Irr files

Bilbao Crystallographic Server irr files

Information given in the irr files

The first row in the file gives the names of the topological indices in the (magnetic) space group.

Below, the sets of irreps are divided into isolated (gapped) bands, separated by dashed lines. The irreps are ordered according to the value of the energy. The first irreps correspond to the lowest energy.

The next row shows the following information:

Labels of the maximal k-vectors. Below each label, the labels identified irreducible representations are given. The matrices of the irreps can be consulted in REPRESENTATIONS DSG for space groups and in CoRepresentations for magnetic space groups.
dim: dimension of the isolated (gapped) band
type: type of the isolated band. The options are

TRIVIAL: the band can be expressed as linear combination of Elementary Band Representations using non-negative integer coefficients.

FRAGILE: the band can be expressed as linear combination of Elementary Band Representations where at least an integer coefficient must be negative.

STRONG: the band CANNOT be expressed as linear combination of Elementary Band Representations. It is strong topological.
top. ind: values of the (strong) topological indices of the isolated band. The indices are given in the first row of the file.
tot dim: dimension of the whole set of bands from bottom to the given band.
type all: type of the whole set of bands from bottom to the given band. The options are the same as in "type" given above
top. all: values of the (strong) topological indices of the whole set of bands from bottom to the given band. The indices are given in the first row of the file.

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