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

TL;DR

This paper explores the emergence of type-II Weyl and Dirac fermions in semimetals and relativistic systems, their connection to Lifshitz transitions, and potential implications for simulating black hole horizons and room-temperature superconductivity.

Contribution

It introduces the concept of Lifshitz transitions involving type-II fermions and discusses their topological and physical implications, including analogies to black hole horizons and pathways to high-temperature superconductivity.

Findings

Type-II Weyl and Dirac points emerge at Lifshitz transitions.

Fermi surface configurations change during Lifshitz transitions, transferring Berry flux.

Lifshitz transitions can lead to flat bands and singular density of states.

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.