15 years of topological matter

15 years ago, 3D topological insulators were experimentally discovered. Since then, the ever-expanding family of topological materials has provided insights into new physics.

A paper in Advanced Materials shows the coexistence of two surface states topologically protected by different symmetries in a superlattice structure.

A paper in Nature Physics directly measures quantized conductance arising from the bulk states of a topological insulator.

A paper in Nano Letters uses optical excitations to probe the ultrafast carrier dynamics of magnetic topological insulator heterostructures.

A paper in Physical Review B shows that the layer Hall effect can be quantized in ferromagnetic and antiferromagnetic topological insulators.

A paper in Physical Review Letters measures the spatial confinement of chiral edge modes and presents a model to show how it varies depending on disorder.

Solid-state materials have emerged as a platform for probing and manipulating topological phases of matter. This Review surveys topological materials discovery in nonmagnetic crystalline solids, focusing on the role of crystal symmetry and geometry in topological material predictions.

Recent theoretical and experimental progress in identifying and understanding magnetic topological materials is reviewed, highlighting the antiferromagnetic topological insulator MnBi₂Te₄ and the ferromagnetic Weyl semimetal Co₃Sn₂S₂, and future research directions are discussed.

Weyl fermions have yet to be observed as elementary particles but can be realized in topological quantum materials. This Review discusses the theoretical and experimental discovery of emergent Weyl fermions, high-fold chiral fermions, topological Weyl lines and related Dirac phases.

Weyl fermions in solids exhibit unique features such as spin–momentum locking and a diverging Berry curvature corresponding to a magnetic monopole in momentum space. This Review surveys the transport phenomena, magnetic excitations and nonlinear optical effects observed in these systems.

Only in recent years has the Hall effect been predicted and observed in materials with antiferromagnetic order. This Review systematically organizes the current understanding of anomalous antiferromagnetic materials that generate a Hall effect, discussing these systems in the broad context of spintronics, topological condensed matter and multipole magnetism.

Recent key developments in the exploration of kagome materials are reviewed, including fundamental concepts of a kagome lattice, realizations of Chern and Weyl topological magnetism, flat-band many-body correlations, and unconventional charge-density waves and superconductivity.

Light–matter interaction in 2D and topological materials provides a fascinating control knob for inducing emergent, non-equilibrium properties and achieving new functionalities in the ultrafast timescale. This Review discusses recent experimental progress on the light-induced phenomena and provides perspectives on the opportunities of proposed light-induced phenomena, as well as open experimental challenges.

Thouless pumping is a dynamical quantum effect that results in a quantized response of a many-body system. It stems from the topological properties of the band structure that emerge under a periodic drive in the adiabatic limit. This Review addresses the robustness of topology in adiabatically driven systems exploring fundamental issues regarding the roles of interactions, disorder and higher dimensions in quantum transport.

The interplay of topological properties and non-Hermitian symmetry breaking has been implemented for a range of classical-wave systems. Recent advances, challenges and opportunities are reviewed across the different physical platforms.

Non-Hermitian theory consists of mathematical structures that are used to describe open systems, which can give rise to non-Hermitian topology not found in Hermitian systems. This Review provides an overview of non-Hermitian band topology and discusses recent developments, such as the non-Hermitian skin effect and non-Hermitian topological classifications.

The recent discovery of higher-order band topology in topological insulators has unveiled the hierarchical structure of topological band theory. This Perspective reviews this rapidly developing field and discusses future directions, including open challenges, future trends, synergy and its use in other fields and potential applications.

The chiral anomaly, originally studied in pion decay, leads to related effects in Dirac and Weyl semimetals. This Review surveys recent experiments that address the appearance of the anomaly in parallel electric and magnetic fields.

Topological materials are extensively studied in condensed matter physics and several have been studied to the point where it is now time to ask if these unique materials have a role to play in next generation technologies. The author reviews the current status of well-characterized topological materials such as Bi₂Se₃ for electronic device applications, focusing on selected technological aspects and their promise for engineering applications.

Topological insulators are unique materials giving rise to unconventional quantum phenomena. This Technical Review discusses how various physics effects can only be observed in devices carefully fabricated to address them, including topological superconductivity, quantum anomalous Hall states, spintronic functionalities and topological mesoscopic physics.

Hybrid devices of superconductors and semiconductor nanowires may be topological and host majorana. This Perspective summarizes the current situation of the field, and highlights the developments in materials science required to make progress.

Topological qubits are attractive because of the potential to store quantum information in a topologically protected manner; however, they are challenging to realize. This Review surveys the recent attempts to realize topological qubits out of materials systems that combine superconductivity, spin–orbit coupling and a magnetic field, and surveys both theoretical ideas and experimental results.

Spin currents, which are generated by chiral structures, can be used to manipulate chiral topological magnetic excitations. This Review brings together advances in chiral molecules, chiral magnetic structures and chiral topological matter to provide an outlook towards potential applications.

Spin–orbit coupling can be leveraged to enable new functional properties in oxide materials, in particular, for spintronics applications. This Review surveys significant recent advances in the field of oxide spin-orbitronics and discusses its future perspectives.

Topological quantum materials host protected, high-mobility surface states which can be used for energy conversion and storage. This Perspective discusses recent progress in using topological materials for water splitting, batteries and supercapacitors.