In contrast to the usual bulk-boundary correspondence, topological states localized within the bulk of the system have been numerically identified in quasicrystalline structures, termed bulk localized transport (BLT) states. These states exhibit properties that are different from edge states, with one example being that the number of BLT states scales with the system size, while the number of edge states scales with the system perimeter. Here, we define a procedure to identify BLT states, which is based on the physically motivated crosshair marker and robustness analyses. Applying the procedure to the Hofstadter model on the Ammann-Beenker tiling, we find that the BLT states appear mainly for magnetic fluxes within a specific interval. While edge states appear at low densities of states, we find that BLT states can appear at many different densities of states. Many of the BLT states are found to have real-space localization that follows geometric patterns characteristic of the given quasicrystal. Furthermore, BLT states can appear both isolated and in groups within the energy spectrum, which could imply greater robustness for the states within such groups. The spatial localization of the states within a certain group can change, depending on the Fermi energy.

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• Chern number
• Quantum Hall effect
• Topological phases of matter
• Quasicrystals
• Lattice models in condensed matter