Physics:Quantum wire - Revision history

WikiHarold: Remove imported red links from Quantum page

2026-05-23T23:48:37Z

Remove imported red links from Quantum page

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

	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>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 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>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>
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	{{reflist}}		{{reflist}}

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

	{{Sourceattribution\|Quantum wire}}		{{Sourceattribution\|Quantum wire}}

WikiHarold: Clean Quantum page image and red links

2026-05-23T23:35:57Z

Clean Quantum page image and red links

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	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	'''wire''' is a Book I topic in the Quantum Collection. 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. A quantum wire confines charge carriers in two transverse directions so that motion is effectively one-dimensional. This confinement quantizes transverse modes and changes conductance, density of states, and scattering behavior. Quantum wires are studied in semiconductor nanostructures, carbon nanotubes, atomic chains, and mesoscopic devices where coherence and finite-size effects become measurable.		'''wire''' is a Book I topic in the Quantum Collection. In mesoscopic physics, a '''quantum wire''' is an electrically conducting 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. A quantum wire confines charge carriers in two transverse directions so that motion is effectively one-dimensional. This confinement quantizes transverse modes and changes conductance, density of states, and scattering behavior. Quantum wires are studied in semiconductor nanostructures, carbon nanotubes, atomic chains, and mesoscopic devices where coherence and finite-size effects become measurable.
	</div>		</div>

	<div style="width:300px;">		<div style="width:300px;">
	[[File:~~File not found~~.~~png~~\|thumb\|280px\|~~No image available~~.]]		[[File:Quantum_wire_concept_map.svg\|thumb\|280px\|wire in the Quantum Collection.]]
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	== Quantum effects ==		== 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,		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 quantization is that the classical formula for calculating the electrical resistance of a wire,
	: <math>R = \rho \frac{l}{A},</math>		: <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).		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>		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 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.		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 of the electrons. Physically, this means that it will depend on how conduction electrons interact with the atoms within a given material. In practice, semiconductors 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.

	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.		For metals, 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 ==		== 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)]]		thumb\|Band structures computed using [[tight binding approximation for (6,0) CNT (zigzag, metallic), (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 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>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>		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 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=Chemical Reviews\|volume=105\|pages=3643–3696\|year=2005\|doi=10.1021/cr030093d\|issue=10\|last2=Chen\|pmid=16218563}}</ref>

	== See also ==		== See also ==

WikiHarold: Expand short Quantum intro

2026-05-23T22:59:02Z

Expand short Quantum intro

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	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.		'''wire''' is a Book I topic in the Quantum Collection. 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. A quantum wire confines charge carriers in two transverse directions so that motion is effectively one-dimensional. This confinement quantizes transverse modes and changes conductance, density of states, and scattering behavior. Quantum wires are studied in semiconductor nanostructures, carbon nanotubes, atomic chains, and mesoscopic devices where coherence and finite-size effects become measurable.
	</div>		</div>

WikiHarold: Use Quantum See also index module

2026-05-23T22:26:29Z

Use Quantum See also index module

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	== See also ==		== See also ==
	* [[Physics:Conductance quantum\|Conductance quantum]]		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also/Matter}}
	* [[Physics:~~Quantum dot~~\|~~Quantum dot]]~~
	* [[Physics:Quantum point contact\|~~Quantum point contact]]~~
	* [[Physics:Quantum ~~well\|Quantum well]]~~

	== References ==		== References ==

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	<div style="width:300px;">		<div style="width:300px;">
	~~<!--~~ No ~~lead~~ image available ~~in existing page~~. ~~-->~~		[[File:File not found.png\|thumb\|280px\|No image available.]]
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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 ==

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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}}