Role of long-range quasiperiodic order in electronic properties

Determine the specific contributions of long-range quasiperiodic order to electronic properties in quasiperiodic structures, including how such order influences quantum diffusion, transport regimes, and the emergence of critical or sub-diffusive states across energies and dimensions.

Background

The paper reviews quantum diffusion in quasiperiodic tilings (Penrose and octagonal) and discusses how long-range order can produce unconventional transport regimes that depart from semiclassical Bloch-Boltzmann behavior. While numerical evidence shows both sub- and super-diffusive behavior depending on energy, the general mechanistic role of long-range quasiperiodicity remains unresolved.

Clarifying this role is central to understanding when and why quasiperiodic systems exhibit insulating-like versus metallic-like transport without conventional disorder, and how these regimes are affected by perturbations such as Anderson-type disorder.