Conductance quantum

The conductance quantum (G₀) is the quantized unit of electrical conductance. It is defined as G₀ = 2e²/h = 7.7480917346(25)×10⁻⁵ Ω⁻¹ ≈ ¹⁄_{12906.4037217} Ω⁻¹.^[1] 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.

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.^[2]

An intuitive motivation from the uncertainty principle

A simple, intuitive motivation of the conductance quantum can made using the Heisenberg uncertainty principle, which states that the minimum energy-time uncertainty is ΔEΔt ~ h, where h is the Planck constant. The current I in a quantum channel can be expressed as e/τ, where τ is transit time and the e is electron charge. Applying a voltage V results in an energy E = eV. If we assume that the energy uncertainty is of order E and the time uncertainty is of order τ, we can write ΔEΔt ~ (eV)(e/I) ~ h. Using the fact that the electrical conductance G = I/V, this becomes G ~ e²/h.

References

See also

• Mesoscopic physics
• Quantum point contact
• Quantum wire
• Thermal conductance quantum