40 years of the quantum Hall effect

A transformative experiment is yielding fresh insights 40 years after the effect’s discovery — and energizing transdisciplinary collaborations.

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.

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.

‘Fragile topology’ is the latest addition to a group of quantum phenomena that give materials exotic — and exciting — properties.

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.

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.

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

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.

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.

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.

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.

Time-periodic fields provide a versatile platform for inducing non-equilibrium topological phenomena in quantum systems. We discuss how such fields can be used for topological band structure engineering, and the conditions for observing robust topological behaviour in a many-body setting.

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.

This Review describes topological phenomena that can be realized in acoustic and mechanical systems. Methods of symmetry breaking are described, along with the consequences and rich phenomena that emerge.

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.

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.

Topological states of various kinds may find application in spintronic devices. The authors review recent progress in this area.

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.

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.

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.

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.

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.

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.

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.

This is an overview of the new physics that emerges in van der Waals heterostructures consisting of graphene and hexagonal boron nitride, including the integer and fractional quantum Hall effects, novel plasmonic states and the effects of emergent moiré superlattices.

This Perspective discusses design strategies for engineering quantum behavior in electron quantum metamaterials based on van der Waals heterostructures

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.

Recent advances and future directions for the research of magnetic two-dimensional van der Waals materials are reviewed.

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

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.

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.

Angle-resolved photoemission spectroscopy (ARPES) is a tool for directly probing the electronic structure of solids and has had a crucial role in studying topological materials. In this Technical Review, we discuss the latest developments of various ARPES techniques and their applications to topological materials