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Mott insulators are a class of materials that are expected to conduct
Electrical conductivity

Electrical conductivity or specific conductance is a measure of a material's ability to electrical conduction an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current....
 electricity
Electricity

Electricity is a general term that encompasses a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena such as lightning and static electricity, but in addition, less familiar concepts such as the electromagnetic field and electromagnetic induction....
 under conventional band theories
Electronic band structure

In solid-state physics, the electronic band structure of a solid describes ranges of energy that an electron is "forbidden" or "allowed" to have....
, but which in fact turn out to be insulators when measured (particularly at low temperatures). This effect is due to electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
-electron interactions which are not considered in the formulation of conventional band theory.

History
Although the band theory of solids had been very successful in describing various electrical properties of materials, in 1937 Jan Hendrik de Boer
Jan Hendrik de Boer

Jan Hendrik de Boer was a Netherlands physicist and chemist.De Boer was born in Ruinen, now De Wolden, and died in 's-Gravenzande. He studied at the University of Groningen and was later employed in industry....
 and Evert Johannes Willem Verwey pointed out that a variety of transition metal oxides that are predicted to be conductors by band theory (because they have an odd number of electrons per unit cell) are in fact insulators.






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Mott insulators are a class of materials that are expected to conduct
Electrical conductivity

Electrical conductivity or specific conductance is a measure of a material's ability to electrical conduction an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current....
 electricity
Electricity

Electricity is a general term that encompasses a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena such as lightning and static electricity, but in addition, less familiar concepts such as the electromagnetic field and electromagnetic induction....
 under conventional band theories
Electronic band structure

In solid-state physics, the electronic band structure of a solid describes ranges of energy that an electron is "forbidden" or "allowed" to have....
, but which in fact turn out to be insulators when measured (particularly at low temperatures). This effect is due to electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
-electron interactions which are not considered in the formulation of conventional band theory.

History


Although the band theory of solids had been very successful in describing various electrical properties of materials, in 1937 Jan Hendrik de Boer
Jan Hendrik de Boer

Jan Hendrik de Boer was a Netherlands physicist and chemist.De Boer was born in Ruinen, now De Wolden, and died in 's-Gravenzande. He studied at the University of Groningen and was later employed in industry....
 and Evert Johannes Willem Verwey pointed out that a variety of transition metal oxides that are predicted to be conductors by band theory (because they have an odd number of electrons per unit cell) are in fact insulators. Nevill Mott and R. Peierls then (also in 1937) predicted that this anomaly can be explained by including interactions between electrons.

In 1949, in particular, Mott proposed a model for NiO
Nickel(II) oxide

Nickel oxide is the chemical compound with the formula NickelOxygen. It is notable as being the only well characterised oxide of nickel although there have been many reports of others ....
 as an insulator, in which conduction can be understood based on the formula

2 Ni3+O2− + Ni1+O2−.

In this situation, the formation of an energy gap preventing conduction can be understood as the competition between the Coulomb potential U between 3d electrons and the transfer integral t of 3d electrons between neighboring atoms (the transfer integral is a part of the tight-binding
Tight binding (physics)

In the tight binding model for a solid-state lattice of atoms, it is assumedthat the full Hamiltonian of the system may be approximated by theHamiltonian of an isolated atom centred at each Bravais lattice....
 approximation). The total energy gap is then

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 Hubbard model
Hubbard model

The Hubbard model is an approximate model used, especially in solid state physics, to describe the transition between Conductor and Electrical insulation....
.

Applications


Mott insulators are of growing interest in advanced physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
 research, and are not yet fully understood. They have applications in thin-film magnetic heterostructures and high-temperature superconductivity
High-temperature superconductivity

High-temperature superconductors are materials that are have a superconductor transition temperature above 30 K, which was thought to be the highest BCS theory allowed Tc....
, for example.

See also

  • Hubbard model
    Hubbard model

    The Hubbard model is an approximate model used, especially in solid state physics, to describe the transition between Conductor and Electrical insulation....
  • Tight-binding approximation
    Tight binding (physics)

    In the tight binding model for a solid-state lattice of atoms, it is assumedthat the full Hamiltonian of the system may be approximated by theHamiltonian of an isolated atom centred at each Bravais lattice....
  • Electronic band structure
    Electronic band structure

    In solid-state physics, the electronic band structure of a solid describes ranges of energy that an electron is "forbidden" or "allowed" to have....
  • Mottness
    Mottness

    In condensed matter physics, mottness is a term which denotes the additional ingredient, aside from antiferromagnetic ordering, which is necessary to fully describe a Mott Insulator....
  • Mott Criterion
    Mott Criterion

    The Mott criterion describes the critical point of the metal-insulator transition. The criterion isWhere is the electron density of the material and the effective bohr radius....


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