Identification and properties of topological states in the bulk of quasicrystals

TL;DR

This paper identifies and characterizes bulk localized transport (BLT) states in quasicrystals, revealing their properties, conditions for appearance, and potential robustness, which differ from traditional edge states.

Contribution

The paper introduces a new procedure to identify BLT states in quasicrystals and analyzes their properties and conditions for emergence in the Hofstadter model.

Findings

BLT states scale with system size, unlike edge states.

BLT states appear mainly within specific magnetic flux intervals.

Many BLT states exhibit geometric localization patterns.

Abstract

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 different from edge states, one example being that the number of BLT states scales with system size, while the number of edge states scales with 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.