Abstract
The quantised Hall effect is studied using the relation of the Hall current to the energy change of the system against a gauge transformation. The numerical result on the ground Landau sub-band confirms that, with a rearrangement of some states at the boundaries to ensure the periodic dependence of the system on the magnetic flux with a period of one flux quantum, the Hall current exhibits a plateau in the localised regime with the quantised value, sigma xy=-e2/h.
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