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.

Weyl and Dirac semimetals in three-dimensional solids

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Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

Bound states in the continuum (BICs) are waves that remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their very existence defies conventional wisdom. Although BICs were first proposed in quantum mechanics, they are a general wave phenomenon and have since been identified in electromagnetic waves, acoustic waves in air, water waves and elastic waves in solids. These states have been studied in a wide range of material systems, such as piezoelectric materials, dielectric photonic crystals, optical waveguides and fibres, quantum dots, graphene and topological insulators. In this Review, we describe recent developments in this field with an emphasis on the physical mechanisms that lead to BICs across seemingly very different materials and types of waves. We also discuss experimental realizations, existing applications and directions for future work. The fascinating wave phenomenon of ‘bound states in the continuum’ spans different material and wave systems, including electron, electromagnetic and mechanical waves. In this Review, we focus on the common physical mechanisms underlying these bound states, whilst also discussing recent experimental realizations, current applications and future opportunities for research.

Bound states in the continuum

A M was supported by the King Abdullah University of Science and Technology (KAUST) T J acknowledges support from the EU FET Open RIA Grant No 766566, the Ministry of Education of the Czech Republic Grant No LM2015087 and LNSM-LNSpin, and the Grant Agency of the Czech Republic Grant No 19-28375X J S acknowledges the Alexander von Humboldt Foundation, EU FET Open Grant No 766566, EU ERC Synergy Grant No 610115, and the Transregional Collaborative Research Center (SFB/TRR) 173 SPIN+X K G and P G acknowledge stimulating discussions with C O Avci and financial support by the Swiss National Science Foundation (Grants No 200021-153404 and No 200020-172775) and the European Commission under the Seventh Framework Program (spOt project, Grant No 318144) A T acknowledges support by the Agence Nationale de la Recherche, Project No ANR-17-CE24-0025 (TopSky) J Ž acknowledges the Grant Agency of the Czech Republic Grant No 19-18623Y and support from the Institute of Physics of the Czech Academy of Sciences and the Max Planck Society through the Max Planck Partner Group programme

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Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems

Materials harbouring exotic quasiparticles, such as massless Dirac and Weyl fermions, have garnered much attention from physics and material science communities due to their exceptional physical properties such as ultra-high mobility and extremely large magnetoresistances. Here, we show that the highly stable, non-toxic and earth-abundant material, ZrSiS, has an electronic band structure that hosts several Dirac cones that form a Fermi surface with a diamond-shaped line of Dirac nodes. We also show that the square Si lattice in ZrSiS is an excellent template for realizing new types of two-dimensional Dirac cones recently predicted by Young and Kane. Finally, we find that the energy range of the linearly dispersed bands is as high as 2 eV above and below the Fermi level; much larger than of other known Dirac materials. This makes ZrSiS a very promising candidate to study Dirac electrons, as well as the properties of lines of Dirac nodes.

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Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS.

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Dirac Semimetals in Two Dimensions

A narrow-band transmission filter is demonstrated near normal incidence that operates through relaxation of supported-mode selection rules and is explained in the context of group theory. We calculated the transverse magnetic and transverse electric dispersion relations of a dielectric grating in the subwavelength and near-wavelength region using finite element modal analysis and determine the modes' corresponding irreducible representations. Coupling to select transverse magnetic modes at normal incidence is optimized to yield broadband high reflectance that acts as the background for the transmission filter. While some modes couple at normal incidence, others are shown to remain inaccessible due to symmetry mismatch. Away from normal incidence, the reduced symmetry relaxes the selection rules, enabling weak coupling between the incident field and these symmetry-protected modes. This weak coupling produces narrow transmission bands within the opaque background. Furthermore, by choosing the plane of incidence to include or exclude the grating periodicity, we show that orthogonal mode sets can independently be selected to couple to the incident light, yielding separate transmission bands. This spectral filtering is experimentally demonstrated with a suspended silicon grating in the infrared spectrum ($7--14\ensuremath{\mu}\mathrm{m}$), which agrees well with simulated transmittance spectra and modal analysis.

Symmetry-protected mode coupling near normal incidence for narrow-band transmission filtering in a dielectric grating

We experimentally demonstrate a simple narrowband transmission filter using a silicon/air grating, exhibiting broadband high-reflectance between 8 and 14 μm and narrow transmission peaks at slightly off-normal incidence. We explain the response in terms of guided modes in a dielectric slab waveguide, with numerical modal analysis corroborating an intuitive slab waveguide picture and the experimental results. The filtered wavelength depends predictably on the grating period, making wavelength selection straightforward, while the length-scale independent operation principle shows promise for enabling similar filtering capabilities at higher frequencies.

Narrowband mid-infrared transmission filtering of a single layer dielectric grating

Single-photon detectors have achieved impressive performance and have led to a number of new scientific discoveries and technological applications. Existing models of photodetectors are semiclassical in that the field-matter interaction is treated perturbatively and time-separated from physical processes in the absorbing matter. An open question is whether a fully quantum detector, whereby the optical field, the optical absorption, and the amplification are considered as one quantum system, could have improved performance. Here we develop a theoretical model of such photodetectors and employ simulations to reveal the critical role played by quantum coherence and amplification backaction in dictating the performance. We show that coherence and backaction lead to trade-offs between detector metrics and also determine optimal system designs through control of the quantum-classical interface. Importantly, we establish the design parameters that result in a ideal photodetector with 100% efficiency, no dark counts, and minimal jitter, thus paving the route for next-generation detectors.

Fundamental limits to single-photon detection determined by quantum coherence and backaction

It is well known that defects, such as holes, inside an infinite photonic crystal can sustain localized resonant modes whose frequencies fall within a forbidden band. Here we prove that finite, defect-free photonic crystals behave as mirrorless resonant cavities for frequencies within but near the edges of an allowed band, regardless of the shape of their outer boundary. The resonant modes are extended, surface-avoiding (nearly-Dirichlet) states that may lie inside or outside the light cone. Independent of the dimensionality, quality factors and finesses are on the order of, respectively, (L/λ)3 and L/λ, where λ is the vacuum wavelength and L >> λ is a typical size of the crystal. Similar topological modes exist in conventional Fabry-Perot resonators, and in plasmonic media at frequencies just above those at which the refractive index vanishes.

Steve Young

Papers

Dirac Semimetals in Two Dimensions

Symmetry-protected mode coupling near normal incidence for narrow-band transmission filtering in a dielectric grating

Narrowband mid-infrared transmission filtering of a single layer dielectric grating

Fundamental limits to single-photon detection determined by quantum coherence and backaction

Photonic crystals as topological high-Q resonators