THE DECAGONAL PLANE-WAVE MODEL FOR 2D AND 3D QUASI-CRYSTALS

We examine the free electron model for some rational approximants of 2 D quasicrystals and quasi-lattices that exhibit quasiperiodicity in (x , y) planes and periodicity along the z-direction. Our study is based on a scattering potential with ten symmetrically oriented plane-wave c omponents in the (k(x), k(y)) plane for the 2D case, and two additiona l plane-wave components in directions perpendicular to the plane for t he 3D case. We calculate the band structure and the density of states for the rational approximants and examine the formation of a gap or a pseudogap in such systems. The relevance of this study to the stabilit y and electrical conduction property of decagonal quasicrystals is dis cussed.