A
Mott
Mott is both an English surname and given name. Notable people with the name include:
Surname B
*Basil Mott (1859–1938), British civil engineer
*Bitsy Mott (1918–2001), American baseball player C
* Charles James Mott (1880–1918), British bar ...
transition is a metal-nonmetal transition in
condensed matter
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the su ...
. Due to
electric field screening
In physics, screening is the damping of electric fields caused by the presence of mobile charge carriers. It is an important part of the behavior of charge-carrying fluids, such as ionized gases (classical plasmas), electrolytes, and charge c ...
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
A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
at low temperatures, each 'site' (
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, and ...
or group of atoms) contains a certain number of
electrons
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no ...
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
of energy is available per site, the
Boltzmann distribution
In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution or probability measure that gives the probability t ...
predicts that a significant fraction of electrons will have enough energy to escape their site, leaving an
electron hole
In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle which is the lack of an electron at a position where one could exist in an atom or atomic lattice. Since in a normal atom or ...
behind and becoming conduction electrons that conduct
current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
. 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
The Bohr radius (''a''0) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an ...
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 NH
3 solutions, transition metal chalcogenides and transition metal oxides.
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 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, 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 minute
activation energy
In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules pe ...
, the semiconductor has undergone a Mott transition and become metallic.
Other examples of
metal–insulator transition
Metal–insulator transitions are transitions of a material from a metal (material with good electrical conductivity of electric charges) to an insulator (material where conductivity of charges is quickly suppressed). These transitions can be ach ...
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. V
2O
3 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.
* 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.
History
The theory was first proposed by
Nevill Francis Mott
Sir Nevill Francis Mott (30 September 1905 – 8 August 1996) was a British physicist who won the Nobel Prize for Physics in 1977 for his work on the electronic structure of magnetic and disordered systems, especially amorphous semiconductors. ...
in a 1949 paper.
Mott also wrote a review of the subject (with a good overview) in 1968.
The subject has been thoroughly reviewed in a comprehensive paper by Imada, Fujimori and Tokura. A recent proposal of a "Griffiths-like phase close to the Mott transition" has been reported in the literature.
[{{cite journal , journal=Journal of Applied Physics , volume=128 , pages=225102 , date=2020 , doi=10.1063/5.0018604, arxiv=2003.11866 , title=Griffiths-like phase close to the Mott transition , last1=Mello , first1=Isys F. , last2=Squillante , first2=Lucas , last3=Gomes , first3=Gabriel O. , last4=Seridonio , first4=Antonio C. , last5=De Souza , first5=Mariano , issue=22 , bibcode=2020JAP...128v5102M , s2cid=214667402 ]
See also
*
Metal–insulator transition
Metal–insulator transitions are transitions of a material from a metal (material with good electrical conductivity of electric charges) to an insulator (material where conductivity of charges is quickly suppressed). These transitions can be ach ...
References
Electric current
Phase transitions