Specific role of long‑range quasiperiodic order in electronic properties

Ascertain the specific role of long‑range quasiperiodic order in determining the electronic properties of quasiperiodic materials and quasiperiodic tilings, including how this order influences quantum diffusion and the emergence of critical or sub‑diffusive states across the spectrum.

Background

The paper analyzes wave-packet spreading and transport in quasiperiodic systems such as Penrose and octagonal tilings, identifying regimes ranging from super‑diffusive to sub‑diffusive depending on energy and timescales. Although extensive numerical evidence shows that quasiperiodicity can induce critical and sub‑diffusive states, the authors emphasize that the precise influence of long‑range quasiperiodic order on electronic properties has not been fully established.

They present results indicating two characteristic length scales (L1 and L2) that govern transitions from near‑diffusive to power‑law spreading and show marked sensitivity to disorder, but a comprehensive understanding of how long‑range order dictates these behaviors remains unresolved.