Download Dirac and Weyl fermions in condensed matter systems: an introduction

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3D Weyl fermions: Weyl semimetals
2-band degeneracy point in k-space with linear dispersions.
NO symmetry needed to protect this degeneracy.
Such Weyl nodes must appear in pairs of opposite chirality.
Weyl nodes of opposite chirality can be mutually gapped out
if they meet in k-space. Break inversion and/or TR symmetry
to separate them. [Burkov&Balents, PhysRevLett'11]
Weyl nodes are difficult to locate
(usually not on high symmetry lines)
Example: TaAs.
no inversion symmetry,
12 pairs of Weyl nodes.