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40 years of the quantum Hall effect

The discovery of the quantum Hall effect in 1980 marked a turning point in condensed matter physics. The measurement of the Hall resistance showed that electronic resistance could be defined precisely in terms of fundamental constants, even in a disordered and irregular sample. Over the past 40 years, this discovery has inspired new theories and led to experimental discoveries in a range of fields including topology, magnetism and 2D systems. This Collection of Review, News and Commentary articles from various Nature Research journals celebrates the diverse legacy of this discovery.

Quantum Hall effect

Over the past 40 years, the quantum Hall effect (QHE) has inspired new theories and led to experimental discoveries in a range of fields going beyond solid-state electronics to photonics and quantum entanglement. In this Viewpoint, physicists reflect on how the QHE has influenced their research.

Viewpoint | | Nature Reviews Physics

Why the Hall conductance is quantized was an open problem in condensed matter theory for much of the past 40 years. Spyridon Michalakis who worked on the solution — published in 2015 — gives a personal take on how the field evolved.

Comment | | Nature Reviews Physics

Topology

Heusler compounds, Weyl semimetals and the Berry phase are three current research fields of great interest. In this Review, we discuss the connection between the Berry phase and Weyl physics in the context of highly tunable Heusler compounds.

Review Article | | Nature Reviews Materials

Topological nanomaterials exhibit enhanced topological surface states and are thus promising for next-generation electronic devices and quantum computations. This Review discusses synthesis and transport results of topological nanomaterials, with a special focus on 1D topological superconductivity realized using topological insulator nanowires.

Review Article | | Nature Reviews Materials

Topology and collective phenomena give quantum materials emergent functions that provide a platform for developing next-generation quantum technologies, as surveyed in this Review.

Review Article | | Nature Physics

Tetradymite-type materials, such as Bi2Te3, have for decades been of interest as excellent thermoelectrics near ambient temperature and have recently enabled many seminal studies on topological insulators. In this Review, we discuss the recent progress in optimizing the properties of bulk and thin-film tetradymites for such studies.

Review Article | | Nature Reviews Materials

Novel non-equilibrium phases of matter have recently become the focus of intense interest. The realization of topological phases which cannot exist under the constraints of thermodynamic equilibrium is a key aim.

News & Views | | Nature Physics

Synthetic dimensions provide a way to artificially engineer extra spatial dimensions through other degrees of freedom. We review how synthetic dimensions have emerged as a promising tool for quantum simulations of topological lattice models in atomic, molecular and optical systems.

Perspective | | Nature Reviews Physics

Pseudo-electromagnetic fields emerge in inhomogeneous materials. This Review discusses the properties of such fields in the context of 3D topological semimetals, the origin and consequences of pseudo-fields in real materials and their field theory description.

Review Article | | Nature Reviews Physics

Artificial magnetic fields have been constructed in 2D and 3D acoustic structures to manipulate sound, in much the same way as Dirac and Weyl fermions respond to magnetic fields in their quantum levels.

News & Views | | Nature Physics

For both fundamental and applied sciences topological states of matter is an area of intense research and most investigations are dedicated to realizing these materials using electronic and optical methods. Here the authors review recent efforts in a third avenue of research which seeks to emulate topological states using acoustics.

Review Article | Open Access | | Communications Physics

A material that has electrically conducting surfaces has been found to show, when cooled, a type of magnetic ordering that reduces conduction at the surfaces. Such remarkable behaviour could have practical applications.

News & Views | | Nature

Magnetic topological insulators enable the investigation of the interplay between magnetism and topological electronic states. This Review summarizes the basic notions of magnetic topological insulators and the progress in the experimental realization of exotic topological phenomena.

Review Article | | Nature Reviews Physics

Magnetic skyrmions are topologically protected spin whirls that hold promise for applications because they can be controllably moved, created and annihilated. In this Review, the underlying physics of the stabilization of skyrmions at room temperature and their prospective use for spintronic applications are discussed.

Review Article | | Nature Reviews Materials

2D systems

Two-dimensional transition metal dichalcogenides (TMDCs) exhibit attractive electronic and mechanical properties. In this Review, the charge density wave, superconductive and topological phases of TMCDs are discussed, along with their synthesis and applications in devices with enhanced mobility and with the use of strain engineering to improve their properties.

Review Article | | Nature Reviews Materials

Understanding the physics of two-dimensional materials beyond graphene is of both fundamental and practical interest. Recent theoretical and experimental advances uncover the interplay between real spin and pseudospins in layered transition metal dichalcogenides.

Review Article | | Nature Physics

The energy extrema of an electronic band are referred to as valleys. In 2D materials, two distinguishable valleys can be used to encode information and explore other valleytronic applications.

Review Article | | Nature Reviews Materials

A rich pattern of fractional quantum Hall states in graphene double layers can be naturally explained in terms of two-component composite fermions carrying both intra- and interlayer vortices.

News & Views | | Nature Physics

The identification of superconductivity and strong interactions in twisted bilayer 2D materials prompted many questions about the interplay of these phenomena. This Perspective presents the status of the field and the urgent issues for future study.

Perspective | | Nature Physics

Understanding entanglement in many-body systems provided a description of complex quantum states in terms of tensor networks. This Review revisits the main tensor network structures, key ideas behind their numerical methods and their application in fields beyond condensed matter physics.

Review Article | | Nature Reviews Physics

Techniques

Klaus von Klitzing tells the story of the quantum Hall effect's impact on metrology.

Measure for Measure | | Nature Physics

Very accurate measurements of the quantum Hall effect with massless particles in single sheets of carbon atoms could help metrologists in their efforts to improve the standard for electrical resistance, and possibly even redefine the kilogram.

News & Views | | Nature Nanotechnology

Angle-resolved photoemission spectroscopy (ARPES) is a powerful experimental technique that can directly visualize electronic structures of materials. In this Review, the basic principles of ARPES are introduced, and its application to quantum materials, with a focus on topological quantum materials and transition metal dichalcogenides, is discussed.

Review Article | | Nature Reviews Materials