Electronic Structure of Quasicrystals

Pierangelo Gröning, Swiss Federal Laboratories for Materials Testing and Research (EMPA)

Since their first public report by the end of 1984 [1], quasicrystals (QCs) have attracted a lot of scientific interest due to their extraordinary crystal structure and their unusual physical properties. QCs are characterized by the absence of translational symmetry, however in combination with a well defined atomic arrangement and rotational symmetry, which situates this class of materials between crystalline and disordered solids. QCs exhibit very particular mechanical, magnetic, electronic transport and surface properties, which have been partly associated whit the aperiodic atomic structure. The aperiodicity of QCs has triggered particular interest with regard to the valence electronic structure as the Bloch Theorem, fundamental to the electron band picture of classical crystalline solids, cannot be applied anymore and the concept of a well defined Brillouin zone and associated zone-folding breaks down. It has been suggested by theory that the valence electron states of QC should exhibit, due to the absence of translational symmetry, a new character lying in between the extended states of a classical periodic crystal and the localized states of a random atomic arrangement [2]. These new class of states was denoted as “critical states”, neither being extended nor localized. Associated with these critical states a so-called “spiky” density of states (DOS) was postulated showing a fractal-like appearance of peaks and pseudo gaps. However this spiky DOS could not be corroborated by experiments.

Figure 1
a) High-resolution STM image of the 5-fold surface of icosahedral Al70Pd21Mn9.
b) Model structure according to the Kastner-Papadopolos model. Characteristic features being the “white flower” (deep blue circle) and the “starfish” (light blue circle) have been high-lighted and compared to the structure model.


We have to best of our knowledge for the first time investigated the local density of states (LDOS) of different QCs using low temperature (5.3 K) Scanning Tunnelling Spectroscopy (STS) with sub-nanometer resolution.  Figure 2 shows differential conductance spectra measured at different positions in the “starfish” region (Fig.1). The spectra show a clear variability in peak and pseudogap position in this very small 2 nm wide area. In general we observe peaks in the LDOS of 30-50 meV FWHM confined to regions of 1 nm or less. We think that this is a strong indication of the spiky DOS predicted by the theory, which has not been observed before as the spiky aspect is lost when the LDOS is averaged over surface areas as small as some tens nm2.

Figure 2
Differential conductance spectra (dI/dV vs. bias voltage) measured on 6 positions (central star + 5 surrounding pentagons) in the so-called “starfish” structure (Fig. 1).


[1] D. Schechtman, I. Blech, D. Gratias, and J.W. Cahn, Phys. Rev. Lett. 53 (1984) 1951
[2] T. Fujiwara and T. Yokokawa, Phys. Rev. Lett. 66 (1991) 333
[3] O. Gröning, R. Widmer, P. Ruffieux, P. Gröning, Phil. Mag. 86 (2006) 773
[4] R. Widmer, O. Gröning, P. Ruffieux, P. Gröning, Phil. Mag. 86 (2006) 781


[Released: February 2008]