Quaternionic Berry connection by the Kramers multiplet and physical applications

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Recently a theory of the Berry connection of the Kramers multiplet with the time-reversal symmetry is formulated by Hatsugai. The present project is to develop this embryonic research area and to pursue the use of quaternionic Berry connections to define topological order parameters. The basic idea is applied for pyrochlore/Kagome lattice systems with Sp(1) gauge symmetry as a series of models in any dimensions. Further their topological characters are clarified.