Mott transition

A Mott transition is a metal-nonmetal transition in condensed matter. Due to electric field screening the potential energy becomes much more sharply (exponentially) peaked around the equilibrium position of the atom and electrons become localized and can no longer conduct a current.

In a semiconductor at low temperatures, each 'site' (atom or group of atoms) contains a certain number of electrons and is electrically neutral. For an electron to move away from a site requires a certain amount of energy, as the electron is normally pulled back toward the (now positively charged) site by Coulomb forces. If the temperature is high enough that ${\displaystyle {\tfrac {1}{2}}k_{B}T}$ of energy is available per site, the Boltzmann distribution predicts that a significant fraction of electrons will have enough energy to escape their site, leaving an electron hole behind and becoming conduction electrons that conduct current. The result is that at low temperatures a material is insulating, and at high temperatures the material conducts.

While the conduction in an n- (p-) type doped semiconductor sets in at high temperatures because the conduction (valence) band is partially filled with electrons (holes) with the original band structure being unchanged, the situation is different in the case of the Mott transition where the band structure itself changes. Mott argued that the transition must be sudden, occurring when the density of free electrons N and the Bohr radius ${\displaystyle a_{H}}$ satisfies ${\displaystyle N^{1/3}a_{H}\simeq 0.2}$.

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