lattice Wannier functions

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Presentation transcript:

lattice Wannier functions R. Caracas & X. Gonze WORKSHOP ABINIT 2002 Louvain-la-Neuve Crystallography and lattice Wannier functions in ABINIT

CRYSTALLOGRAPHY Crystal structure = Unit cell + Symmetry + mainly pre-processing tools Crystal structure = Unit cell + Symmetry + Atomic positions all symmetries space group all atoms asymmetric atoms check primitivity

space groups Space group number (spgroup) 1 .. 230 “International tables for crystallography” Space group number (spgroup) Bravais lattice (brvltt) Axis orientation (spgaxor) Axis origin (spgorig) 1 .. 230 P,F,I,A,B,C,R Hexagonal/Rhombohedral abc-cab-bca-acb-bac-cba 1/2

compute ALL Symmetries symmetry recognition structural data: ALL atoms + lattice parameters compute ALL Symmetries space group point group

magnetic space groups A’4 I 230 non-colored groups II 230 gray groups III 674 colored black/white groups IV 517 colored black/white groups Shubnikov 32+32+52 point groups magnetic symbol A4 230 space groups 32 point groups

R 33 32 31 23 22 21 13 12 11 {B/W} {R|t} S = t 3 2 1

miscellaneous Determination of the wave vector symmetry group {R|t} leaving invariant q symmetrize the dynamical matrix D Symmetrization of the stresses (relaxations) Check of the translation group

CRYSTALLOGRAPHIC LIBRARY future work non-magnetic space groups : improve generators magnetic space groups : further testing + improvements automatic recognition CRYSTALLOGRAPHIC LIBRARY

LATTICE WANNIER FUNCTIONS R. Caracas & X. Gonze WORKSHOP ABINIT 2002 LATTICE WANNIER FUNCTIONS Louvain - la - Neuve LATTICE WANNIER FUNCTIONS maximally localized LWF iterative procedure : interpolation of a certain group of bands by maximizing the overlap between neighbouring q points strict symmetry constraints atomic displacement pattern

kb ka kg ka = 0.4 kb = 0.1 kg = -1.0 avoided crossing X G X

G X X G R. Caracas & X. Gonze WORKSHOP ABINIT 2002 LATTICE WANNIER FUNCTIONS Louvain - la - Neuve G X G X

the lattice Wannier function: R. Caracas & X. Gonze WORKSHOP ABINIT 2002 LATTICE WANNIER FUNCTIONS Louvain - la - Neuve the lattice Wannier function: amplitude R

lwf in ABINIT : DEBUGGING stage special features: R. Caracas & X. Gonze WORKSHOP ABINIT 2002 LATTICE WANNIER FUNCTIONS Louvain - la - Neuve in ABINIT : lwf DEBUGGING stage special features: energy window of frozen states future development transformation to regions of frozen states of the BZ pinning of the ynq to general or high-symmetry points