Inverse conductance quantum

This is the conductance quantum written as a resistance: h/2e², exactly half the von Klitzing constant. It is the smallest resistance a single quantum channel can present, and it is unavoidable. A ballistic conductor with no scattering at all still measures 12.9 kΩ, because the resistance lives in the mismatch between the wide electron reservoirs at each end and the single mode connecting them — Rolf Landauer's insight that conduction is transmission.

The number is a hard design limit for nanoelectronics. A single-walled carbon nanotube has two conducting channels, so its best possible resistance is about 6.5 kΩ regardless of length or purity, which is why nanotube interconnects have never displaced copper for long runs. It also appears in graphene, in break junctions, and in the resistance quantum that shows up whenever a quantum point contact opens one mode at a time.