1樓：Raul Peng
Weyl points are singularities (conduction and valence bands touch) in band structure of odd dimensions. Near the Weyl point , the effective Hamiltonian is
with the Fermi velocity along different directions. Here are generators of an irreducible representation of the odd complex Clifford algebra .
The chirality is given by
.The chirality tells us whether the Weyl point is a source or a sink of Chern flux in the Brillouin zone.
Weyl points can only be annihilated in pairs, with positive and negative chirality.
The chirality of Weyl nodes in a Weyl semimetal is very similar to the moving directions (left/right) in a 1D chiral fermionic systems. In the presence of electric field, the occupation of isolated left/right branch is not conserved. There is a transfer of occupation from one branch to another, known as the chiral anomaly.
For a 3D Weyl semimetal, in the presence of EM field, the occupation at Weyl points with different chiralities will be incresed/decreased depdending on the chirality, this is the topological magnetoelectric effect. But if you sum over all Weyl nodes, the total occupation is conserved.
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