Electronic Structure of 1D and 2D Quasiperiodic Systems

This Demonstration shows the electronic levels of 1D and 2D aperiodic systems compared with the related electronic density of states (DOS) and integrated DOS (IDOS). The latter are computed as histograms, counting the number of electronic levels in a given energy bin. The electronic structure is calculated using the tight-binding method [1].

The 1D and 2D systems are the octonacci chain and the labyrinth tiling considered in the previous Demonstration by the author: Labyrinth Tiling from Quasiperiodic Octonacci Chains. You can choose the DOS or the IDOS of a 1D or 2D system to see the differences between the two systems.

By lowering the value of the ratio you can drive the system from periodic order (), in which the bond lengths in the octonacci systems are the same everywhere, to aperiodic order, in which there are both short and long bonds. At the same time, the systems experience a transition from a metallic to an insulating state. You can see this from the appearance of gaps in the electronic level spectra and DOS profile. In the IDOS plots, note the presence of plateaus in the profile, since there are no electronic levels to be counted in those energy ranges (see snapshot 6).

Snapshot 1: electronic density of states for the 1D system with periodic order ()

Snapshot 2: electronic density of states for the 2D system with periodic order ()

Snapshot 3: electronic density of states for the 2D system with aperiodic order ()

Snapshot 4: integrated electronic density of states for the 1D system with periodic order ()

Snapshot 5: integrated electronic density of states for the 2D system with periodic order ()

Snapshot 6: integrated electronic density of states for the 2D system with aperiodic order ()

Reference

[1] U. Grimm and M. Schreiber, "Energy Spectra and Eigenstates of Quasiperiodic Tight-Binding Hamiltonians," in Quasicrystals: Structure and Physical Properties (H.-R. Trebin, ed.), Weinheim, Germany: Wiley-VCH, 2003 pp. 210–235. arxiv.org/abs/cond-mat/0212140.