Thursday, July 11, 2013

1307.2577 (Kevin A. Madsen et al.)

Topological equivalence of crystal and quasicrystal band structures    [PDF]

Kevin A. Madsen, Emil J. Bergholtz, Piet W. Brouwer
A number of recent articles have reported existence of topologically non-trivial states and associated end states in one-dimensional incommensurate lattice models that would usually only be expected in higher dimensions. Using an explicit construction, we here argue that the end states have precisely the same origin as their counterparts in commensurate models and that incommensurability does in fact not provide a meaningful connection to the topological classification of systems in higher dimensions. In particular, we show that it is possible to smoothly interpolate between states with commensurate and incommensurate modulation parameter without closing the band gap and without states crossing the band gap.
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