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| In [[condensed matter physics]], a '''quantum wire''' is an [[electrical conductor|electrically conducting]] [[wire]] in which [[quantum mechanics|quantum]] effects influence the transport properties.
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| == Quantum effects ==
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| 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 quantized into a series of discrete values. One consequence of this [[Quantization (physics)|quantization]] is that the classical formula for calculating the [[electrical resistance]] of a wire:
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| <center><math>R=\rho{l \over A}</math></center>
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| is not valid for quantum wires (where <math>\rho</math> is the [[resistivity]], <math>l</math> is the length, and <math>A</math> is the cross-sectional area of the wire).
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| 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 [[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 [[electron charge]] and <math>h</math> is the [[Planck constant]]. The factor of two arises from [[spin (physics)|spin]] degeneracy. A single [[ballistic transport|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>
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| The importance of the quantization is inversely proportional to the diameter of the [[nanowire]] for a given material. From material to material, it is dependent on the electronic properties, especially on the [[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, [[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 [[absolute zero]]) where the thermal energy is lower than the inter-mode energy separation.
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| For metals, [[Quantization (physics)|quantization]] corresponding to the lowest [[energy state]]s 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.
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| ==Carbon nanotubes as quantum wires==
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| The [[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 [[conductance quantum]], <math>4e^2/h</math>. The factor of two arises because carbon nanotubes have two spatial channels.<ref>M. S. Dresselhaus, G. Dresselhaus, and Phaedon Avouris, ''Carbon nanotubes: synthesis, structure, properties, and applications'', Springer, 2001, ISBN 3-540-41086-4</ref>
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| ==See also==
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| * [[Conductance quantum]]
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| * [[Quantum point contact]]
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| * [[Quantum well]]
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| * [[Quantum dot]]
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| * [[Carbon nanotube]]
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| * [[Mesoscopic physics]]
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| ==References==
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| <references/>
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| [[Category:Nanoelectronics]]
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| [[Category:Quantum electronics]]
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| [[Category:Semiconductor structures]]
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| [[Category:Mesoscopic physics]]
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