Electronic states of the icosahedral quasiperiodic systems in magnetic fields

The electronic properties of the icosahedral quasiperiodic system in a tile-dependent or uniform magnetic field is studied by quasi-Bloch scheme and the general solutions are obtained for the electronic states. The behavior of the three-dimensional (3D) non-interacting electrons in an icosahedral quasiperiodic system may be treated as the projection of that of the non-interacting pseudo-electrons in 6D. In the presence of the tile-dependent magnetic field, the non-interacting electrons are quasi-Bloch electrons, while they are partial quasi-Bloch electrons when the magnetic field is uniform.