Bulk localized transport states in infinite and finite quasicrystals via magnetic aperiodicity

Robust edge transport can occur when charged particles in crystalline lattices interact with an applied external magnetic field. Such systems have a spectrum composed of bands of bulk states and in-gap edge states. For quasicrystalline systems, we still expect to observe the basic characteristics of bulk states and current-carrying edge states. We show that, for quasicrystals in magnetic fields, there is an additional third option - bulk localized transport (BLT) states. BLT states share the in-gap nature of the well-known edge states and can support transport, but they are fully contained within the bulk of the system, with no support along the edge. Thus, transport is possible along the edge and within distinct regions of the bulk. We consider both finite-size and infinite-size systems, using rigorous error controlled computational techniques that are not prone to finite-size effects. BLT states are preserved for infinite-size systems, in stark contrast to edge states. This allows us to observe transport in infinite-size systems, without any perturbations, defects, or boundaries being introduced. We confirm the in-gap topological nature of BLT states for finite- and infinite-size systems by computing the Bott index and local Chern marker (common topological measures). BLT states form due to magnetic aperiodicity, arising from the interplay of lengthscales between the magnetic field and the quasiperiodic lattice. BLT could have interesting applications similar to those of edge states, but now taking advantage of the larger bulk of the lattice. The infinite-size techniques introduced here, especially the calculation of topological measures, could also be widely applied to other crystalline, quasicrystalline, and disordered models.