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

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Recap: electrons in crystals
Effective Hamiltonian: for bands n...(n+m-1),
Usually use k-indep. Bloch basis,
w/ hermitian “Hamiltonian”
m bands are degenerate [H(k) prop. to identity matrix] :
in general k needs to satisfy (m2-1) conditions
Symmetries may reduce the number of conditions
Without symmetry, only m=2 and k in 3D can have generic
point solution of band degeneracy (usually 3D Weyl points).
Usually expand H(k) around the degenerate points (“nodes”)
to linear order in k: 3D Dirac/Weyl are
vi are (anisotropic) velocities.
2015/12/[email protected]