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\begin_layout Chapter
Topological insulators 
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name "sec:TI-Module"

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topological insulator
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TI
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\begin_layout Standard
For topological insulators the Z2 invariants 
\begin_inset Formula $\nu_{0};\left(\nu_{1}\nu_{2}\nu_{3}\right)$
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 can be calculated.
 There is a 
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 submenu with a corresponding help screen to explain the input.
 In the newer version it is possible to calculate the invariants for systems
 with and without inversion symmetry.
 The latter uses Wannier centers to find the invariants.
 This is a rather involved topic, which requires intent user participation.
 The essentials are explained in the context of the 
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 module elsewhere 
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../pyfplo/pyfplo.pdf
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 since internally the same code is used.
 Note, that if calculated by 
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 the details of the results differ, since an all-orbital Wannier basis is
 constructed.
 while in 
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 a user defined reduced basis Wannier model is constructed.
 The topology should not change.
 However, the 
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-version of the algorithm is naturally slower and usually shows more Wannier
 centers (semi core and other fully occupied orbitals, ommited in the reudced
 Wannier model).
 If surface states are desired it is always better to first construct a
 Wannier model and to use 
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.
 This is just faster at the end.
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