The quantum Hall effect leads to topologically protected edge states, and for a long time was thought to exclusively emerge in the presence of an external magnetic field. But in 1988, Duncan Haldane proposed a model in which this exotic electronics structure arises without this requirement. He proposed that, in a honeycomb lattice with a staggered flux, the necessary ingredients for a quantum Hall effect would be inherent in the material itself. The principles behind this concept were later recruited to design topological insulators, but in its original expression, the Haldane model has not been observed in the laboratory. In this issue of Nature, two groups report on progress connected to the Haldane model. Gregor Jotzu et al. report the first realization of the Haldane model and Pedram Roushan et al. show how it can be precisely measured. Jotzu et al. use ultracold fermions to realize the breaking of time-reversal and inversion symmetry — the two main requirements of the model — by implementing a circular modulation of the lattice position and an energy offset between neighbouring sites. Roushan et al. use superconducting quantum circuits — a Josephson junction sandwiched between superconducting electrodes — to realize a non-interacting form of the Haldane model with a single qubit and an interacting two-qubit model through a new experimental setup called 'gmon' coupling architecture. Their setup allows them to characterize both cases by measuring the Berry curvature, a feature that all topological structures have in common.
- Gregor Jotzu,
- Michael Messer ⋯
- Tilman Esslinger

First-principles calculations predict that Bi2Se3, Bi2Te3 and Sb2Te3 are topological insulators—three-dimensional semiconductors with unusual surface states generated by spin–orbit coupling—whose surface states are described by a single gapless Dirac cone. The calculations further predict that Bi2Se3 has a non-trivial energy gap larger than the energy scale kBT at room temperature.
- Haijun Zhang,
- Chao-Xing Liu ⋯
- Shou-Cheng Zhang

Three-dimensional Dirac semimetals are a recently discovered state of condensed matter considered as the 3D analogue of graphene. Here, Yang et al. propose a general framework to classify stable 3D Dirac semimetals in systems with time-reversal, inversion and uniaxial rotational symmetries.
- Bohm-Jung Yang &
- Naoto Nagaosa

Physics in a two-dimensional environment is very different from what we observe in the three-dimensional world. If dimensionality is reduced, thermal fluctuations destroy a system's spatial order and most phase transitions, like those responsible for ferromagnetism for instance, cannot occur. But there is a particular type of phase transition, involving the pairing of vortices, that does exist in two dimensions. First predicted 30 years ago by Berezinskii, Kosterlitz and Thouless, the ‘BKT transition’ has now been observed directly for the first time in a planar gas of ultracold rubidium atoms.
- Zoran Hadzibabic,
- Peter Krüger ⋯
- Jean Dalibard

When doped with copper, the topological insulator Bi2Se3 becomes superconducting. But for new physics and applications the search is not for just any superconductor; the material must retain its topological character. And indeed that is the case with doped Bi2Se3.
- L. Andrew Wray,
- Su-Yang Xu ⋯
- M. Zahid Hasan

The mathematical connection between isostatic lattices—which are relevant for granular matter, glasses and other ‘soft’ systems—and topological quantum matter is as deep as it is unexpected.
- C. L. Kane &
- T. C. Lubensky

The fractional quantum Hall effect occurs when electrons move in Landau levels. In this study, using a theoretical flat-band lattice model, the fractional quantum Hall effect is observed in the presence of repulsive interactions when the band is one third full and in the absence of Landau levels.
- D.N. Sheng,
- Zheng-Cheng Gu ⋯
- L. Sheng

The fabrication of oxide thin-film heterostructures has improved considerably over the past few years. The first demonstration of the fractional quantum Hall effect in an oxide now attests to the potential of these compounds to rival conventional semiconductors.
- A. Tsukazaki,
- S. Akasaka ⋯
- M. Kawasaki

Non-trivial topological phases can allow for one-way spin-polarized transport along the interfaces of topological insulators but they are relatively uncommon in the condensed state of matter. By arranging judiciously designed metamaterials into two-dimensional superlattices, a photonic topological insulator has now been demonstrated theoretically, enabling unidirectional spin-polarized photon propagation without the application of external magnetic fields or breaking of time-reversal symmetry.
- Alexander B. Khanikaev,
- S. Hossein Mousavi ⋯
- Gennady Shvets

Multi-terminal superconducting Josephson junctions are used to induce topologically protected transitions between gapless and gapped states, showing the potential for creating artificial topological materials.
- E. Strambini,
- S. D'Ambrosio ⋯
- F. Giazotto