constant

magnetic flux quantum

Superconducting flux quantum, h/(2e), the fundamental unit of magnetic flux in a superconductor
Value
\(\Phi_0 = 2.067833848 \times 10^{-15}\)weber
19 related articles · 1 formulas

Description

The magnetic flux quantum is the smallest possible unit of magnetic flux that can exist inside a superconductor. It is defined as h/(2e), where h is Planck's constant and e is the elementary charge. This quantization arises because the superconducting state is described by a macroscopic quantum wavefunction, and the flux through any closed loop must be an integer multiple of this fundamental value.

History

The concept was predicted by Fritz London in 1948, and the precise value h/(2e) was confirmed experimentally in 1961 by Deaver and Fairbank, and independently by Doll and Näbauer.

How it works

In a superconductor, electrons pair up into Cooper pairs that share a single quantum state. The wavefunction of these pairs must be single-valued around any closed loop, which forces the magnetic flux threading the loop to be quantized in units of h/(2e). This is analogous to how the angular momentum of an electron in an atom is quantized, but here it applies to the magnetic field trapped in a superconducting ring or vortex.

In practice

It is the basis for superconducting quantum interference devices (SQUIDs), which are extremely sensitive magnetometers used in medical imaging (MEG) and geological surveys.

Fun fact

The magnetic flux quantum is so small that the Earth's magnetic field would thread about 2×10^7 flux quanta through a typical superconducting ring of 1 cm² area.

Concept graph →

Formulas

$$\Delta Q = \nu \frac{e \Delta \Phi}{\Phi_0}$$
Charge quantization in superconductors relates flux change to accumulated charge.
What is in the formula
\Delta QvariableAccumulated charge change in the superconductor — electric charge coulomb
\Delta \PhivariableChange in magnetic flux through the superconducting loop — magnetic flux weber
\nuvariableFilling factor (integer or fractional) of the quantum Hall state — dimensionless
econstantMagnitude of the electric charge of a single electron or proton — elementary charge = 1.602176634e-19 coulomb
\Phi_0constantSuperconducting flux quantum, h/(2e), the fundamental unit of magnetic flux in a superconductor — magnetic flux quantum = 2.067833848e-15 weber

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