Topological bands in one-dimensional periodic potentials

Abstract

We study the properties of the quantum states in the one-dimensional system with a shifted periodic potential in both the discrete model and the continuous model. With open boundary conditions, the edge states appear in the energy gaps which indicate non-trivial topological structures. The Chern numbers with respect to the Bloch vector and the potential shift angle are computed. In the limit of the continuous model, the Chern number of each band is exactly one. We demonstrate the particle number pumped by the adiabatically shift of the potential is directly related to the topological invariants.

5 pages, 3 figures, 1 table

References in corpus (12)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Berry Phase Effects on Electronic Properties
• Topological Insulators with Inversion Symmetry
• Quantum Spin Hall Effect
• Topological States and Adiabatic Pumping in Quasicrystals
• Topological orders and Edge excitations in FQH states
• Experimental demonstration of the topological surface states protected by the time-reversal symmetry
• Edge states and topological phases in one-dimensional optical superlattices
• Real-time control of the periodicity of a standing wave: an optical accordion

Cited by in corpus (5)

• Topology, edge states, and zero-energy states of ultracold atoms in 1D optical superlattices with alternating onsite potentials or hopping coefficients
• Topological states in the Kronig-Penney model with arbitrary scattering potentials
• Magnonics along the wall in Bimeron Chain Domain Walls
• Engineering Topological Nodal Line Semimetals in Rashba Spin-Orbit Coupled Atomic Chains
• Topological control of the nonlinear-optical response of hybrid quantum systems