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Some topological invariant of high order topological insulator, e.g. quadrupole moment $Q_{xy}$, may also be considered, which can be computed by Wilson loop.
Currently we have Wilson loop methods which are very general and can be used to calculate
However, when calculating the total Chern number
We should add a direct Chern number calculation based on plaquettes, as in eg
a. Fukui et al https://doi.org/10.1143/JPSJ.74.1674
b. Zhao et al https://doi.org/10.1364/OE.380077
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