Topological insulators (TIs) are a new quantum state of matter discovered in recent years. They are beyond the spontaneous symmetry-breaking description by Landau and are instead characterized by topological invariants, and described by topological field theory. Their topological nature is similar to the quantum Hall effect, a major discovery of condensed-matter physics in 1980s (Klaus von Klitzing, Nobel Prize in Physics, 1985). The manifestation of the topological effect is the existence of robust gapless surface states inside the bulk energy gap. The topological surface states exhibit Dirac-cone-like energy dispersion with strong spin-momentum locking. Potential future applications cover areas such as spintronics, thermoelectrics, quantum computing and beyond.
It is remarkable that TIs have been realized in many common materials, without the requirement of extreme conditions such as high magnetic field and low temperature. The first TI was predicted in 2006 and experimentally realized in 2007 in HgTe quantum wells. Soon afterwards, three traditionally well-known binary chalcogenides, Bi2Se3, Bi2Te3 and Sb2Te3, were predicted and observed to be TIs with a large bulk gap and a metallic surface state consisting of a single Dirac cone. The discovery of these topological materials opened up the exciting field of topological insulators. Extensive experimental and theoretical efforts are devoted to synthesizing and optimizing samples, characterizing the topological states by surface sensitive spectroscopy, transport measurements, device fabrications, and searching for new material candidates.
The field of TIs is now expanding at a rapid pace in the communities of physics, chemistry and materials science. In this Focus Issue, we intend to present a high-quality snapshot of the materials and applications aspect of this field.
We present ten Review papers from both experiment and theory aspects. Five experimental papers [1–5] overview recent status and challenges of TI nanostructures , magnetotransport and induced superconductivity , chemistry of Bi-based TI materials , molecular beam epitaxial growth of TI thin films , and angle-resolved photoemission spectroscopy (ARPES) with circular dichroism . On the other hand, five theoretical papers [6–10] report the progress from different perspectives: materials design by first-principles calculations [6, 7], the relations between TIs and thermoelectric materials , Floquet TIs , and the classification of topological states .
We present ten Letters that cover various aspects, ranging from ARPES, transport measurement and devices, thin film growth to first-principles simulations and fundamental theory. Letters on ARPES [11–14] report the surface states of HgTe , Bi2Se3 [12, 13] and Bi2Te3 [11, 14], in which the surface modification, defect doping and electron–phonon coupling are discussed; a paper on transport experiments  demonstrates the coexistence of electron- and hole-type charge carriers in devices of Sb2Te3/Bi2Te3 heterostructures; the growth of YPtSb thin film is reported , which is a Heusler compound near the boundary of topological trivial–nontrivial transition. Corresponding to the ARPES experiments, a Letter of band structure calculations  also reveals the effect of vacancy defects on Bi2Se3 surface states; another paper  shows the dependence of edge state dispersion on edge geometry of graphene. Last but not the least, two papers on phenomenological models [19, 20] report the maximally localized flat-band Hamiltonians and the spectra flow for Aharonov–Bohm rings, respectively.
We hope that this Focus Issue will be helpful for your research and stimulate more activity in the exciting field of topological insulators (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)