We study some spectral properties of a simple two-dimensional model for small angle defects in crystals and alloys. Starting from a periodic potential , we let in the right half-plane and in the left half-plane , where is the usual matrix describing rotation of the coordinates in by an angle . As a main result, it is shown that spectral gaps of the periodic Schrödinger operator fill with spectrum of as . Moreover, we obtain upper and lower bounds for a quantity pertaining to an integrated density of states measure for the surface states.
Cite this article
Rainer Hempel, Martin Kohlmann, Spectral properties of grain boundaries at small angles of rotation. J. Spectr. Theory 1 (2011), no. 2, pp. 197–219DOI 10.4171/JST/9