Electrical charges on the boundaries of topological insulators favour forward motion over back-scattering at impurities, producing low-dissipation, metallic states that exist up to room temperature in ambient conditions. These states have the promise to impact a broad range of applications from electronics to the production of energy, which is one reason why topological insulators have become the rising star in condensed-matter physics. There are many challenges in the processing of these exotic materials to use the metallic states in functional devices, and they present great opportunities for the chemistry and materials science research communities.
Figures at a glance
Figure 1: Exotic electronic states in topological insulators. 
a, The metallic edge (shown in yellow) of a 2D topological insulator, in which spin-up and spin-down electrons counter-propagate (left), and the corresponding idealized spin-resolved band structure of the edge states (right). The pink line is the chemical potential μ. b, The metallic surface of 3D topological insulators (left), and the corresponding idealized spin-resolved band structure of the surface states (right) revealing how the electron spin rotates as its momentum moves on the Fermi surface. c, The quantum Hall effect in a 2D electron system, with a dissipationless metallic edge. d, Any potential backscattering process on a topological insulator surface with a non-magnetic impurity (purple circle) is prohibited, owing to the conservation of spin angular momentum. e, On the left, an ordinary semiconductor and corresponding band diagram with coexisting surface (green lines) and bulk states (grey area). After surface modification, both surface and bulk electronic properties are modified (right). In this particular case, surface states no longer contribute to the transport process (no states available at μ). f, A topological insulator and the corresponding band structure (left). After surface functionalization, the surface states remain intact, whereas μ shifts (right).
Figure 2: Evidence of topological insulators. 
a, Calculated band diagram of a (Hg,Cd)Te quantum well with metallic edge states (red and blue traces) in the bulk bandgap50. The structure of the quantum well is shown in the inset. b, Layered crystal structure of 3D topological insulators in binary chalcogenide with Bi2Se3 as an example (left). Each layer consists of five atomic sheets (a quintuple layer), which are bonded together by van der Waals interactions along the c axis. The electronic structure of Bi2Se3 measured by spin-resolved ARPES (right), in which surface states form a quasi-linear, V-shape band inside the bulk bandgap (Dirac cone)13. The chemical potential of this crystal and many other as-grown samples lies in the bulk conduction band, indicating bulk carriers would dominate the charge-transport properties. Suppression of the bulk carrier density is thus required for topological insulators to make use of their attractive electric and optical properties. c, Magnetoresistance of a Bi2Se3 nanoribbon in a radial magnetic field, where the periodic resistance oscillations come from the Aharonov–Bohm interference of the topological surface states25. Inset: a scanning electron microscope (SEM) image of the corresponding Bi2Se3 nanoribbon device. The direction of the magnetic field (B) is indicated by an arrow. Figures reproduced from: a, ref. 50, © 2010 APS; b (left), c, ref. 25, © 2010 NPG; b (right), ref. 13 © 2009 NPG.
Figure 3: Nanostructures of topological insulators. 
a, SEM images of Bi2Se3 nanoribbons prepared by metal-catalysed chemical vapour deposition25. b, An optical microscope image of ultrathin Bi2Te3 nanoplates grown on oxidized silicon reveals thickness-dependent colour and contrast. The number of quintuple layers is labelled on the image (a quintuple layer is about 1 nm thick)35. c, STM image of a 80-nm-thick Bi2Te3 MBE film (left), and the corresponding band structure measured by in situ ARPES39, revealing surface states (SS) and the bulk valance band (VB) (right). Note that film has the chemical potential intrinsically lying in the bulk bandgap in the absence of compensation dopants. d, Schematic diagram of lithium (green circles) intercalation and exfoliation of layered topological insulators (orange). Lithiated crystals are exfoliated by the rapid release of hydrogen (indicated by the yellow symbols) in water. Exfoliated layers can restack back into crystals by controlled evaporation. e, Exfoliation of Bi2Se3 nanoribbons using an AFM, in which multiple layers of the materials are 'knocked off' by the tip42. Figures reproduced from: a, ref. 25, © 2010 NPG; b, ref. 35, © 2010 ACS; c, ref. 39, © 2010 Wiley; e, ref. 42, © 2010 ACS.
Figure 4: Heterostructures of topological insulators. 
Composite topological insulators, made up of various topological insulators from the same family, offer the opportunity to engineer the bulk properties but preserve the topological surface states. Functional topological insulators are expected to be covered by an encapsulation layer, protecting the surface states from environmental contamination. Novel particles and phases may be created at the interface between topological insulators and other exotic materials, such as superconductors, to expand the application areas of these remarkable materials.
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