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I can't understand why the number of electrons pumped per cycle of a quantum pump is protected topologically. enter image description here As for me this number is an integer in any case, because the number of electrons in every potential well cannot be continuous.

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  • $\begingroup$ What do you mean by "in any case"? $\endgroup$ – Dominic Else Dec 10 '18 at 14:03
  • $\begingroup$ I mean you cannot get the fractional number of electrons in a well, I forgot to write that chemical potential does not coincide with the level of electron in a well $\endgroup$ – Phys Dag Dec 10 '18 at 14:37
  • $\begingroup$ I still am missing your point. If you agree that the pumped charge is quantized then what is the distinction between "topological" or not? I will note though that the Thouless pump is much more general than this simple potential well picture, that is just an illustrative example. $\endgroup$ – Dominic Else Dec 10 '18 at 14:40
  • $\begingroup$ Can we say that quantization of pumping charge follows from that every electron cannot have a fractional charge? you can pump only entire electron or nothing $\endgroup$ – Phys Dag Dec 10 '18 at 14:46
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    $\begingroup$ Yes, even in the most general formulation of the Thouless pump, the quantization is ultimately a consequence of the fact that electric charge is quantized, or equivalently the symmetry group for charge conservation is U(1). $\endgroup$ – Dominic Else Dec 10 '18 at 14:49

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