The Lifshitz transition from type-I to type-II Weyl states is equivalent to a black hole horizon, featuring a Dirac-line Fermi surface with nontrivial topological invariant and critical chiral anomaly.
Nodal-knot semimetals
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abstract
Topological nodal-line semimetals are characterized by one-dimensional lines of band crossing in the Brillouin zone. In contrast to nodal points, nodal lines can be in topologically nontrivial configurations. In this paper, we study the simplest topologically nontrivial forms of nodal line, namely, a single nodal line taking the shape of a knot in the Brillouin zone. We introduce a generic construction for various "nodal-knot semimetals", which yields the simplest trefoil nodal knot and other more complicated nodal knots in the Brillouin zone. The knotted-unknotted transitions by nodal-line reconnections are also studied. Our work brings the knot theory to the subject of topological semimetals.
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cond-mat.mes-hall 1years
2026 1verdicts
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Dirac-Line Criticality and Emergent Horizons in Weyl Lifshitz Transitions
The Lifshitz transition from type-I to type-II Weyl states is equivalent to a black hole horizon, featuring a Dirac-line Fermi surface with nontrivial topological invariant and critical chiral anomaly.