We study some spectral properties of a simple two-dimensional model for small
angle defects in crystals and alloys. Starting from a periodic potential V:R2→R, we let Vθ(x,y)=V(x,y) in the right half-plane
{x≥0} and Vθ=V∘M−θ in the left half-plane {x<0}, where Mθ∈R2×2 is the usual matrix describing
rotation of the coordinates in R2 by an angle θ. As a main result,
it is shown that spectral gaps of the periodic Schr\"odinger operator H0=−Δ+V fill with spectrum of Rθ=−Δ+Vθ as 0=θ→0. Moreover, we obtain upper and lower bounds for a quantity
pertaining to an integrated density of states measure for the surface states.Comment: 22 pages, 3 figure