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How is Laughlin's gauge argument explaining integer quantum hall effect(IQHE)?

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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?

This post imported from StackExchange Physics at 2014-04-07 08:29 (UCT), posted by SE-user Jia Yiyang
asked Jan 21, 2014 in Theoretical Physics by Jia Yiyang (2,465 points) [ no revision ]

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