Electronic level degeneracy in nonsymmorphic periodic or aperiodic crystals
Authors:
- 1 December 1997
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 56 (21) , 13607-13610
Abstract
The theory of space-group representations is extended to aperiodic crystals by reformulating it as the theory of symmetry-required degeneracies of electronic levels that emerges from the Fourier-space approach to crystal symmetry. As an illustration it is shown that the nonvanishing of a simple linear combination of phase functions belonging to commuting elements from the little group of q requires the degeneracy of all levels with generalized Bloch wave vector q. This condition is applied to all cubic and icosahedral centrosymmetric nonsymmorphic space groups, and to the two nonsymmorphic space groups of periodic crystals that have no systematic extinctions.Keywords
This publication has 7 references indexed in Scilit:
- Extinctions in scattering from periodic or aperiodic crystalsPhysica Status Solidi (a), 1995
- The space groups of icosahedral quasicrystals and cubic, orthorhombic, monoclinic, and triclinic crystalsReviews of Modern Physics, 1992
- The space groups of axial crystals and quasicrystalsReviews of Modern Physics, 1991
- Scale equivalence of quasicrystallographic space groupsPhysical Review B, 1988
- Ray representations of point groups and the irreducible representations of space groups and double space groupsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1966
- Symmetry of Fourier spaceActa Crystallographica, 1962
- Group Theory and its Applications to Physical ProblemsAmerican Journal of Physics, 1962