It seems essential in Laughlin's gauge argument that the sample has to be cylindrical(or with similar toplogy), so that we can "thread" a thin solenoid through to control the gauge function on the surface of the cylinder. However, most IQHE experiments are done on flat samples, so how is Laughlin's argument really explaining IQHE?

Certainly I can imagine some experiments being done on cylindrical samples, but the confusion comes from the fact that, in various sources that I've read, after an exposition of flat-sample IQHE experiment(and maybe a calculation of Landau levels), they would pose Laughlin's argument immediately as an explanation, so I guess somehow it does work for flat samples but there is something simple I missed?

  • $\begingroup$ the Laughlin cylinder is equivalent to a flat 2D sample with periodic boundary conditions in one direction. so the question then becomes a question about why a finite macroscopic sample can be modelled with periodic boundary conditions. $\endgroup$
    – Praan
    Jun 28 '17 at 17:21

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