Lifshitz transitions via the type-II Dirac and type-II Weyl points
K. Zhang+*, G. E. Volovik*× 1)
+State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University,
030006 Taiyuan, P. R. China
*Low Temperature Laboratory, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland
×Landau Institute for Theoretical Physics, Russian Academy of Sciences, 119334 Moscow, Russia
The type-II Weyl and type-II Dirac points emerge in semimetals and
also in relativistic systems. In particular, the type-II Weyl fermions
may emerge behind the event horizon of black holes.
The type-II Weyl and Dirac points also emerge as the intermediate
states of the topological Lifshitz transitions.
In one case the type-II Weyl point connects
the Fermi pockets, and the Lifshitz transition corresponds to the transfer of
the Berry flux between the Fermi pockets. In the other case the type-II Weyl
point connects the outer and inner Fermi surfaces. At the Lifshitz transition
the Weyl point is released from both Fermi surfaces. They loose their Berry
flux, which guarantees the global stability, and without the topological
support the inner surface disappears after shrinking to a point at the second
These examples reveal the complexity and universality of topological Lifshitz
transitions, which originate from the ubiquitous interplay of a variety of
topological characters of the momentum-space manifolds.