Structure factor and the electronic structure in quadratic Gauss chains: A hidden symmetry revealed

Abstract

We consider the quadratic Gauss chain, a 1D nonperiodic lattice (Citrin, 2023 [6]) showing that although the chain is nonperiodic, the transfer matrix is periodic with period depending on the free-space wavevector k revealing the hidden symmetry of the quadratic Gauss chain. We obtain an exact expression for the structure factor and the extended-state electronic structure in a Kronig-Penney model in the infinite-length chain limit based on a transfer-matrix approach. In the limit of weak potential, we can express the extended-state spectrum in terms of the structure factor, indicating that feature in the structure factor will be reflected to some extent in the electronic structure.