Conductance quantum

The conductance quantum, denoted by the symbol G₀ is the quantized unit of electrical conductance. It is defined as:

${\displaystyle G_{0}={\frac {2e^{2}}{h}}}$= 6995774809173100000♠7.7480917310(18)×10⁻⁵ S.

It appears when measuring the conductance of a quantum point contact, and, more generally, is a key component of Landauer formula which relates the electrical conductance of a quantum conductor to its quantum properties. It is twice the reciprocal of the von Klitzing constant (2/R_K).

Note that the conductance quantum does not mean that the conductance of any system must be an integer multiple of G₀. Instead, it describes the conductance of two quantum channels (one channel for spin-up and one channel for spin-down) if the probability for transmitting an electron that enters the channel is unity, i.e. if transport through the channel is ballistic. If the transmission probability is less than unity, then the conductance of the channel is less than G₀. The total conductance of a system is equal to the sum of the conductances of all the parallel quantum channels that make up the system.

In a 1D wire adiabaticly connecting two reservoirs of potential ${\displaystyle u_{1}}$ and ${\displaystyle u_{2}}$:

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