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
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
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
Ouvrages de mathématiques et physique élaborés à l'HES (informations communiquées par les visiteurs des années académiques 1970/71 et 1971/72)
TRAVAIL SCIENTIFIQUE
MATHEMATIQUES
PHYSIQUE
IHES
F3.2.5.1/3
IHES
21x29,7
12 f.
FR
TEXTE
RAPPORT
F3_2_5_1_3.pdf
1972
Lyapunov exponents and Hodge theory
EXPOSANTS DE LIAPOUNOV
THEORIE DE HODGE
KONTSEVICH
ZORICH
M/97/13
IHES
01/1997
A4
9 f.
EN
TEXTE
PREPUBLICATION
M_97_13.pdf
1997
Listes de visiteurs et de candidats à examiner pour le comité scientifique du 1er mars 1977
COMITE SCIENTIFIQUE
VISITEUR
MATHEMATICIEN
PHYSICIEN
H1.1.4.3.3/1
IHES
21x29,7
4 f.
EN
TEXTE
LISTE
H1_1_4_3_3_1.pdf
1977
Liste des visiteurs admis en 1971 : mathématiciens
VISITEUR
MATHEMATIQUES
IHES
F3.2.3.1/8
IHES
21x29,7
1 f.
FR
TEXTE
RAPPORT
F3_2_3_1_8.pdf
1971
Applications of Group Theory to Quantum Physics : Algebraic Apects
THEORIE DES GROUPES
THEORIE QUANTIQUE
CONGRES ET CONFERENCES
ATOMES
MOLECULES
PHYSIQUE NUCLEAIRE
SYMETRIE
HADRONS
Lectures given at the 1969 Battelle Summer Rencontres in Mathematics and Physics. Seattle - Washington - USA
MICHEL
P/69/X032
IHES
09/1969
A4
97 f.
EN
TEXTE
PREPUBLICATION
P_69_X032.pdf
1969