Quantum wire
Encyclopedia
In condensed matter physics
, a quantum wire is an electrically
conducting
wire
, in which quantum
effects are affecting transport properties. Due to the quantum confinement of conduction electrons in the transverse direction of the wire, their transverse energy is quantized into a series of discrete values
("ground state" energy, with lower value), 
,... (see particle in a box
, quantum harmonic oscillator
). One consequence of this quantization
is that the classical formula for calculating the electrical resistivity
of a wire:
is not valid for quantum wires (where
is the resistivity, 
is the length, and 
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 resistance is also found to be quantized.
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. In simple words, it means that it will depend on how conduction electrons interact with the atoms within a given material. In practice, semiconductor
s 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 temperature (few kelvins) where the thermal excitation energy is lower than the inter-mode energy separation.
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 perfectly observable at room temperature.
carbon nanotube
s, at least in limited quantities. The advantages of making wires from carbon nanotubes include their high electrical conductivity (due to a high electron mobility
), light weight, small diameter
, low chemical reactivity, and high tensile strength
. The major drawback (as of 2005) is cost.
It has been claimed that it is possible to create macroscopic quantum wires. With a rope of carbon nanotubes, it is not necessary for any single fiber to travel the entire length, since quantum tunneling will allow electron
s to jump from strand to strand. This makes quantum wires interesting for commercial uses.
In April 2005, NASA
invested $11 million over four years with Rice University
to develop quantum wire with 10 times better conductivity than copper
at one-sixth the weight. It would be made with carbon nanotubes and would help reduce the weight of the next generation shuttle
; but can also have wide ranging apps..
Condensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...
, a quantum wire is an electrically
Electricity
Electricity is a general term encompassing a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning, static electricity, and the flow of electrical current in an electrical wire...
conducting
Electrical conductor
In physics and electrical engineering, a conductor is a material which contains movable electric charges. In metallic conductors such as copper or aluminum, the movable charged particles are electrons...
wire
Wire
A wire is a single, usually cylindrical, flexible strand or rod of metal. Wires are used to bear mechanical loads and to carry electricity and telecommunications signals. Wire is commonly formed by drawing the metal through a hole in a die or draw plate. Standard sizes are determined by various...
, in which quantum
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...
effects are affecting transport properties. Due to the quantum confinement of conduction electrons in the transverse direction of the wire, their transverse energy is quantized into a series of discrete values
("ground state" energy, with lower value), ,... (see particle in a boxParticle in a box
In quantum mechanics, the particle in a box model describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems...
, quantum harmonic oscillator
Quantum harmonic oscillator
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics...
). One consequence of this quantization
Quantization (physics)
In physics, quantization is the process of explaining a classical understanding of physical phenomena in terms of a newer understanding known as "quantum mechanics". It is a procedure for constructing a quantum field theory starting from a classical field theory. This is a generalization of the...
is that the classical formula for calculating the electrical resistivity
Resistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...
of a wire:
is not valid for quantum wires (where
is the resistivity, is the length, and 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 resistance is also found to be quantized.
The importance of the quantization is inversely proportional to the diameter of the nanowire
Nanowire
A nanowire is a nanostructure, with the diameter of the order of a nanometer . Alternatively, nanowires can be defined as structures that have a thickness or diameter constrained to tens of nanometers or less and an unconstrained length. At these scales, quantum mechanical effects are important —...
for a given material. From material to material, it is dependent on the electronic properties, especially on the effective mass
Effective mass
In solid state physics, a particle's effective mass is the mass it seems to carry in the semiclassical model of transport in a crystal. It can be shown that electrons and holes in a crystal respond to electric and magnetic fields almost as if they were particles with a mass dependence in their...
of the electrons. In simple words, it means that it will depend on how conduction electrons interact with the atoms within a given material. In practice, 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...
s 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 temperature (few kelvins) where the thermal excitation energy is lower than the inter-mode energy separation.
For metals, quantization
Quantization (physics)
In physics, quantization is the process of explaining a classical understanding of physical phenomena in terms of a newer understanding known as "quantum mechanics". It is a procedure for constructing a quantum field theory starting from a classical field theory. This is a generalization of the...
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 perfectly observable at room temperature.
Carbon nanotubes as quantum wires
It is possible to make quantum wires out of metallicMetal
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...
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...
s, at least in limited quantities. The advantages of making wires from carbon nanotubes include their high electrical conductivity (due to a high electron mobility
Electron mobility
In solid-state physics, the electron mobility characterizes how quickly an electron can move through a metal or semiconductor, when pulled by an electric field. In semiconductors, there is an analogous quantity for holes, called hole mobility...
), light weight, small diameter
Nanotechnology
Nanotechnology 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...
, low chemical reactivity, and high tensile strength
Tensile strength
Ultimate tensile strength , often shortened to tensile strength or ultimate strength, is the maximum stress that a material can withstand while being stretched or pulled before necking, which is when the specimen's cross-section starts to significantly contract...
. The major drawback (as of 2005) is cost.
It has been claimed that it is possible to create macroscopic quantum wires. With a rope of carbon nanotubes, it is not necessary for any single fiber to travel the entire length, since quantum tunneling will allow 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 to jump from strand to strand. This makes quantum wires interesting for commercial uses.
In April 2005, NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...
invested $11 million over four years with Rice University
Rice University
William Marsh Rice University, commonly referred to as Rice University or Rice, is a private research university located on a heavily wooded campus in Houston, Texas, United States...
to develop quantum wire with 10 times better conductivity than copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
at one-sixth the weight. It would be made with carbon nanotubes and would help reduce the weight of the next generation shuttle
Space Shuttle program
NASA's Space Shuttle program, officially called Space Transportation System , was the United States government's manned launch vehicle program from 1981 to 2011...
; but can also have wide ranging apps..
External links
- Armchair Quantum Wire and Richard Smalley's view for the future of energy