We propose a realization of a two-dimensional higher-order topological insulator with ultracold atoms loaded into orbital angular momentum (OAM) states of an optical lattice. The symmetries of the OAM states induce relative phases in the tunneling amplitudes that allow to describe the system in terms of two decoupled lattice models. Each of these models displays one-dimensional edge states and zero-dimensional corner states that are correlated with the topological properties of the bulk. We show that the topologically nontrivial regime can be explored in a wide range of experimentally feasible values of the parameters of the physical system. Furthermore, we propose an alternative way to characterize the second-order topological corner states based on the computation of the Zak's phases of the bands of first-order edge states.

%B Phys. Rev. B %V 100 %P 205109 %8 Nov %U https://link.aps.org/doi/10.1103/PhysRevB.100.205109 %R 10.1103/PhysRevB.100.205109 %0 Journal Article %J Phys. Rev. A %D 2019 %T Topological edge states and Aharanov-Bohm caging with ultracold atoms carrying orbital angular momentum %A G. Pelegrí %A A. M. Marques %A R. G. Dias %A A. J. Daley %A J. Mompart %A V. Ahufinger %XWe show that bosonic atoms loaded into orbital angular momentum l=1 states of a lattice in a diamond-chain geometry provide a flexible and simple platform for exploring a range of topological effects. This system exhibits robust edge states that persist across the gap-closing points, indicating the absence of a topological transition. We discuss how to perform the topological characterization of the model with a generalization of the Zak's phase and we show that this system constitutes a realization of a square-root topological insulator. Furthermore, the relative phases arising naturally in the tunneling amplitudes lead to the appearance of Aharanov-Bohm caging in the lattice. We discuss how these properties can be realized and observed in ongoing experiments.

%B Phys. Rev. A %V 99 %P 023613 %8 Feb %U https://link.aps.org/doi/10.1103/PhysRevA.99.023613 %R 10.1103/PhysRevA.99.023613 %0 Journal Article %J Phys. Rev. A %D 2019 %T Topological edge states with ultracold atoms carrying orbital angular momentum in a diamond chain %A G. Pelegrí %A A. M. Marques %A R. G. Dias %A A. J. Daley %A V. Ahufinger %A J. Mompart %XWe study the single-particle properties of a system formed by ultracold atoms loaded into the manifold of l=1 orbital angular momentum (OAM) states of an optical lattice with a diamond-chain geometry. Through a series of successive basis rotations, we show that the OAM degree of freedom induces phases in some tunneling amplitudes of the tight-binding model that are equivalent to a net π flux through the plaquettes. These effects give rise to a topologically nontrivial band structure and protected edge states which persist everywhere in the parameter space of the model, indicating the absence of a topological transition. By taking advantage of these analytical mappings, we also show that this system constitutes a realization of a square-root topological insulator. In addition, we demonstrate that quantum interferences between the different tunneling processes involved in the dynamics may lead to Aharanov-Bohm caging in the system. All these analytical results are confirmed by exact diagonalization numerical calculations.

%B Phys. Rev. A %V 99 %P 023612 %8 Feb %U https://link.aps.org/doi/10.1103/PhysRevA.99.023612 %R 10.1103/PhysRevA.99.023612