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{{Short description|An electrically conducting wire in which quantum effects influence the transport properties}}
In [[Physics:Mesoscopic physics|mesoscopic physics]], a '''quantum wire''' is an [[Physics:Electrical conductor|electrically conducting]] [[Engineering:Wire|wire]] in which [[Physics:Quantum mechanics|quantum]] effects influence the transport properties. Usually such effects appear in the dimension of nanometers, so they are also referred to as nanowires.

== Quantum effects ==
If the diameter of a wire is sufficiently small, electrons will experience quantum confinement in the transverse direction. As a result, their transverse energy will be limited to a series of discrete values. One consequence of this [[Physics:Quantization|quantization]] is that the classical formula for calculating the [[Physics:Electrical resistance|electrical resistance]] of a wire,
: <math>R = \rho \frac{l}{A},</math>
is not valid for quantum wires (where <math>\rho</math> is the material's resistivity, <math>l</math> is the length, and <math>A</math> is the cross-sectional area of the wire).

Instead, an exact calculation of the transverse energies of the confined electrons has to be performed to calculate a wire's resistance. Following from the quantization of electron energy, the [[Physics:Electrical conductance|electrical conductance]] (the inverse of the resistance) is found to be quantized in multiples of <math>2e^2/h</math>, where <math>e</math> is the [[Physics:Electron charge|electron charge]] and <math>h</math> is the [[Physics:Planck constant|Planck constant]]. The factor of two arises from [[Physics:Spin|spin]] degeneracy. A single ballistic quantum channel (i.e. with no internal scattering) has a conductance equal to this quantum of conductance. The conductance is lower than this value in the presence of internal scattering.<ref>S. Datta, ''Electronic Transport in Mesoscopic Systems'', Cambridge University Press, 1995, {{ISBN|0-521-59943-1}}.</ref>

The importance of the quantization is inversely proportional to the diameter of the [[Physics:Nanowire|nanowire]] for a given material. From material to material, it is dependent on the electronic properties, especially on the [[Physics:Effective mass (solid-state physics)|effective mass]] of the electrons. Physically, this means that it will depend on how conduction electrons interact with the atoms within a given material. In practice, [[Physics:Semiconductor|semiconductor]]s can show clear conductance quantization for large wire transverse dimensions (~100 nm) because the electronic modes due to confinement are spatially extended. As a result, their Fermi wavelengths are large and thus they have low energy separations. This means that they can only be resolved at cryogenic temperatures (within a few degrees of [[Physics:Absolute zero|absolute zero]]) where the thermal energy is lower than the inter-mode energy separation.

For metals, [[Physics:Quantization|quantization]] corresponding to the lowest energy states is only observed for atomic wires. Their corresponding wavelength being thus extremely small they have a very large energy separation which makes resistance quantization observable even at room temperature.

== Carbon nanotubes ==
thumb|Band structures computed using [[tight binding approximation for (6,0) CNT (zigzag, [[Chemistry:Metal|metal]]lic), (10,2) CNT (semiconducting) and (10,10) CNT (armchair, metallic)]]

The [[Physics:Carbon nanotube|carbon nanotube]] is an example of a quantum wire. A metallic single-walled carbon nanotube that is sufficiently short to exhibit no internal scattering (ballistic transport) has a conductance that approaches two times the [[Physics:Conductance quantum|conductance quantum]], <math>2e^2/h</math>. The factor of two arises because carbon nanotubes have two spatial channels.<ref>{{cite book|last1=Dresselhaus|first1=M. S.|last2=Dresselhaus|first2=G.|last3=Avouris|first3=Ph.|author-link3=Phaedon Avouris|title=Carbon nanotubes: synthesis, structure, properties, and applications|publisher= Springer|date= 2001|ISBN=3-540-41086-4}}</ref>

The structure of a nanotube strongly affects its electrical properties. For a given (''n'',''m'') nanotube, if ''n'' = ''m'', the nanotube is metallic; if ''n'' − ''m'' is a multiple of 3, then the nanotube is semiconducting with a very small band gap, otherwise the nanotube is a moderate [[Physics:Semiconductor|semiconductor]]. Thus all armchair (''n'' = ''m'') nanotubes are metallic, and nanotubes (6,4), (9,1), etc. are semiconducting.<ref name="Curvature">{{cite journal|first1=X.|last1=Lu|first2=Z.|title=Curved Pi-Conjugation, Aromaticity, and the Related Chemistry of Small Fullerenes (C<sub>60</sub>) and Single-Walled Carbon Nanotubes|journal=[[Chemistry:Chemical Reviews|Chemical Reviews]]|volume=105|pages=3643–3696|year=2005|doi=10.1021/cr030093d|issue=10|last2=Chen|pmid=16218563}}</ref>

== See also ==
* [[Physics:Conductance quantum|Conductance quantum]]
* [[Physics:Quantum dot|Quantum dot]]
* [[Physics:Quantum point contact|Quantum point contact]]
* [[Physics:Quantum well|Quantum well]]

== References ==

{{reflist}}

[[Category:Quantum electronics]]
[[Category:Semiconductor structures]]
[[Category:Mesoscopic physics]]

{{Sourceattribution|Quantum wire}}

Physics:Quantum wire - Revision history

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