Shou-Cheng Zhang

Topological insulators and superconductors

Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells

We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluride–cadmium telluride semiconductor quantum wells. When the thickness of the quantum well is varied, the electronic state changes from a normal to an “inverted” type at a critical thickness dc. We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss methods for experimental detection of the QSH effect.

Quantum Spin Hall Insulator State in HgTe Quantum Wells

Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e2/h, where e is the electron charge and h is Plancks constant. The residual conductance was independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field–induced insulator-to-metal transition. These observations provide experimental evidence of the quantum spin Hall effect.

Experimental realization of a three-dimensional topological insulator, Bi2Te3.

Three-dimensional topological insulators are a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. By investigating the surface state of Bi{sub 2}Te{sub 3} with angle-resolved photoemission spectroscopy, we demonstrate that the surface state consists of a single nondegenerate Dirac cone. Furthermore, with appropriate hole doping, the Fermi level can be tuned to intersect only the surface states, indicating a full energy gap for the bulk states. Our results establish that Bi{sub 2}Te{sub 3} is a simple model system for the three-dimensional topological insulator with a single Dirac cone on the surface. The large bulk gap of Bi{sub 2}Te{sub 3} also points to promising potential for high-temperature spintronics applications.Topological Insulators Topological insulators are a recently discovered state of matter, in which the bulk is an insulator while the surface is metallic with counterpropagating spin states. The surface states are protected by the topology, or structure, of the Fermi surface in the bulk gap and are described by a Dirac cone showing linear dispersion behavior meeting at the Dirac point. Chen et al. (p. 178, published online 11 June) provide a comprehensive photoemission study on Bi2Te3 showing that it too falls into the category of topological band insulators. Moreover, there is just a single surface state with a single Dirac point in the photoemission spectrum. The identification of a material with a single Dirac point removes the ambiguity arising from multiple surface states and provides an ideal test-bed to probe the physics of these exotic new materials. Bi2Te3 is identified as a three-dimensional topological insulator with a single metallic surface state. Three-dimensional topological insulators are a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. By investigating the surface state of Bi2Te3 with angle-resolved photoemission spectroscopy, we demonstrate that the surface state consists of a single nondegenerate Dirac cone. Furthermore, with appropriate hole doping, the Fermi level can be tuned to intersect only the surface states, indicating a full energy gap for the bulk states. Our results establish that Bi2Te3 is a simple model system for the three-dimensional topological insulator with a single Dirac cone on the surface. The large bulk gap of Bi2Te3 also points to promising potential for high-temperature spintronics applications.

Dissipationless Quantum Spin Current at Room Temperature

Although microscopic laws of physics are invariant under the reversal of the arrow of time, the transport of energy and information in most devices is an irreversible process. It is this irreversibility that leads to intrinsic dissipations in electronic devices and limits the possibility of quantum computation. We theoretically predict that the electric field can induce a substantial amount of dissipationless quantum spin current at room temperature, in hole-doped semiconductors such as Si, Ge, and GaAs. On the basis of a generalization of the quantum Hall effect, the predicted effect leads to efficient spin injection without the need for metallic ferromagnets. Principles found here could enable quantum spintronic devices with integrated information processing and storage units, operating with low power consumption and performing reversible quantum computation.

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator

Quantized and Anomalous The Hall effect, an electromagnetic phenomenon with a straightforward explanation, has many exotic counterparts, including a quantized version occurring independently of the presence of external magnetic fields. Inspired by a theoretical prediction of the quantum anomalous Hall (QAH) effect in magnetically doped topological insulator thin films, Chang et al. (p. 167, published online 14 March; see the Perspective by Oh) prepared thin films of the compound Cr0.15(Bi0.1Sb0.9)1.85Te3, with Cr as the magnetic dopant. They observed a plateau in the Hall resistance as a function of the gating voltage without any applied magnetic fields, signifying the achievement of the QAH state. An elusive effect emerges in thin films of a bismuth-antimony-telluride topological insulator doped with magnetic chromium. [Also see Perspective by Oh] The quantized version of the anomalous Hall effect has been predicted to occur in magnetic topological insulators, but the experimental realization has been challenging. Here, we report the observation of the quantum anomalous Hall (QAH) effect in thin films of chromium-doped (Bi,Sb)2Te3, a magnetic topological insulator. At zero magnetic field, the gate-tuned anomalous Hall resistance reaches the predicted quantized value of h/e2, accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect may lead to the development of low-power-consumption electronics.

Quantum Spin Hall Effect

The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. The existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external magnetic field. In this work, we predict a quantized spin Hall effect in the absence of any magnetic field, where the intrinsic spin Hall conductance is quantized in units of 2(e/4pi). The degenerate quantum Landau levels are created by the spin-orbit coupling in conventional semiconductors in the presence of a strain gradient. This new state of matter has many profound correlated properties described by a topological field theory.

Quantized Anomalous Hall Effect in Magnetic Topological Insulators

Quantum Anomalous Hall Effect In addition to the Hall effect, which appears as a voltage change in conductors in response to an external magnetic field, ferromagnets exhibit the anomalous Hall effect, which is often proportional to their magnetization and independent of the presence of the magnetic field. This effect, first observed more than a century ago, has not been realized in its quantized form. Yu et al. (p. 61, published online 3 June) propose a realization of a quantum anomalous Hall system by magnetically doping thin films of three-dimensional topological insulators and calculate the effects of various dopants and film thicknesses. The resulting insulators are predicted to have long-range ferromagnetic order, potentially joining dilute magnetic semiconductors as candidates for spintronic applications. Magnetically doped topological insulators are predicted to be ferromagnetic and exhibit the quantum anomalous Hall effect. The anomalous Hall effect is a fundamental transport process in solids arising from the spin-orbit coupling. In a quantum anomalous Hall insulator, spontaneous magnetic moments and spin-orbit coupling combine to give rise to a topologically nontrivial electronic structure, leading to the quantized Hall effect without an external magnetic field. Based on first-principles calculations, we predict that the tetradymite semiconductors Bi2Te3, Bi2Se3, and Sb2Te3 form magnetically ordered insulators when doped with transition metal elements (Cr or Fe), in contrast to conventional dilute magnetic semiconductors where free carriers are necessary to mediate the magnetic coupling. In two-dimensional thin films, this magnetic order gives rise to a topological electronic structure characterized by a finite Chern number, with the Hall conductance quantized in units of e2/h (where e is the charge of an electron and h is Planck’s constant).

The quantum spin Hall effect and topological insulators

In topological insulators, spin–orbit coupling and time-reversal symmetry combine to form a novel state of matter predicted to have exotic physical properties.

Epitaxial growth of two-dimensional stanene

Following the first experimental realization of graphene, other ultrathin materials with unprecedented electronic properties have been explored, with particular attention given to the heavy group-IV elements Si, Ge and Sn. Two-dimensional buckled Si-based silicene has been recently realized by molecular beam epitaxy growth, whereas Ge-based germanene was obtained by molecular beam epitaxy and mechanical exfoliation. However, the synthesis of Sn-based stanene has proved challenging so far. Here, we report the successful fabrication of 2D stanene by molecular beam epitaxy, confirmed by atomic and electronic characterization using scanning tunnelling microscopy and angle-resolved photoemission spectroscopy, in combination with first-principles calculations. The synthesis of stanene and its derivatives will stimulate further experimental investigation of their theoretically predicted properties, such as a 2D topological insulating behaviour with a very large bandgap, and the capability to support enhanced thermoelectric performance, topological superconductivity and the near-room-temperature quantum anomalous Hall effect.