Layer groups

The symmetry of crystalline layers and multilayers is described by the layer (or diperiodic) groups. Their irreducible representations are classified and tabulated (B. Nikolic). Rolling up relations of the symmetry of layers to the line groups of nanotubes are established.

This is basis for a number of investigations of physical properties of layers.
YBa2Cu3O7 (123) BREAKDOWN of the Jahn-Teller theorem is predicted for few structures only.
CuO2 conducting plane of HTS compounds is among them. 
The theorem broken by the electronic states enabling d(x2-y2) pairing.
Brillouine zone for CuO2

Computer implementation of diperiodic symmetry is developping (program for the irreducible representations is available).

I. Milosevic, M. Krcmar, B. Nikolic and M. Damnjanovic,
Vibronic (In)Stability for Mono- and Di- periodic Systems,
VI International Conference on "Mathematical Results in Quantum Mechanics",
Ascona, Switzerland, (1996) 26.
I. Milosevic, M. Krcmar, B. Nikolic and M. Damnjanovic ,
The Breakdown of the Jahn-Teller Theorem in CuO2Layers,
in Proceedings of the XXI International Colloquium on Group Theoretical
Methods in Physics: Physical Applications and Mathematical Aspects of
Geometry, Groups and Algebras, eds. H.-D. Doebner, W. Scherer and C. Schulte,
Vol. II, pg. 810-4, World Scientific, Singapore, 1997.
I. Milosevic, B. Nikolic, M. Damnjanovic and M. Krcmar,
Irreducible Representations of Diperiodic Groups (pdf 328 KB)
J. Phys. A: Math. Gen. 31 (1998) 3652-48.

          B. Nikolic, M. Damnjanovic and I. Milosevic,
          Electron-phonon Coupling Reduction in Tetragonal and Hexagonal Layers,
          2D Conductivity in Surface States and Monolayers, 5-8 March 2001, Bad Honnef, Germany