Quantum wire networks have recently become of great interest. Here we deal with a novel nano material structure of a double gyroid wire network. We use methods of commutative and noncommutative geometry to describe this wire network. Its noncommutative geometry is closely related to noncommutative 3-tori as we discuss in detail.
Cite this article
Ralph M. Kaufmann, Sergei Khlebnikov, Birgit Wehefritz-Kaufmann, The geometry of the double gyroid wire network: quantum and classical. J. Noncommut. Geom. 6 (2012), no. 4, pp. 623–664DOI 10.4171/JNCG/101