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lattice Wannier functions

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Presentation on theme: "lattice Wannier functions"— Presentation transcript:

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

2 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

3 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) P,F,I,A,B,C,R Hexagonal/Rhombohedral abc-cab-bca-acb-bac-cba 1/2

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

5 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 point groups magnetic symbol A4 230 space groups 32 point groups

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

7 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

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

9 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

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

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

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

13 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

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