Quantum wire

In condensed matter physics, a quantum wire is an electrically conducting wire in which quantum effects influence the transport properties. Usually such effects appear in the dimension of nanometers, so they are also referred to as nanowires.

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,

is not valid for quantum wires (where ${\displaystyle \rho }$ is the material's resistivity, ${\displaystyle l}$ is the length, and ${\displaystyle A}$ is the cross-sectional area of the wire).

...
Wikipedia