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

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Prerequisite: Berry curvature in k-space
For a band with Bloch function
its (Abelian) Berry
Berry curvature
Analogue of vector potential & mag. field in k-space.
Semiclassical equations of motion of electron on this band:
red term: anomalous velocity[Sundaram&Niu, PhysRevB'99]
The Chern number over a closed surface in k-space,
is an integer, if the band is non-degenerate on this surface.
Intrinsic anomalous Hall conductivity for 2D system
Fully occupied band w/ Chern
number shows quantum anomalous Hall effect.