%0 Journal Article
%T Are there quantum oscillations in an incommensurate charge density wave?
%A Yi Zhang
%A Akash V. Maharaj
%A Steven A. Kivelson
%J Physics
%D 2014
%I arXiv
%R 10.1103/PhysRevB.91.085105
%X Because a material with an incommensurate charge density wave (ICDW) is only quasi-periodic, Bloch's theorem does not apply and there is no sharply defined Fermi surface. We will show that, as a consequence, there are no quantum oscillations which are truly periodic functions of $1/B$ (where $ B$ is the magnitude of an applied magnetic field). For a weak ICDW, there exist broad ranges of $1/B$ in which approximately periodic variations occur, but with frequencies that vary inexorably in an unending cascade with increasing $1/B$. For a strong ICDW, e.g. in a quasi-crystal, no quantum oscillations survive at all. Rational and irrational numbers really are different.
%U http://arxiv.org/abs/1410.5108v2