[Physics] Connection between Weyl fermions and Fermi arcs

Question

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I am looking for references (such as research or review articles) that discuss the theoretical origin of Fermi arcs in certain materials and their connection to Weyl fermion physics. In particular, how do Fermi arcs in systems with Weyl fermions differ from those that don't have Weyl fermions? I know that Fermi arcs come about from a breaking of either time-reversal or parity symmetry, but where does the Weyl physics come in? Any references or explanation would be appreciated.

Answer 1

You can think of a Weyl point as a magnetic monopole in the Berry connection, and the Fermi arc represents the (homology class of the) Dirac string connecting these two monopoles. Fermi arcs are impossible to realize in intrinsicly 2d band structures because bands are not allowed to end (but they are allowed to "flow" into the bulk, in the sense of anomaly in-flow). Weyl physics appears at the monopoles because of the famous correlary of the Atiyah-Singer index theorem that monopoles coupled to Dirac fermions trap chiral zero modes.

These slides (pdf) by Haldane are very nice. Also check out the original article by Wan, Turner, Vishwanath, and Savrasov, it's very nice as well.