Quantum Limit
When a conductor has spatial dimensions close to, where is Fermi wavevector of the conducting material, Ohm's law does not hold anymore. These small devices are called quantum point contacts. Their conductance must be an integer multiple of the value, where is the electronic charge and is Planck's constant. Quantum point contacts behave more like waveguides than the classical wires of everyday life and may be described by the Landauer scattering formalism. Point-contact tunneling is an important technique for characterizing superconductors.
Read more about this topic: Contact Resistance
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