The symmetry of crystalline layers and multilayers is described by the diperiodic groups. Their irreducible representations are classified and tabulated. On this basis some physical properties are investigated.

YBa2Cu3O7 (123) BREAKDOWN of the Jahn-Teller theorem is predicted for few structures only.
CuO2conducting 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 CuO2 Layers, 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

B. Nikolic, M.Sci Thesis
Vibronska (ne)stabilnost diperiodicnih sistema (pdf 616 KB)