Miniband and Gap Evolution in Gauss Chains.

The Gauss chain is a one-dimensional quasiperiodic lattice with sites at zj=jnd, where j∈{0, 1, 2, …, N-1}, n∈{2, 3, 4, …}, and is the underlying lattice constant. We numerically study the formation of a hierarchy of minibands and gaps as increases using a Kronig-Penney model. Increasing empirically results in a more fragmented miniband and gap structure due to the rapid increase in the number of minibands and gaps as increases, in agreement with previous studies. We show that the Gauss chain zj=j2d and a specific generalized Gauss chain, zj=(j2±12j)d, are treatable by a real-space renormalization group approach. These appear to be the only Gauss chains treatable by this approach, suggesting a hidden symmetry for the quadratic cases.