Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates
TL;DR: In this paper, the topological semimetal, a three-dimensional phase of a magnetic solid, is described and it may be realized in a class of pyrochlore iridates based on calculations using the LDA+U$ method.
Abstract: We investigate novel phases that emerge from the interplay of electron correlations and strong spin-orbit interactions. We focus on describing the topological semimetal, a three-dimensional phase of a magnetic solid, and argue that it may be realized in a class of pyrochlore iridates (such as ${\mathrm{Y}}_{2}$Ir${}_{2}$O${}_{7}$) based on calculations using the $\text{LDA}+U$ method. This state is a three-dimensional analog of graphene with linearly dispersing excitations and provides a condensed-matter realization of Weyl fermions that obeys a two-component Dirac equation. It also exhibits remarkable topological properties manifested by surface states in the form of Fermi arcs, which are impossible to realize in purely two-dimensional band structures. For intermediate correlation strengths, we find this to be the ground state of the pyrochlore iridates, coexisting with noncollinear magnetic order. A narrow window of magnetic ``axion'' insulator may also be present. An applied magnetic field is found to induce a metallic ground state.
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TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.
Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.
11,092 citations
TL;DR: Weyl and Dirac semimetals as discussed by the authors are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry, and they have generated much recent interest.
Abstract: Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.
3,407 citations
Cites background from "Topological semimetal and Fermi-arc..."
...Such a term is forbidden by Lorentz symmetry for the Weyl Hamiltonian in vacuum but it can generically appear in a linearized long wavelength theory near an isolated twofold band cross- 9 ing in a crystal (Soluyanov et al., 2015; Wan et al., 2011)....
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...When inversion symmetry is present a Weyl node at k must be accompanied by a partner node at −k at the same energy that carries the opposite topological charge (Burkov and Balents, 2011; Wan et al., 2011)....
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...…was introduced to describe a phase where the chemical potential is near the Weyl nodes and a potential realization of such a state in a family of materials, the pyrochlore iridates, was proposed along with the prediction of a special all-in, all-out magnetic ordering pattern (Wan et al., 2011)....
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...In a crystal with cubic symmetry, where T breaking Weyl nodes may appear as proposed in the pyrochlore iridates (Wan et al., 2011; Wang et al., 2017; Witczak-Krempa and Kim, 2012), symmetry enforces vanishing of the anomalous Hall effect, due to the absence of a preferred axis....
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...These band touchings of Herring were named “Weyl nodes” in (Wan et al., 2011)....
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TL;DR: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light as mentioned in this paper, which holds great promise for applications.
Abstract: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.
3,052 citations
Cites methods from "Topological semimetal and Fermi-arc..."
...lations presented by Wang et al. (2009) and shown in Figs....
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...Shortly afterward, following a realistic proposal from Wang et al. (2008), the idea of Haldane and Raghu was experimentally implemented using the twodimensional magneto-optical photonic crystal structure in the microwave domain sketched in Figs....
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TL;DR: The experimental discovery of a Weyl semimetal, tantalum arsenide (TaAs), using photoemission spectroscopy, which finds that Fermi arcs terminate on the Weyl fermion nodes, consistent with their topological character.
2,789 citations
TL;DR: In this article, the experimental discovery of a Weyl semimetal, tantalum arsenide (TaAs), was reported, which is a new state of matter that hosts Weyl fermions as emergent quasiparticles and admits a topological classification that protects Fermi arcs on the boundary of a bulk sample.
Abstract: A Weyl semimetal is a new state of matter that hosts Weyl fermions as emergent quasiparticles and admits a topological classification that protects Fermi arc surface states on the boundary of a bulk sample. This unusual electronic structure has deep analogies with particle physics and leads to unique topological properties. We report the experimental discovery of a Weyl semimetal, tantalum arsenide (TaAs). Using photoemission spectroscopy, we directly observe Fermi arcs on the surface, as well as the Weyl fermion cones and Weyl nodes in the bulk of TaAs single crystals. We find that Fermi arcs terminate on the Weyl fermion nodes, consistent with their topological character. Our work opens the field for the experimental study of Weyl fermions in physics and materials science.
2,272 citations