Saturday, April 6, 2019

condensed matter - The anomalous Hall effect in Weyl semimetals


Suppose the semimetal - the solid material, in which the conducting and valence zones are intersected at isolated points - the so-called Weyl nodes. Near this points, the Hamiltonian of electrons is effectively reduced to the Weyl-like Hamiltonian, HW=±vFσ(pp±) where "±" is what we called the chirality in solid bodies, and vF<1 is the velocity of their propagation.



Suppose p±=±b, so that there is non-zero distance 2b between the Weyl nodes for left and right fermions in momentum space. Such semimetal is the particular case of so-called Weyl semimetal.


How to explain qualitatively that non-zero b implies the existence of anomalous Hall effect (AHE), namely, the current JAHEe22π[b×E], in presence of electric field?




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