Electronic structure and transport in approximants of the Penrose tiling

Abstract

We present numerical calculations of electronic structure and transport in Penrose approximants. The electronic structure of perfect approximants shows a spiky density of states and a tendency to localization that is more pronounced in the middle of the band. Near the band edges the behavior is more similar to that of free electrons. These calculations of band structure and in particular the band scaling suggest an anomalous quantum diffusion when compared to normal ballistic crystals. This is confirmed by a numerical calculation of quantum diffusion which shows a crossover from normal ballistic propagation at long times to anomalous, possibly insulator-like, behavior at short times. The time scale t*(E) for this crossover is computed for several approximants and is detailed. The consequences for electronic conductivity are discussed in the context of the relaxation time approximation. The metallic like or non metallic like behavior of the conductivity is dictated by the comparison between the scattering time due to defects and the time scale t*(E).

10 pages, 3 figures

References in corpus (4)

• Spin waves and local magnetizations on the Penrose tiling
• Energy levels and their correlations in quasicrystals
• Anomalous electronic transport in Quasicrystals and related Complex Metallic Alloys
• Electronic transport in AlMn(Si) and AlCuFe quasicrystals: Break-down of the semiclassical model

Cited by in corpus (5)

• Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
• Theory of spin Bott index for quantum spin Hall states in non-periodic systems
• Electronic properties of asymmetrically doped twisted graphene bilayers
• Sub-diffusive electronic states in octagonal tiling
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals