The Role of Quasiperiodicity on the Electronic Structure of Elements

The discovery of quasicrystals established that long-range atomic order does not require translational periodicity. Yet whether quasiperiodic order alone determines electronic structure—specifically the pseudogap at the Fermi level—remains unresolved. Here we present a definitive computational test using alkali metal (Na, K) monolayers on icosahedral Al-Pd-Mn, a system where quasiperiodic order is isolated from chemical complexity. Contrary to the prevailing hypothesis, we find no pseudogap in these perfectly ordered quasiperiodic monolayers. The density of states is indistinguishable from free-electron behavior with 𝑁(𝐸𝐹) = 0.32 ± 0.03 (Na) and 0.28 ± 0.03 (K) states/eV/atom. The quasiperiodic potential strength is an order of magnitude too weak (∣ 𝑉(𝐆∥) ∣≈ 0.05 eV), and the Hume-Rothery condition 2𝑘𝐹 =∣ 𝐆∥ ∣ fails by 8% (Na) and 12% (K). Orbital decomposition reveals negligible 𝑠 -𝑑 hybridization with charge transfer <0.05𝑒 per atom. These results establish that quasiperiodicity alone is insufficient to induce a pseudogap; strong orbital hybridization and precise Fermi surface resonance are required. We present a unified phase diagram that collapses all calculated data onto a single scaling function, enabling quantitative predictions for strain engineering (8% tensile on Na) and alloying (7% Pb in Na). This work resolves a fundamental question in quasicrystal physics and provides design principles for aperiodic materials.