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In this talk, I will try simple picture based presentation for students rather than providing exhaustive or rigorous presentation.
Hall effect, discovered in 19th century, has been undoubtedly used in industry as well as in fundamental physics.
Several variants of the original Hall effect have been established: anomalous Hall effect (AHE), spin Hall effect (SHE), quantum Hall effect (QHE),
and more to list up.
Topology plays an important role in understanding aforementioned phenomena, where Berry phase is commonly used in interpretation.
As a concrete example, Heusler compound Mn3A is visited, whose total magnetization vanishes but AHE exists.
This is indeed against the conventional wisdom, where topology or Berry phase plays some role.
Group theoretical approach is adapted for analysis - where we suggest to distinguish simple anti-crossing and nodal lines.