Creating topological interfaces and detecting chiral edge modes in a two-dimensional optical lattice

We propose a general scheme to create chiral topological edge modes within the bulk of two-dimensional engineered quantum systems. Our method is based on the implementation of topological interfaces, designed within the bulk of the system, where topologically protected edge modes localize and freely propagate in a unidirectional manner. This scheme is illustrated through an optical-lattice realization of the Haldane model for cold atoms [G. Jotzu et al., Nature (London) 515, 237 (2014)], where an additional spatially varying lattice potential induces distinct topological phases in separated regions of space. We present two realistic experimental configurations, which lead to linear and radial-symmetric topological interfaces, which both allow one to significantly reduce the effects of external confinement on topological edge properties. Furthermore, the versatility of our method opens the possibility of tuning the position, the localization length, and the chirality of the edge modes, through simple adjustments of the lattice potentials. In order to demonstrate the unique detectability offered by engineered interfaces, we numerically investigate the time evolution of wave packets, indicating how topological transport unambiguously manifests itself within the lattice. Finally, we analyze the effects of disorder on the dynamics of chiral and nonchiral states present in the system. Interestingly, engineered disorder is shown to provide a powerful tool for the detection of topological edge modes in cold-atom setups.