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A concept is introduced for physical equivalence of energy bands in solids: two energy bands are physically equivalent if their branches have identical continuity chords (symmetries) and identical Berry phases. 14 pairs of simple bands exist that are described by equivalent band representations but are nevertheless physically inequivalent because they have different topologies. Examples are given of physically equivalent and physically inequivalent composite energy bands. All simple bands on different Wyckoff positions are physically inequivalent and they correspond therefore to different energy bands.
Michel et al. (Fri,) studied this question.
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