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Everett You
Everett You
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A simple argument: suppose our Brillouin zone is a cubic. If we have a Chern flux penetrating the upper surface, then the same flux with the same magnitude and direction will penetrate the lower surface. Same is true for the front and back, left and right surface. Therefore the total flux penetrating the whole BZ is zero.

This is caused by the periodicity of the latticeBrillouin zone, the upper and lower surface of the Brillouin zone are the same, so they should have same physical objects "decorated" onBerry curvature, and hence the same Berry flux.

A simple argument: suppose our Brillouin zone is a cubic. If we have a Chern flux penetrating the upper surface, then the same flux with the same magnitude and direction will penetrate the lower surface. Same is true for the front and back, left and right surface. Therefore the total flux penetrating the whole BZ is zero.

This is caused by the periodicity of the lattice, the upper and lower surface of the Brillouin zone are the same, so they should have same physical objects "decorated" on.

A simple argument: suppose our Brillouin zone is a cubic. If we have a Chern flux penetrating the upper surface, then the same flux with the same magnitude and direction will penetrate the lower surface. Same is true for the front and back, left and right surface. Therefore the total flux penetrating the whole BZ is zero.

This is caused by the periodicity of the Brillouin zone, the upper and lower surface of the Brillouin zone are the same, so they should have same Berry curvature, and hence the same Berry flux.

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an offer can't refuse
an offer can't refuse
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A simple argument: suppose our Brillouin zone is a cubic. If we have a Chern flux penetrating the upper surface, then the same flux with the same magnitude and direction will penetrate the lower surface. Same is true for the front and back, left and right surface. Therefore the total flux penetrating the whole BZ is zero.

This is caused by the periodicity of the lattice, the upper and lower surface of the Brillouin zone are the same, so they should have same physical objects "decorated" on.