Mott transition
Encyclopedia
A Mott
transition is a metal-nonmetal transition in condensed matter
. Due to electric field screening
the potential energy becomes much sharper (exponentially) peaked around the equilibrium position of the atom and electrons become localized and can no longer conduct a current.
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
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.
The Mott transition is the point in between. Mott argued that the transition must be sudden, occurring when the density of free electrons N and the Bohr radius
satisfies 
.
Simply, Mott Transition is changes of materials’ 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. Specifically for transition metal oxides, it has electrical properties from good insulator to good conductor. Especially when it has an intermediate behavior that allows insulator-metal transition in changing T, P or doping. As observed by Mott in his 1949 publication on Ni-oxide. In Mott’s publication, he mentioned the origin of this behavior is from correlations between electrons and its close relationship to magnetism.
For example, when atoms get closer together in solid, electronic state levels broaden and hybridize. At certain critical distance as they draw closer and closer, there is a point where the bands overlap and the originally insulating materials becomes a metallic one. This can be considered a classic Mott transition from insulator to metal by means of pressure.
In semiconductor, the doping level also affects Mott transition. It is observed that higher doping in semiconductor creates internal stress of increasing free energy (acting as a pressure) of the system, thus reducing the ionization energy as shown by figure below (www.ecse.rpi.edu):
The reduced barrier causes ease of transfer by tunneling or by thermal emission from donor to its adjacent donor. The effect is enhanced when pressure is applied with reason as stated previously. When the transport of carrier reaches minute activation energy, the semiconductor has undergone Mott transition to become metallic.
Other examples of metal-insulator transition include:
in a 1949 paper. Mott also wrote a review of the subject (with a good overview) in 1968.
Nevill Francis Mott
Sir Nevill Francis Mott, CH, FRS was an English physicist. He won the Nobel Prize for Physics in 1977 for his work on the electronic structure of magnetic and disordered systems, especially amorphous semiconductors. The award was shared with Philip W. Anderson and J. H...
transition is a metal-nonmetal transition in condensed matter
Condensed Matter
Condensed matter may refer to several things*Condensed matter physics, the study of the physical properties of condensed phases of matter*European Physical Journal B: Condensed Matter and Complex Systems, a scientific journal published by EDP sciences...
. Due to electric field screening
Electric field screening
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 and conduction electrons in semiconductors and metals....
the potential energy becomes much sharper (exponentially) peaked around the equilibrium position of the atom and electrons become localized and can no longer conduct a current.
Conceptual explanation
In a semiconductorSemiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
at low temperatures, each 'site' (atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
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
Coulomb's law
Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...
. If the temperature is high enough that
of energy is available per site, the Boltzmann distributionBoltzmann distribution
In chemistry, physics, and mathematics, the Boltzmann distribution is a certain distribution function or probability measure for the distribution of the states of a system. It underpins the concept of the canonical ensemble, providing its underlying distribution...
predicts that a significant fraction of electrons will have enough energy to escape their site, leaving an electron hole
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...
behind and becoming conduction electrons that conduct current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
. The result is that at low temperatures a material is insulating, and at high temperatures the material conducts.
The Mott transition is the point in between. Mott argued that the transition must be sudden, occurring when the density of free electrons N and the Bohr radius
Bohr radius
The Bohr radius is a physical constant, approximately equal to the most probable distance between the proton and 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 atom...
satisfies .Simply, Mott Transition is changes of materials’ 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. Specifically for transition metal oxides, it has electrical properties from good insulator to good conductor. Especially when it has an intermediate behavior that allows insulator-metal transition in changing T, P or doping. As observed by Mott in his 1949 publication on Ni-oxide. In Mott’s publication, he mentioned the origin of this behavior is from correlations between electrons and its close relationship to magnetism.
For example, when atoms get closer together in solid, electronic state levels broaden and hybridize. At certain critical distance as they draw closer and closer, there is a point where the bands overlap and the originally insulating materials becomes a metallic one. This can be considered a classic Mott transition from insulator to metal by means of pressure.
In semiconductor, the doping level also affects Mott transition. It is observed that higher doping in semiconductor creates internal stress of increasing free energy (acting as a pressure) of the system, thus reducing the ionization energy as shown by figure below (www.ecse.rpi.edu):
The reduced barrier causes ease of transfer by tunneling or by thermal emission from donor to its adjacent donor. The effect is enhanced when pressure is applied with reason as stated previously. When the transport of carrier reaches minute activation energy, the semiconductor has undergone Mott transition to become metallic.
Other examples of metal-insulator transition include:
- 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 Tc, europium’s valence electrons have enough energy to cross the trap levels due to vacancies on the oxygen sites. This transfer of electrons transform EuO into metallic state.
- The Mott transition in doped semiconductors, e.g., Si:P, Si:As, Si:B, Si:Ga, etc. Such transitions have been effectively investigated and demonstrated using electronic Raman scattering.
History
The theory was first proposed by Nevill Francis MottNevill Francis Mott
Sir Nevill Francis Mott, CH, FRS was an English physicist. He won the Nobel Prize for Physics in 1977 for his work on the electronic structure of magnetic and disordered systems, especially amorphous semiconductors. The award was shared with Philip W. Anderson and J. H...
in a 1949 paper. Mott also wrote a review of the subject (with a good overview) in 1968.