Lifshitz transitions, type-II Dirac and Weyl fermions, event horizon and all that

Abstract

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. In this case the horizon with Painleve-Gullstrand metric serves as the surface of the Lifshitz transition. This relativistic analogy allows us to simulate the black hole horizon and Hawking radiation using the fermionic superfluid with supercritical velocity, and the Dirac and Weyl semimetals with the interface separating the type-I and type-II states. The difference between such type of the artificial event horizon and that which arises in acoustic metric is discussed. At the Lifshitz transition between type-I and type-II fermions the Dirac lines may also emerge, which are supported by the combined action of topology and symmetry. The type-II Weyl and Dirac points also emerge as the intermediate states of the topological Lifshitz transitions. Different configurations of the Fermi surfaces, involved in such Lifshitz transition, are discussed. 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. 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. For the interacting electrons, the Lifshitz transitions may lead to the formation of the dispersionless (flat) band with zero energy and singular density of states, which opens the route to room-temperature superconductivity.

arXiv comment18 pages, 8 figures, title changed, prepared for proceeding of ECT workshop "Superfluidity and pairing phenomena"

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• Self-biased current, magnetic interference response, and superconducting vortices in tilted Weyl semimetals with disorder
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• Macroscopic quantum tunneling: from quantum vortices to black holes and Universe
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• Engineering Dirac states in graphene: Coexisting type-I and type-II Floquet-Dirac fermions
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• ${}^3$He Universe 2020
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• Chiral Spin-Chain Interfaces Exhibiting Event-Horizon Physics
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• Tilt induced vortical response and mixed anomaly in inhomogeneous Weyl matter
• $\mathcal{P}\mathcal{T}$ symmetry-protected exceptional cones and analogue Hawking radiation
• Online Search Tool for Graphical Patterns in Electronic Band Structures
• Realization of a transition between type-I and type-II Dirac semimetals in monolayers
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• Tilted Dirac Cones in Two-Dimensional Materials: Impact on Electron Transmission and Pseudospin Dynamics
• Analogue Hawking radiation as a tunneling in a two-level $\mathcal{P}\mathcal{T}$-symmetric system
• Optimally scrambling chiral spin-chain with effective black hole geometry
• Common and not so common high-energy theory methods for condensed matter physics
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• Quantum Criticality of Type-I and Critically Tilted Dirac Semimetals