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Author: Fulga, Ion Cosma × Subject: Topological insulators ×

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    Anomalous levitation and annihilation in Floquet topological insulators
    (College Park, MD : APS, 2020) Liu, Hui; Fulga, Ion Cosma; Asbóth, János K.
    Anderson localization in two-dimensional topological insulators takes place via the so-called levitation and pair annihilation process. As disorder is increased, extended bulk states carrying opposite topological invariants move towards each other in energy, reducing the size of the topological gap, eventually meeting and localizing. This results in a topologically trivial Anderson insulator. Here, we introduce the anomalous levitation and pair annihilation, a process unique to periodically driven, or Floquet, systems. Due to the periodicity of the quasienergy spectrum, we find it is possible for the topological gap to increase as a function of disorder strength. Thus, after all bulk states have localized, the system remains topologically nontrivial, forming an anomalous Floquet-Anderson insulator (AFAI) phase. We show a concrete example for this process, adding disorder via on-site potential “kicks” to a Chern insulator model. By changing the period between kicks, we can tune which type of (conventional or anomalous) levitation and annihilation occurs in the system. We expect our results to be applicable to generic Floquet topological systems and to provide an accessible way to realize AFAIs experimentally, without the need for multistep driving schemes.
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    Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors
    (Amsterdam : SciPost Foundation, 2021) Geier, Max; Fulga, Ion Cosma; Lau, Alexander
    We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct d-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to (d−2)-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.