Conductance quantum

Squeeze a conductor down until it is narrower than the electron wavelength and its conductance stops being a property of material and geometry. It becomes quantised: each transverse mode that fits carries exactly 2e²/h, the factor of 2 being spin. Bas van Wees in Delft and David Wharam in Cambridge both saw the staircase in 1988, in split-gate constrictions in a semiconductor heterostructure, and you can see it in a lecture demonstration by touching two gold wires together and pulling them slowly apart — the current drops in visible steps as the contact thins to a single atom.

The reciprocal of this constant is a resistance of about 12.9 kΩ, the irreducible contact resistance of a perfect single-channel conductor. It is not dissipation in the wire — it is the price of squeezing a wide reservoir of electrons into one quantum channel, and it sets the ultimate floor for the resistance of a molecular or carbon-nanotube interconnect.