Instability of quasicrystalline order in the local Kalugin-Kitaev-Levitov model

Abstract

In 1978 Alexander and McTague noticed that a very simple Landau theory of crystallization led naturally to the consideration of structures that we would now describe as icosahedral quasicrystals. They concluded, however, that a body-centered-cubic (bcc) crystal would be the most favored phase. Shortly after the experimental discovery of such quasicrystals, Kalugin, Kitaev, and Levitov (KKL) argued that a very natural extension of the Alexander-McTague model could easily stabilize the icosahedral quasicrystal over the bcc crystal. Both investigations considered only the quadratic and cubic terms in the bulk free energy. It has been pointed out, however, that if the free energy with a local quartic term is directly minimized, then the quasicrystal is never a global minimum. We show here, in addition, that in the presence of a local quartic term the quasicrystal is not even metastable in the KKL model, being unstable against a collapse to the bcc crystal.