2011-01-06# Van der Waals force and von Klitzing resistance in metallic nano-contacts |

The von Klitzing fundamental constant is the quantum of resistance, denoted as RK = h/e/e, where h is Planck's constant and e is the charge of the electron. The value of the von Klitzing constant is RK = 25.8 kOhms. Now Markus Ternes from IBM and Max Planck Institute and collaborators have observed that the resistance of adjustable metallic contacts approaches resistance twice lower than RK. This result can be explained by the fact that electrons in metals come in two varieties, namely those "rotating" clockwise (“spin up”) and counterclockwise (“spin down”). Each of these two varieties provides one quantum of conductance, i.e. each variety gives the resistance to the contact that equals RK. Together they give the resistance half that of RK, because currents flow in parallel through the nano-contact. The experiments and matching calculations, reported in Physical Review Letters [Vol.106 p.016802 (2011)], show that as two tips are approached, the force and the resistance change exponentially, with essentially the same exponent. Initially two approaching metallic tips attract each other. At some small distance (of the order of an Angstrom or 0.1 nanometer) the attractive force is the maximum. At that distance the Klitzing resistance, for each variety of electrons, is realized, at least approximately. Further approach of the tips leads to a strong repulsion between the metallic tips. Yet, the resistance remains close to the Klitzing constant resistance (for each electronic spin).

## Van der Waals force and von Klitzing resistance in metallic nano-contacts