In Laughlin's gedanken experiment which aims to explain quantization of Hall conductance, one takes the adiabatic derivative of the Hamiltonian with respect to vector potential. Now it seems that it is claimed that flux change by a flux quantum would leave the Hamiltonian unchanged upto a gauge transformation and so the quantization follows. My question is that, is there a general principle which guarantees flux(enclosed) changes by flux quantum has no effect on physical quantities? Let me also state that it does seem to be the case because
- Aharonov-Bohm oscillations are invariant under flux quantum change.
- All properties of an electron in a ring enclosing a flux are insensitive to a change by flux quantum. etc.
But is this true when we have impurities, arbitrary potential etc? It seems to me that this is related to Byers-Yang work on superconductor flux quantization. Thoughts?