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

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.

Topological Photonics

In recent years an increasing amount of attention has been devoted to quantum materials with topological characteristics that are robust against disorder and other perturbations. In this context it was discovered that topological materials can be classified with respect to their dimension and symmetry properties. This review provides an overview of the classification schemes of both fully gapped and gapless topological materials and gives a pedagogical introduction into the field of topological band theory.

Classification of topological quantum matter with symmetries

Annual review of condensed matter physics

Head and neck squamous cell carcinomas (HNSCCs) arise in the mucosal linings of the upper aerodigestive tract and are unexpectedly heterogeneous in nature. Classical risk factors are smoking and excessive alcohol consumption, and in recent years, the role of human papillomavirus (HPV) has emerged, particularly in oropharyngeal tumours. HPV-induced oropharyngeal tumours are considered a separate disease entity, which recently has manifested in an adapted prognostic staging system while the results of de-intensified treatment trials are awaited. Carcinogenesis caused by HPV in the mucosal linings of the upper aerodigestive tract remains an enigma, but with some recent observations, a model can be proposed. In 2015, The Cancer Genome Atlas (TCGA) consortium published a comprehensive molecular catalogue on HNSCC. Frequent mutations of novel druggable oncogenes were not demonstrated, but the existence of a subgroup of genetically distinct HPV-negative head and neck tumours with favourable prognoses was confirmed. Tumours can be further subclassified based on genomic profiling. However, the amount of molecular data is currently overwhelming and requires detailed biological interpretation. It also became apparent that HNSCC is a disease characterized by frequent mutations that create neoantigens, indicating that immunotherapies might be effective. In 2016, the first results of immunotherapy trials with immune checkpoint inhibitors were published, and these may be considered as a paradigm shift in head and neck oncology.

The molecular landscape of head and neck cancer

We theoretically study three-dimensional topological semimetals (TSMs) with nodal lines protected by crystalline symmetries. Compared to TSMs with point nodes, e.g., Weyl semimetals and Dirac semimetals, where the conduction and the valence bands touch at discrete points, in these TSMs the two bands cross at closed lines in the Brillouin zone. We propose two different classes of symmetry protected nodal lines in the absence and in the presence of spin-orbital coupling (SOC), respectively. In the former, we discuss nodal lines that are protected by a combination of inversion symmetry and time-reversal symmetry, yet, unlike previously studied nodal lines in the same symmetry class, each nodal line has a ${Z}_{2}$ monopole charge and can only be created (annihilated) in pairs. In the second class, with SOC, we show that a nonsymmorphic symmetry (screw axis) protects a four-band crossing nodal line in systems having both inversion and time-reversal symmetries.

Topological nodal line semimetals with and without spin-orbital coupling

The Dirac equation for relativistic electron waves is the parent model for Weyl and Majorana fermions as well as topological insulators. Simulation of Dirac physics in three-dimensional photonic crystals, though fundamentally important for topological phenomena at optical frequencies, encounters the challenge of synthesis of both Kramers double degeneracy and parity inversion. Here we show how type-II Dirac points---exotic Dirac relativistic waves yet to be discovered---are robustly realized through the nonsymmorphic screw symmetry. The emergent type-II Dirac points carry nontrivial topology and are the mother states of type-II Weyl points. The proposed all-dielectric architecture enables robust cavity states at photonic-crystal---air interfaces and anomalous refraction, with very low energy dissipation.

/pdf/type-ii-dirac-photons-3lz49akihp.pdf

Type-II Dirac Photons

The Dirac equation for relativistic electron waves is the parent model for Weyl and Majorana fermions as well as topological insulators. Simulation of Dirac physics in three-dimensional photonic crystals, though fundamentally important for topological phenomena at optical frequencies, encounters the challenge of synthesis of both Kramers double degeneracy and parity inversion. Here we show how type-II Dirac points—exotic Dirac relativistic waves yet to be discovered—are robustly realized through the nonsymmorphic screw symmetry. The emergent type-II Dirac points carry nontrivial topology and are the mother states of type-II Weyl points. The proposed all-dielectric architecture enables robust cavity states at photonic-crystal—air interfaces and anomalous refraction, with very low energy dissipation. Crystalline symmetries can be used to create and tune topological points in photonic crystals. If a material’s structure has energy bands that linearly disperse and touch at a point, quasiparticle can emerge that are described by the relativistic Dirac or Weyl equations. This is true for both electronic and photonic systems, but as light is bosonic—rather than fermionic—in nature, the physics is not directly analogous. An international team of researchers led by Jian-Hua Jiang from Soochow Universty and Hae-Young Kee from the University of Toronto and Canadian Institute for Advanced Research now predict that crystalline symmetries can be used to create different types of Dirac and Weyl points in all-dielectric photonic crystals, similar to those seen in their electronic counterparts, which also provide robust surface states that could be exploited for applications.

/pdf/type-ii-dirac-photons-4wiptaysaq.pdf

Type-II Dirac photons

There have been increasing efforts in realizing topological metallic phases with nontrivial surface states. It was suggested that orthorhombic perovskite iridates are classified as a topological crystalline metal (TCM) with flat surface states protected by lattice symmetries. Here we perform first-principles electronic structure calculations for epitaxially stabilized orthorhombic perovskite iridates. Remarkably, two different types of topological surface states are found depending on surface directions. On side surfaces, flat surface states protected by lattice symmetries emerge, manifesting the topological crystalline character. On the top surface, on the other hand, an unexpected Dirac cone appears, indicating surface states protected by a time-reversal symmetry, which is confirmed by the presence of a nontrivial topological $\\mathbb{Z}_2$ index. These results suggest that the orthorhombic iridates are unique systems exhibiting both lattice- and global-symmetry-protected topological phases and surface states. Transitions to weak and strong topological insulators and implications of surface states in light of angle resolved photoemission spectroscopy are also discussed.

/pdf/surface-states-of-perovskite-iridates-airo-3-signatures-of-2lkyskf9f9.pdf

Surface States of Perovskite Iridates AIrO$_3$; Signatures of Topological Crystalline Metal with Nontrivial $Z_2$ Index

Topological phases in Iridium oxide superlattices: quantized anomalous charge or valley Hall insulators

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