Imaging Quasi-Periodic Electronic States in a Synthetic Penrose Tiling

TL;DR

This study visualizes and analyzes electronic states in a synthetic quasicrystal using atomic manipulation and scanning tunneling microscopy, revealing how quasiperiodic order influences electronic wave functions.

Contribution

It demonstrates the assembly of a Penrose tiling-based potential landscape and directly images quasiperiodic electronic states in a controlled setting.

Findings

Electronic wave functions exhibit quasiperiodic order.

Resonant state energies relate to local vertex structures.

Fourier analysis links electronic states to tiling geometry.

Abstract

Quasicrystals possess long-range order but lack the translational symmetry of crystalline solids. In solid state physics, periodicity is one of the fundamental properties that prescribes the electronic band structure in crystals. In the absence of periodicity and the presence of quasicrystalline order, the ways that electronic states change remain a mystery. Scanning tunneling microscopy and atomic manipulation can be used to assemble a two-dimensional quasicrystalline structure mapped upon the Penrose tiling. Here, carbon monoxide molecules are arranged on the surface of Cu(111) one at a time to form the potential landscape that mimics the ionic potential of atoms in natural materials by constraining the electrons in the two-dimensional surface state of Cu(111). The real-space images reveal the presence of the quasiperiodic order in the electronic wave functions and the Fourier analysis of our results links the energy of the resonant states to the local vertex structure of the quasicrystal.