Physics:Mott transition
A Mott transition is a metal-insulator 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. It is named after physicist Nevill Francis Mott.
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, it 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 [math]\displaystyle{ \tfrac 1 2 k_{\mathrm B} T }[/math] 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 [math]\displaystyle{ a_0 }[/math] satisfies [math]\displaystyle{ N^{1/3} a_0 \simeq 0.2 }[/math].
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 Nevill Francis 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 carrier density becomes too high (e.g. due to 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, e.g. by pressure (i.e. a semiconductor/insulator).
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.
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 minimum activation energy, the semiconductor has undergone a Mott transition and become metallic.
The Mott transition is usually first order, and involves discontinuous changes of physical properties. Theoretical studies of the Mott transition in the limit of large dimension find a first order transition. However in low dimensions and when the lattice geometry leads to frustration of magnetic ordering, it may be only weakly first order or even continuous (i.e second order). Weakly first order Mott transitions are seen in some quasi-two dimensional organic materials. Continuous Mott transitions have been reported in semiconductor moire materials. A theory of a continuous Mott transition is available if the Mott insulating phase is a quantum spin liquid with an emergent fermi surface of neutral fermions.
History
The theory was first proposed by Nevill Francis Mott in a 1949 paper.[3] Mott also wrote a review of the subject (with a good overview) in 1968.[4] The subject has been thoroughly reviewed in a comprehensive paper by Masatoshi Imada, Atsushi Fujimori, and Yoshinori Tokura.[5] A recent proposal of a "Griffiths-like phase close to the Mott transition" has been reported in the literature.[6]
See also
References
- ↑ Cyrot, M. (1972). "Theory of mott transition : Applications to transition metal oxides". Journal de Physique (EDP Sciences) 33 (1): 125–134. doi:10.1051/jphys:01972003301012500. ISSN 0302-0738.
- ↑ 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): 345–353. doi:10.1098/rspa.1986.0057. Bibcode: 1986RSPSA.405..345B.
- ↑ Mott, N F (1 June 1949). "The Basis of the Electron Theory of Metals, with Special Reference to the Transition Metals". Proceedings of the Physical Society. Section A (IOP Publishing) 62 (7): 416–422. doi:10.1088/0370-1298/62/7/303. ISSN 0370-1298. Bibcode: 1949PPSA...62..416M.
- ↑ MOTT, N. F. (1 September 1968). "Metal-Insulator Transition". Reviews of Modern Physics (American Physical Society (APS)) 40 (4): 677–683. doi:10.1103/revmodphys.40.677. ISSN 0034-6861. Bibcode: 1968RvMP...40..677M.
- ↑ M. Imada; A. Fujimori; Y. Tojura (1998). "Metal-Insulator Transitions". Rev. Mod. Phys. 70 (4): 1039. doi:10.1103/RevModPhys.70.1039. Bibcode: 1998RvMP...70.1039I.
- ↑ Mello, Isys F.; Squillante, Lucas; Gomes, Gabriel O.; Seridonio, Antonio C.; De Souza, Mariano (2020). "Griffiths-like phase close to the Mott transition". Journal of Applied Physics 128 (22): 225102. doi:10.1063/5.0018604. Bibcode: 2020JAP...128v5102M.
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