[GROUP 1: Derivation]
– In a 1D wire, connecting two reservoirs of potential, the density of states is given by dψ/dE = 2/(h^2).
– The factor 2 comes from electron spin degeneracy.
– h is the Planck constant.
– v is the electron velocity.
– The voltage across the wire is given by V = – (V₁ – V₂)/e, where e is the electron charge.
[GROUP 2: Occurrence]
– Quantized conductance occurs in wires that are ballistic conductors.
– This happens when the elastic mean free path (λ) is much larger than the length of the wire (L).
– B. J. van Wees et al. first observed the effect in a point contact in 1988.
– Carbon nanotubes exhibit quantized conductance independent of diameter.
– The quantum hall effect can be used to precisely measure the conductance quantum value.
[GROUP 3: Related Concepts]
– Mesoscopic physics.
– Quantum point contact.
– Quantum wire.
– Thermal conductance quantum.
[GROUP 4: Notes]
– The unit of conductance is the siemens (S).
[GROUP 5: References]
– 2018 CODATA Value: conductance quantum. The NIST Reference on Constants, Units, and Uncertainty.
– S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, 1995, ISBN 0-521-59943-1.
– B.J. van Wees et al. (1988). Quantized Conductance of Point Contacts in a Two-Dimensional Electron Gas. Physical Review Letters, 60 (9): 848–850. doi:10.1103/PhysRevLett.60.848.
– S. Frank, P. Poncharal, Z. L. Wang, W. A. de Heer (1998). Carbon Nanotube Quantum Resistors. Science, 280 (1744–1746): 1744–6. doi:10.1126/science.280.5370.1744.
– Bueno, P. R. (2020). Electron transfer and conductance quantum. Physical Chemistry Chemical Physics, 22 (45): 26109–26112. doi:10.1039/D0CP04522E. Source: https://en.wikipedia.org/wiki/Conductance_quantum
The conductance quantum, denoted by the symbol G0, is the quantized unit of electrical conductance. It is defined by the elementary charge e and Planck constant h as:
- = 7.748091729...×10−5 S.
It appears when measuring the conductance of a quantum point contact, and, more generally, is a key component of the 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/RK).
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.
