Fermi point

Fermi point

The term Fermi point has two applications but refers to the same phenomena (special relativity): [ [http://www.physics.wustl.edu/~visser/Analog/talks.html#volovik Effective gravity and quantum field theory in superfluids] ]
*Fermi point (Quantum Field Theory)
*Fermi point (Nanotechnology)

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. [ [http://www.pnas.org/cgi/content/full/96/11/6042 Field theory in superfluid 3He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?] ]
In nanotechnology this concept can be applied to electron behavior. [http://theory.physics.lehigh.edu/rotkin/newdata/mypreprs/ncts04.pdf METFET] ] An electron when as single particle is a Fermion obeying the Pauli exclusion principle.

Fermi point (Quantum Field Theory)

Fermionic systems that have a Fermi surface (FS) belong to a universality class in quantum field theory. 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. [ [http://www.pnas.org/cgi/content/full/96/11/6042 Field theory in superfluid 3He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?] ]

Fermi point (Nanotech)

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 metallic. As the structure of a carbon nanotube determines the energy levels that the carbon's electrons may occupy, the structure affects macroscopic properties of the nanotube structure, most notably electrical and thermal conductivity. [Sundaram, Vivek. Dept. of Mechanical Engineering University of Colorado at Boulder. [http://ucsub.colorado.edu/~sundarav/nrg_files/Info%20on%20CNT.pdf CARBON NANOTUBES: One of the best discoveries man has ever made in Science] . Retrieved April 1, 2006.]

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. [Gross, Michael. chembytes e-zine. [http://www.chemsoc.org/chembytes/ezine/2002/gross_may02.htm The smallest revolution] . Retrieved April 1, 2006.] [ [http://www.crhc.uiuc.edu/ece497nc/scribe/nanotube1.pdf Carbon Nanotubes and Nanotube Transistors] .]

Chirality

For a given ("n","m") nanotube, if "n" - "m"=3"q" (where "q" is an integer), then the nanotube is metallic, otherwise the nanotube is a semiconductor. Thus all armchair nanotubes ("n"="m") are metallic, and nanotubes (5,0), (6,4), (9,1), etc. are semiconducting.

See also

*Fermi energy
*Fermi surface
*Bandgap

Notes


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