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## Main Question or Discussion Point

Hi there, I am currently learning about the quantum hall effect and am a bit confused about the edge states picture and how this fits in with the rest of the theory.

In most books/review texts the theory is dicussed from the point of view of an infinite 2D system the magneteic field collapses the density of states in landau levels and then disorder in the system breaks the degeneracy of these landau levels. This broadens the landau levels so that extended states exist at the centtre of the landau levels and localized states in the tails. These localised states mean that there is a mobility gap between the different landau levels and this can then explain some of the features of the experimental data. After books have discussed this idea they present a real system for example hall bar where the energy of the lada level rises at the edges of the smaple becasue of the confinement. Where these landau levels meet the fermi level then 1D channels are formed and these are presented as the means by which curren traveles through the sample. What I am struggling to understand is how this edge state model fits with the infinite sample idea where you get extended staes percolating through the bulk and mobility gaps form localised states. Do you just ignore all these ideas in a real system with confinement at the edges of the sample? How do locallised states fit with edge states? Are the landau states at the edges broadened by disorder?

Thanks

Matt

In most books/review texts the theory is dicussed from the point of view of an infinite 2D system the magneteic field collapses the density of states in landau levels and then disorder in the system breaks the degeneracy of these landau levels. This broadens the landau levels so that extended states exist at the centtre of the landau levels and localized states in the tails. These localised states mean that there is a mobility gap between the different landau levels and this can then explain some of the features of the experimental data. After books have discussed this idea they present a real system for example hall bar where the energy of the lada level rises at the edges of the smaple becasue of the confinement. Where these landau levels meet the fermi level then 1D channels are formed and these are presented as the means by which curren traveles through the sample. What I am struggling to understand is how this edge state model fits with the infinite sample idea where you get extended staes percolating through the bulk and mobility gaps form localised states. Do you just ignore all these ideas in a real system with confinement at the edges of the sample? How do locallised states fit with edge states? Are the landau states at the edges broadened by disorder?

Thanks

Matt