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We study some spectral properties of a simple two-dimensional model for smallangle defects in crystals and alloys. Starting from a periodic potential $V\colon \R^2 \to \R$, we let $V_\theta(x,y) = V(x,y)$ in the right half-plane$\{x \ge 0\}$ and $V_\theta = V \circ M_{-\theta}$ in the left half-plane $\{x< 0\}$, where $M_\theta \in \R^{2 \times 2}$ is the usual matrix describingrotation of the coordinates in $\R^2$ by an angle $\theta$. As a main result,it is shown that spectral gaps of the periodic Schr\"odinger operator $H_0 =-\Delta + V$ fill with spectrum of $R_\theta = -\Delta + V_\theta$ as $0 \ne\theta \to 0$. Moreover, we obtain upper and lower bounds for a quantitypertaining to an integrated density of states measure for the surface states.

Spectral Properties of Grain Boundaries at Small Angles of Rotation