Topology, edge states, and zero-energy states of ultracold fermionic atoms in 1D optical superlattices

Recent advance in generating optical superlattices offers opportunities for exploring interesting band structures. The simplest, dimerized superlattice is known to be a topological insulator when modeled as the Su-Schrieffer-Heeger model. By generalizing the modulation of onsite potential and hopping coefficient to higher periods, more topological and geometrical properties can emerge in superlattices. We show that a 1D optical superlattice with modulating onsite potentials can have nonzero Chern numbers, and the bulk-boundary correspondence leads to localized edge states. We show possibilities of assembling two superlattices with different topologies into a ring, and two internal boundaries with localized edge states can be generated. In the presence of modulating hopping coefficients, there are symmetry-related modes showing localization or zero-energy. Selected schemes for measuring those special states by depleting the mobile particles away from the boundary or probing the local density of states will also be discussed. Reference: Y. He, K. Wright, S. Kouachi, and C. C. Chien, arXiv: 1712.06538.