Discussion of electronic properties of quasicrystals

Abstract

This article gives a short review of some important achievements in the field of electronic properties of quasicrystals. It focuses essentially on: the nature of quasicrystals as Hume-Rothery alloys, the energetics of quasicrystals and related phases, the magnetic properties, the localization of electronic states, and the transport properties. For each part we emphasize some promising directions of research. We end by listing some problems that are related to that of electrons in a quasiperiodic potential.

Keywords:

• aperiodic materials
• electronic properties

Acknowledgements

I am grateful to many colleagues: Prof. N.W. Ashcroft, Prof. J. Bellissard, C. Berger, F. Cyrot-Lackmann, J. Delahaye, Prof. T. Fujiwara, Prof. J. Friedel, T. Grenet, Prof. F. Hippert, J.P. Julien, Prof. T. Klein, L. Magaud, J.J. Préjean, P. Quémerais, S. Roche, and F. Triozon. I express special thanks to G. Trambly de Laissardière. This article is motivated by a discussion on the electronic properties of quasicrystals that took place during the conference ‘Quasicrystals–The Silver Jubilee’ and was initiated by the Conference Chair, Ron Lifshitz. The discussion was led by the author who was assisted by a panel of experts consisting of Janez Dolinsek, Francoise Hippert, and Guy Trambly de Laissardiere, to whom the author is grateful. It should be noted that the current article presents the author's personal thoughts and views on the current state of affairs, and is not an attempt to provide an accurate record of the panel discussion.