I am looking for a good reference to an online source or book, on the magnetic Aharonov-Bohm effect. I have read the appropriate sections from the book by Griffiths and Ballentine, and still haven't understood it properly. The reference should also contain topological arguments. I have done QM on the order of 4 chapters of Griffiths, and the first 2.5 chapters of Sakurai.
When I was reading QM course this year the lecturer gave us 2 examples:
- Tonomura et al., Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave, Phys. Rev. Lett. 56, 792 (1986). doi:10.1103/PhysRevLett.56.792.
- Webb et. al, Observation of $h/e$ Aharonov-Bohm Oscillations in Normal-Metal Rings, Phys. Rev. Lett. 54, 2696 (1985). doi:10.1103/PhysRevLett.54.2696, free version
I found one more on the arXiv:
- Ballesteros, M. and Weder, R. The Aharonov-Bohm Effect and Tonomura et al. Experiments. Rigorous Results. J. Math. Phys. 50 122108 (2009). doi:10.1063/1.3266176, arXiv:0903.2609 [math-ph].
I hope this is enough.
UPDATE: I wondered, if there where any papers on the topology on Aharonov-Bohm effect, and I found arXiv:1302.0456 [quant ph].
In the paper they mention, that 'The topology of the Aharonov-Bohm effect is provided by the externa boundary condition for the gauge field'. The reference they give for their statement is the original paper by Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).
I could not find the original paper by Aharonov and Bohm online, but maybe you can find it in your library. I hope that this turns out to be more useful than the previous papers a linked to.
The best reference for AB effect that I have come across until now, is Ryder's QFT. It starts by describing the effect, and calculating the phase change as usual. But, then he digs further and gives the topological explanation of the Aharanov-bohm effect as the non simply connectedness of the gauge group of electromagnetism (U(1)). It also described homotopy and fundamental groups in sufficient detail..