Quantum 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.

Following from the quantization of electron energy, the electrical conductance (the inverse of the resistance) is found to be quantized in multiples of

[1] The importance of the quantization is inversely proportional to the diameter of the nanowire for a given material.

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.

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.

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,