 08177 Emil Prodan
 The edge spectrum of Chern insulators with rough edges
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Oct 3, 08

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Abstract. Chern insulators are periodic band insulators with the property that their projector into the occupied bands have nonzero Chern number. For a Chern insulator with a homogeneous edge, it is known that the insulating gap is filled with continuum spectrum. The local density of states corresponding to this part of the spectrum is localized near the edge, hence the name edge spectrum. An interesting question arises, namely, if a rough edge, which can be seen as a strong random potential acting on these quasi 1dimensional states, would destroy the continuum edge spectrum. The typical argument against such scenario is the absence of backscattering channels, but this argument is difficult to be translated in a complete proof. This paper gives a fairly elementary proof that Chern insulators with random edges have continuous edge spectrum, whose degeneracy is no less than the total Chern number of the occupied bands.
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