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Register a new userLifshitz transitions, type-II Dirac and Weyl fermions, event horizon and all that
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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.
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As a novel type of fermionic state, hybrid nodal loop with the coexistence of both type-I and type- II band crossings has attracted intense research interest. However, it remains a challenge to realize hybrid nodal loop in both two-dimensional (2D) materials and in ferromagnetic (FM) materials. Here, we propose the first FM hybrid nodal loop in 2D CrN monolayer. We show that the material has a high Curie temperature (> 600 K) FM ground state, with the out-of-plane [001] magnetization. It shows a half-metallic band structure with two bands in the spin-up channel crossing each other near the Fermi level. These bands produce both type-I and type-II band crossings, which form a fully spin-polarized hybrid nodal loop. We find the nodal loop is protected by the mirror symmetry and robust against spin-orbit coupling (SOC). An effective Hamiltonian characterizing the hybrid nodal loop is established. We further find the configuration of nodal loop can be shifted under external perturbations such as strain. Most remarkably, we demonstrate that both type-I and type-II Weyl nodes can be realized from such FM hybrid nodal loop by simply shifting the magnetization from out-of-plane to in-plane. Our work provides an excellent candidate to realize FM hybrid nodal loop and Weyl fermions in 2D material, and is also promising for related topological applications with their intriguing properties.
We present detailed pedagogical derivation of covariant derivative of fermions and some related expressions, including commutator of covariant derivatives and energy-momentum tensor of a free Dirac field. The text represents a part of the initial chapter of a one-semester course on semiclassical gravity.
Periodically driven systems provide tunable platforms to realize interesting Floquet topological phases and phase transitions. In electronic systems with Weyl dispersions, the band crossings are topologically protected even in the presence of time-periodic perturbations. This robustness permits various routes to shift and tilt the Weyl spectra in the momentum and energy space using circularly polarized light of sufficient intensity. We show that type-II Weyl fermions, in which the Weyl dispersions are tilted with the appearance of pocket-like Fermi surfaces, can be induced in driven Dirac semimetals and line node semimetals. Under a circularly polarized drive, both semimemtal systems immediately generate Weyl node pairs whose types can be further controlled by the driving amplitude and direction. The resultant phase diagrams demonstrate experimental feasibilities.
We show how transitions between different Lifshitz phases in bilayer Dirac materials with and without spin-orbit coupling can be studied by driving the system. The periodic driving is induced by a laser and the resultant phase diagram is studied in the high frequency limit using the Brillouin-Wigner perturbation approach to leading order. The examples of such materials include bilayer graphene and spin-orbit coupled materials such as bilayer silicene. The phase diagrams of the effective static models are analyzed to understand the interplay of topological phase transitions, with changes in the Chern number and topological Lifshitz transitions, with the ensuing changes in the Fermi surface. Both the topological transitions and the Lifshitz transitions are tuned by the amplitude of the drive.
Transition-metal dichalcogenides (TMDs) offer an ideal platform to experimentally realize Dirac fermions. However, typically these exotic quasiparticles are located far away from the Fermi level, limiting the contribution of Dirac-like carriers to the transport properties. Here we show that NiTe2 hosts both bulk Type-II Dirac points and topological surface states. The underlying mechanism is shared with other TMDs and based on the generic topological character of the Te p-orbital manifold. However, unique to NiTe2, a significant contribution of Ni d orbital states shifts the energy of the Type-II Dirac point close to the Fermi level. In addition, one of the topological surface states intersects the Fermi energy and exhibits a remarkably large spin splitting of 120 meV. Our results establish NiTe2 as an exciting candidate for next-generation spintronics devices.
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