# Flux Quanta in the Arahanov-Bohm effect

I have been reading about the quantum hall effect during which i had to read about the AB effect used in the Laughlin gauge argument. In many sources, it is directly assumed that the flux quantum in the AB effect is $\frac{\hbar c}{e}$. How do I prove this? How do I prove this is the smallest change in magnetic flux that can occur? Why is it called the flux quantum if $\Phi$ is not quantized? How can I prove that it is the smallest flux change that would leave the physics same?

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Not sure if this will help: flux quantization arises in superconducting loops more because of the electrons than the electromagnetic field. The property of being a superconductor sets the boundary conditions which link the electrons and the electromagnetic field, and it's the fact that electrons can only have discrete (orbital) angular momentum around the loop that lead to discrete values for the flux. In turn, the discrete values of the angular momentum come from the purely geometrical fact that the electron wavefunction must have an integer number of cycles (wiggles) around the loop. –  Jess Riedel Apr 22 '13 at 14:20

For the reasoning behind "magnetic flux quantum" itself, in addition to a quantization of the magnetic flux from an electron which angular momenta is quantized; less trivial problem where this value appears is the following. If you consider periodic 2d structure with "element" area S and switch on the magnetic field, then you may choose gauge consistent with periodicity of the structure iff the flux through the area S is exactly integer number of $\frac{\hbar c}e$.