# Edge channels in Quantum Hall effect

Why is the value of Hall conductance directly proportional to the number of edge channels in the sample?

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I think the reason this has gotten no response is because it's unclear what the OP already knows. It seems like if the OP knows words like "edge channels" then they should know the answer already...? –  genneth Oct 21 '12 at 18:29
In fact, the value of Hall conductance is NOT proportional to the number of edge channels in the sample. For example, $\sigma_{xy}=\frac13 \frac{e^2}{h}$ FQH state has one edge channel, and $\sigma_{xy}=\frac25 \frac{e^2}{h}$ FQH state has two edge channels.