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

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2D Dirac/Weyl fermions:
surface states of 3D topological insulators(TI)
Topological field theory description of 3D TI
Couple bulk 3D TI to EM field, integrate out fermions, the
action contains a “topological θ-term”
θ is analogous to the “axion field”. Due to TR symmetry,
θ=0(trivial) or θ=π (TI) mod 2π.
Surface preserves TR, but θ cannot smoothly change from
trivial to TI without breaking TR. To reconcile these,
fermions on surface should be gapless.
On surface, θ jumps by ±π, it seems to produce a ChernSimons term for surface action (quantum anomalous Hall)
2015/12/[email protected]