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.

BREAKDOWN of the
JahnTeller theorem is predicted for few structures
only.
CuO_{2 }conducting
plane of HTS compounds is among them.


Computer implementation of diperiodic symmetry
is developping (program for the irreducible representations is available).
References:
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 JahnTeller 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. 8104, 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) 365248.
B.
Nikolic, M. Damnjanovic and I.
Milosevic,
Electronphonon
Coupling Reduction in Tetragonal and Hexagonal Layers,
2D Conductivity
in Surface States and Monolayers, 58 March 2001, Bad Honnef, Germany