Spectral features of one dimensional phononic quasicrystals

Abstract

Abstract We make an in-depth analysis of phonon frequencies and phononic eigenstates for one-dimensional phononic lattices. The results are analyzed for two different types of lattices, depending on whether the spring constants are uniform or aperiodic. For the first case, we find usual band structures with extended states, while several non-trivial features are obtained for the latter one. We find the eigenfrequencies by solving the set of coupled equations involving the motions of different atoms in the chain. The frequency spectrum reveals a fractal like behaviour and the fractality gradually decreases with the increase of the strength of the aperiodic modulation. The nature of different phonon states is characterized by calculating inverse participation ratio. A finite transition from conducting to non-conducting phase is obtained upon the variation of the modulation strength. We hope the results studied here can easily be tested in a suitable setup.