nLab flux quantum

Idea

In electromagnetism, the standard flux quantization condition (“Dirac charge quantization”) implies that the magnetic flux $\Phi_\Sigma$ through a closed surface $\Sigma$ (which may be the one-point compactification of an open surface if flux is constrained to vanish at infinity) is an integer multiple $N \in \mathbb{N}$ of an indecomposable quantum of magnetic flux $\Phi_0$ :

\Phi_\Sigma \;=\; N \cdot \Phi_0 \,.

Individual magnetic flux quanta are directly observable in experiment:

in the guise of Abrikosov vortices for magnetic flux through effectively 2-dimensional type II superconductors

(since the elementary charge carries in this case are Cooper pairs of electrons what is called the flux quantum for superconductors is in fact $\tfrac{1}{2}\Phi_0$ )
in the guise of solitonic anyon quasi-particles for magnetic flux through effectively 2-dimensional fractional quantum Hall systems

and, hypothetically (conditioned on the existence of magnetic monopoles):

The quantum of magnetic flux is

\phi_0 \;\coloneqq\; \frac{h}{e} \,,

where:

In SI units this is approximately

\begin{aligned} \phi_0 &\equiv\; \frac{h}{e} \\ &\sim\; \frac {6.626 \times 10^{-34} \, J s} {1.602 \times 10^{-19} \, C} \\ &\sim\; 4.136 \times 10^{-15} \, \frac{J s}{C} \\ &=\; 4.136 \times 10^{-15} \, T m^2 \,, \end{aligned}

where in the last step we used that

one Joule is one Newton meter

J \;=\; N m

and one Tesla is one Newton second per Coulomb meter

T \;\coloneqq\; \frac { N s } { C m } \,.