In a semimetal, the map isn’t continuous since the occupied states in the vicinity of a gapless point change discontinuously.
Beyond Band Insulators: Topology of Semi-metals and Interacting Phases
Intuitively, we may imagine a complete Fermi surface being present when we begin with a thin sample of Weyl semimetal.
Beyond Band Insulators: Topology of Semi-metals and Interacting Phases
The surface states are obtained by mapping three dimensional Weyl semimetals to Chern insulators in two dimensions as we now explain.
Beyond Band Insulators: Topology of Semi-metals and Interacting Phases
This observation explains why there are surface states in the Weyl semimetal.
Beyond Band Insulators: Topology of Semi-metals and Interacting Phases
Condensed matter derivation of the anomaly–Consider a Weyl semimetal with cross-sectional area A and length Lz in an electric and a magnetic ﬁeld applied along z .
Beyond Band Insulators: Topology of Semi-metals and Interacting Phases
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