrons such as those filling the lowest orbits of the atoms within a solid, or those filling the low-energy states within electron degenerate matter. A common use of the term is regarding material near 0 K: at exactly 0 K, all the electrons are in the Fermi sea and the Fermi level is the maximum energy of any of them. Small amounts of energy (e.g., heat raising the temperature very slightly higher) only affect electrons at or very near the Fermi surface.
Fermi sea electrons below the Fermi surface are somewhat trapped: all possible quantum states that it might move to have energy levels greater than the Fermi level, and such an electron generally needs to receive sufficient additional energy to reach that level. Electrons at or above the Fermi surface are far more likely to shift position such as in response to an electric field, thus forming a current, i.e., conducting electricity.
The Fermi sea concept is used describing some models of superconductivity.