Fermi point
Encyclopedia
The term Fermi point has two applications but refers to the same phenomena (special relativity
):
For both applications count that the symmetry between particles and anti-particles in weak interactions is violated:
At this point the particle energy E = cp is zero.
In nanotechnology this concept can be applied to electron behavior. An electron when as single particle is a Fermion
obeying the Pauli exclusion principle
.
. Any collection of fermions with weak repulsive interactions belongs to this class. At the fermi point, the break of symmetry can be explained by assuming a vortex or singularity will appear as a result of the spin of a fermi particle (quasiparticle
, Fermion
) in one dimension of the three-dimensional momentum space.
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The Fermi point is one particular electron state. The Fermi point refers to an event chirality
of electrons is involved and the diameter
of a carbon nanotube
for which the nanotube becomes metal
lic. As the structure of a carbon nanotube determines the energy level
s that the carbon
's electron
s may occupy, the structure affects macroscopic properties of the nanotube structure, most notably electrical and thermal conductivity
.
Flat graphite
is a conductor except when rolled up into small cylinders. This circular structure inhibits the internal flow of electrons and the graphite becomes a semiconductor
; a transition point forms between the valence band
and conduction band
. This point is called the Fermi point. If the diameter of the carbon nanotube is sufficiently great, the necessary transition phase disappears and the nanotube may be considered a conductor.
. Thus all armchair nanotubes (n=m) are metallic, and nanotubes (5,0), (6,4), (9,1), etc. are semiconducting.
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
):
- Fermi point (Quantum Field TheoryQuantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
) - Fermi point (NanotechnologyNanotechnologyNanotechnology is the study of manipulating matter on an atomic and molecular scale. Generally, nanotechnology deals with developing materials, devices, or other structures possessing at least one dimension sized from 1 to 100 nanometres...
)
For both applications count that the symmetry between particles and anti-particles in weak interactions is violated:
At this point the particle energy E = cp is zero.
In nanotechnology this concept can be applied to electron behavior. An electron when as single particle is a Fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
obeying the Pauli exclusion principle
Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...
.
Fermi point (Quantum Field Theory)
Fermionic systems that have a Fermi surface (FS) belong to a universality class in quantum field theoryQuantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
. Any collection of fermions with weak repulsive interactions belongs to this class. At the fermi point, the break of symmetry can be explained by assuming a vortex or singularity will appear as a result of the spin of a fermi particle (quasiparticle
Quasiparticle
In physics, quasiparticles are emergent phenomena that occur when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in free space...
, Fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
) in one dimension of the three-dimensional momentum space.
Fermi point (Nanoscience)
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity...
of electrons is involved and the diameter
Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...
of a carbon nanotube
Carbon nanotube
Carbon nanotubes are allotropes of carbon with a cylindrical nanostructure. Nanotubes have been constructed with length-to-diameter ratio of up to 132,000,000:1, significantly larger than for any other material...
for which the nanotube becomes metal
Metal
A metal , is an element, compound, or alloy that is a good conductor of both electricity and heat. Metals are usually malleable and shiny, that is they reflect most of incident light...
lic. As the structure of a carbon nanotube determines the energy level
Energy level
A quantum mechanical system or particle that is bound -- that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels...
s that the carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...
's electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s may occupy, the structure affects macroscopic properties of the nanotube structure, most notably electrical and thermal conductivity
Thermal conductivity
In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....
.
Flat graphite
Graphite
The mineral graphite is one of the allotropes of carbon. It was named by Abraham Gottlob Werner in 1789 from the Ancient Greek γράφω , "to draw/write", for its use in pencils, where it is commonly called lead . Unlike diamond , graphite is an electrical conductor, a semimetal...
is a conductor except when rolled up into small cylinders. This circular structure inhibits the internal flow of electrons and the graphite becomes a semiconductor
Semiconductor
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...
; a transition point forms between the valence band
Valence band
In solids, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature....
and conduction band
Conduction band
In the solid-state physics field of semiconductors and insulators, the conduction band is the range of electron energies, higher than that of the valence band, sufficient to free an electron from binding with its individual atom and allow it to move freely within the atomic lattice of the material...
. This point is called the Fermi point. If the diameter of the carbon nanotube is sufficiently great, the necessary transition phase disappears and the nanotube may be considered a conductor.
Chirality
For a given (n,m) nanotube, if n - m=3q (where q is an integer), then the nanotube is metallic, otherwise the nanotube is 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...
. Thus all armchair nanotubes (n=m) are metallic, and nanotubes (5,0), (6,4), (9,1), etc. are semiconducting.