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.

Conceptual explanation

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 $\tfrac 1 2 k_B T$ 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 $a_H$ satisfies $N^{1/3} a_H \simeq 0.2$ .

Simply put, a Mott Transition is a change in a material's behavior from insulating to metallic due to various factors. This transition is known to exist in various systems: mercury metal vapor-liquid, metal NH₃ solutions, transition metal chalcogenides and transition metal oxides.^[1] In the case of transition metal oxides, the material typically switches from being a good electrical insulator to a good electrical conductor. The insulator-metal transition can also be modified by changes in temperature, pressure or composition (doping). As observed by Mott in his 1949 publication on Ni-oxide, the origin of this behavior is correlations between electrons and the close relationship this phenomenon has to magnetism.

The physical origin of the Mott transition is the interplay between the Coulomb repulsion of electrons and their degree of localization (band width). Once the density becomes too high (e.g. due doping), the energy of the system can be lowered by the localization of the formerly conducting electrons (band width reduction), leading to the formation of a band gap (i.e. a semiconductor/insulator). On the other hand, however, when atoms get closer together in a solid, their electronic state levels broaden and hybridize (band width increase). At a certain critical distance, there is a point where the bands overlap and the originally insulating material becomes metallic. This is a classic Mott transition from insulator to metal induced by changes in pressure.

In a semiconductor, the doping level also affects the Mott transition. It has been observed that higher dopant concentrations in a semiconductor creates internal stresses that increase the free energy (acting as a change in pressure) of the system,^[2] thus reducing the ionization energy as shown in the figure below (www.ecse.rpi.edu):

The reduced barrier causes easier transfer by tunneling or by thermal emission from donor to its adjacent donor. The effect is enhanced when pressure is applied for the reason stated previously. When the transport of carriers overcomes a minute activation energy, the semiconductor has undergone a Mott transition and become metallic.

Other examples of metal–insulator transition include:

Peierls transition /Charge density wave. Changes in the material symmetry leads to the formation of a band gap at Brillouin zone boundaries.
Excitonic insulators exhibit very high exciton binding energies driving the transition to the gapped state.
A Mott–Hubbard transition. Ti-doped V₂O₃ undergoes a transition from antiferromagnetic insulator to disordered magnetic conducting state.
A band crossing transition. EuO orders ferromagnetically from a paramagnetic semiconducting state on cooling below its Curie temperature. Below T_c, europium’s valence electrons have enough energy to cross the trap levels due to vacancies on the oxygen sites. This transfer of electrons transforms EuO into the metallic state.^[3]
The Mott transition in doped semiconductors, e.g., Si:P, Si:As, Si:B, Si:Ga, etc. Such transitions have been investigated and demonstrated using electronic Raman scattering.^[4]

History

The theory was first proposed by Nevill Francis Mott in a 1949 paper.^[5] Mott also wrote a review of the subject (with a good overview) in 1968.^[6]

Notes

↑ Cyrot, M (1972). "Theory of mott transition : Applications to transition metal oxides". Le Journal de Physique 33 (125).
↑ Bose, D. N.; B. Seishu; G. Parthasarathy; E. S. R. Gopal (1986). "Doping Dependence of Semiconductor-Metal Transition in InP at High Pressures". Proceedings of the Royal Society A 405 (1829). doi:10.1098/rspa.1986.0057. JSTOR 2397982.
↑ Michel Schlenker; Etienne du Trémolet de Lacheisserie; Du Trڳemolet de Lacheisserie, Etienne; Du Trémolet de Lacheisserie, Etienne; Damien Gignoux (2005). Magnetism. Berlin: Springer. ISBN 0-387-22967-1.
↑ Jain, K., et al., "Electronic Raman scattering and the metal–insulator transition in doped silicon", Phys. Rev. B, Vol. 13, 5448 (1976).
↑ N. F. Mott, Proc. Phys. Soc. (London) A62, 416 (1949)
↑ N. F. Mott, Rev. Mod. Phys., 40, pp. 677–683.

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