Exact Electron States in 1D (Quasi-) Periodic Arrays of Delta-Potentials

Abstract

In the solid state physics of crystals, an important part is played by the band structure of the electronic states. This band structure arises from the representation of the periodicity in the electronic state space. Powerful computational methods were developed for the calculation of band structures, among them the linear muffin-tin (LMTO) method [17] in the atomic sphere approximation (ASA) [1]. In the physics of quasicrystals, it is believed that the electronic system plays an important part [19]. Here one is lacking the periodic symmetry. To still use the powerful methods of band computations, one must replace the quasicrystal by a periodic approximant. The question arises how such approximant computations approach a quasiperiodic limit In a recent calculation [6] it is shown by a supercell analysis that an approximant computation may lead to artefacts in the electronic density of states (DOS). More detailed local properties of the electrons appear as derivatives of the electronic charge density in Mössbauer studies on quasicrystals [14].