Mott insulator
Condensed matter physics |
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Mott insulators are a class of materials that are expected to
The band gap in a Mott insulator exists between bands of like character, such as 3d electron bands, whereas the band gap in charge-transfer insulators exists between anion and cation states.
History
Although the
In 1949, in particular, Mott proposed a model for NiO as an insulator, where conduction is based on the formula[4]
- (Ni2+O2−)2 → Ni3+O2− + Ni1+O2−.
In this situation, the formation of an energy gap preventing conduction can be understood as the competition between the
- Egap = U − 2zt,
where z is the number of nearest-neighbor atoms.
In general, Mott insulators occur when the repulsive Coulomb potential U is large enough to create an energy gap. One of the simplest theories of Mott insulators is the 1963
Mott reviewed the subject (with a good overview) in 1968.[5] The subject has been thoroughly reviewed in a comprehensive paper by Masatoshi Imada, Atsushi Fujimori, and Yoshinori Tokura.[6] A recent proposal of a "Griffiths-like phase close to the Mott transition" has been reported in the literature.[7]
Mott criterion
The Mott criterion describes the critical point of the metal–insulator transition. The criterion is
where is the electron density of the material and the effective bohr radius. The constant , according to various estimates, is 2.0, 2.78,4.0, or 4.2.
If the criterion is satisfied (i.e. if the density of electrons is sufficiently high) the material becomes conductive (metal) and otherwise it will be an insulator.[8]
Mottness
Mottism denotes the additional ingredient, aside from
Thus, mottism accounts for all of the properties of Mott insulators that cannot be attributed simply to antiferromagnetism.
There are a number of properties of Mott insulators, derived from both experimental and theoretical observations, which cannot be attributed to antiferromagnetic ordering and thus constitute mottism. These properties include:
- Spectral weight transfer on the Mott scale[9][10]
- Vanishing of the single particle Green function along a connected surface in momentum space in the first Brillouin zone[11]
- Two sign changes of the dopinggoes from to (band insulators have only one sign change at )
- The presence of a charge (with the charge of an electron) boson at low energies[12][13]
- A pseudogap away from half-filling ()[14]
Mott transition
A Mott transition is a
Conceptual explanation
In a
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 satisfies .
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.[15] 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,[16] 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.
Applications
Mott insulators are of growing interest in advanced
This kind of insulator can become a conductor by changing some parameters, which may be composition, pressure, strain, voltage, or magnetic field. The effect is known as a Mott transition and can be used to build smaller field-effect transistors, switches and memory devices than possible with conventional materials.[21][22][23]
See also
- Dynamical mean-field theory – method to determine the electronic structure of strongly correlated materials
- Electronic band structure – Describes the range of energies of an electron within the solid
- Hubbard model – Approximate model used to describe the transition between conducting and insulating systems
- Metal–insulator transition – Change between conductive and non-conductive state
- Tight binding – Model of electronic band structures of solids
- Variable-range hopping (Mott)
Notes
- ^ OCLC 633481726.
- .
- .
- .
- ISSN 0034-6861.
- .
- S2CID 214667402.
- ISBN 0-471-41526-X
- ISSN 0003-4916.
- PMID 10008840.
- S2CID 119430461.
- S2CID 37595030.
- S2CID 32553272.
- S2CID 5993172.
- ISSN 0302-0738.
- S2CID 136711168.
- S2CID 205214473.
- .
- S2CID 2581764.
- S2CID 30809135.
- ^ US patent 6121642, Newns, Dennis, "Junction mott transition field effect transistor (JMTFET) and switch for logic and memory applications", published 2000
- S2CID 93921400.
- S2CID 27583830.
References
- Laughlin, R. B. (1997). "A Critique of Two Metals". arXiv:cond-mat/9709195.
- Anderson, P. W.; Baskaran, G. (1997). "A Critique of A Critique of Two Metals". arXiv:cond-mat/9711197.
- Jördens, Robert; Strohmaier, Niels; Günter, Kenneth; Moritz, Henning; Esslinger, Tilman (2008). "A Mott insulator of fermionic atoms in an optical lattice". Nature. 455 (7210): 204–207. S2CID 4426395.