Symmetry and classification of energy bands in crystals
SOLIDES
CLASSIFICATION
ENERGIE
GROUPES SPATIAUX
To appear in Proceedings XVth International Colloquium on Group Theretical Methods in Physics (Varna, June 1987)
Abstract : An energy band in a solid contains an infinite number of states which transform linearly as a space group representation induced from a finite dimensional representation of the isotropy group of a point in space. A band representation is elementary if it cannot be decomposed as a direct sum of band representations; it describes a single band. We give a complete classification of the inequivalent elementary band representations.
MICHEL
BACRY
ZAK
P/87/42
IHES
10/1987
A4
11 f.
EN
TEXTE
PREPUBLICATION
P_87_42.pdf
1987
Structure and classification of band representations
CRISTALLOGRAPHIE
SOLIDES
ASTRONOMIE
ORBITE
ETOILES
MODELISATION
ENERGIE
ATOMES
Abstract : Band representaitons in solids are investigated in the general framework of induced representations by using the concepts of orbits (stars) and strata (Wyckoff positions) in their construction and classification. The connection between band representations and irreducible representations of space groups is established by reducing the former in the basis of quasi-Bloch functions wich are eigenfunctions of translations but ar not, in general, eigenfunctions of the Hamiltonian. While irreducible representations of space group ar fnite-dimensional and are induced from infinite-order little groups Gk for vectors K in the Brillouin zone, band representations are infinite-dimensional adn are induced from finite-order little groups Gr for vectors r in the Wigner-Seitz cell. This connection between irreductible representations and band representations of space groups shedd new light on the duality properties of the Brillouin zone and the Wigner-Seitz cell. As an introduction to band representations the induced representations of point groups wich id applied to the investigation of th equivalency of band representations. Based on this connection and on the properties of the crystallographic point groups a necessary condition id established for the inequivalency of band representations induced from maximal isotropy groups. For using this condition there is need fro the induced representaitons of oint groups and a full list of them is given in the paper. One is especially interested in irreducible-band representations which form the elementary building bricks for band representations. From the point of view of the physics, irreducible-band representations correspond to energy bands with minimal numbers of branches. A method id developped for finding all the inequivalent irreducible-band representations of space groups by using the induction from maximal isotropy groups. As a rule the latter leads to inequivalent irreducible-band representations. There are, however, few exceptions to this rule. A full list of such exceptions is tabulated in the paper. With this list at hand one can construct all the different irreducible-band representations of 2-dimensional space groups. For them we list the continuity chords of all their irreducible-band representations.
MICHEL
BACRY
ZAK
P/86/35
IHES
06/1986
A4
46 f.
EN
TEXTE
PREPUBLICATION
P_86_35.pdf
1986
Symmetry and topology of energy bands in crystals
CRISTAUX
BANDES D'ENERGIES
SYMETRIE
TOPOLOGIE
Lecture given at the internation schoolon Symmetry abd Structural Properties of Condensed Matter. August 27 - September 2, 1998, Zajaczkowo (Posnan), Poland.
MICHEL
P/99/07
IHES
01/1999
A4
9 f.
EN
TEXTE
PREPUBLICATION
P_99_07.pdf
1999
Recent results on the implications of crystal symmetry and time reversal
ZONES DE BRILLOUIN
COMPACTIFICATIONS
CRISTAUX
POLYNOMES
SYMETRIE
ANALYSE NUMERIQUE
Lecture given on August 1rst 1997 at the VIIIth International Conference on Symmetry Methods un Physics. JINR, Dubna, Russia.
MICHEL
P/98/09
IHES
02/1998
A4
7 f.
EN
TEXTE
PREPUBLICATION
P_98_09.pdf
1998
Wigner memorial lecture
CONGRES ET CONFERENCES
WIGNER
MELANGES ET HOMMAGES
Lecture given at Goslar (Germany) on july 16, 1996 to close the Wigner award ceremony during the 21st International Colloquium on Group Theoretical Methods in Physics
MICHEL
P/96/81
IHES
12/1996
A4
7 f.
EN
TEXTE
PREPUBLICATION
P_96_81.pdf
1996
Physical implications of crystal symmetry and time reversal
RESEAUX CRISTALLINS
SYMETRIE
ESPACE ET TEMPS
Lectures given at the international school on Symmetry and Structural Properties of Condensed Matter. August 28 - September 5, 1996, Zajaczkowo (Posnan), Poland.
MICHEL
P/96/80
IHES
12/1996
A4
13 f.
EN
TEXTE
PREPUBLICATION
P_96_80.pdf
1996
Tableau récapitulant les visiteurs en mathématique et physique théorique pour l'année 85-86
VISITEUR
PROFESSEUR PERMANENT
PROFESSEUR LONGUE DUREE
PHYSIQUE THEORIQUE
MATHEMATIQUE
IHES
A3.1.9.6.4/3
IHES
21/11/1985
21x29,7
1 f.
FR
TEXTE
RAPPORT
A3_1_9_6_4_3.pdf
1985