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.

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Topological insulators and superconductors

Research Development on Sodium-Ion Batteries

Graphene’s success has shown that it is possible to create stable, single and few-atom-thick layers of van der Waals materials, and also that these materials can exhibit fascinating and technologically useful properties. Here we review the state-of-the-art of 2D materials beyond graphene. Initially, we will outline the different chemical classes of 2D materials and discuss the various strategies to prepare single-layer, few-layer, and multilayer assembly materials in solution, on substrates, and on the wafer scale. Additionally, we present an experimental guide for identifying and characterizing single-layer-thick materials, as well as outlining emerging techniques that yield both local and global information. We describe the differences that occur in the electronic structure between the bulk and the single layer and discuss various methods of tuning their electronic properties by manipulating the surface. Finally, we highlight the properties and advantages of single-, few-, and many-layer 2D materials in...

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Progress, Challenges, and Opportunities in Two-Dimensional Materials Beyond Graphene

Graphene is very popular because of its many fascinating properties, but its lack of an electronic bandgap has stimulated the search for 2D materials with semiconducting character. Transition metal dichalcogenides (TMDCs), which are semiconductors of the type MX2, where M is a transition metal atom (such as Mo or W) and X is a chalcogen atom (such as S, Se or Te), provide a promising alternative. Because of its robustness, MoS2 is the most studied material in this family. TMDCs exhibit a unique combination of atomic-scale thickness, direct bandgap, strong spin–orbit coupling and favourable electronic and mechanical properties, which make them interesting for fundamental studies and for applications in high-end electronics, spintronics, optoelectronics, energy harvesting, flexible electronics, DNA sequencing and personalized medicine. In this Review, the methods used to synthesize TMDCs are examined and their properties are discussed, with particular attention to their charge density wave, superconductive and topological phases. The use of TMCDs in nanoelectronic devices is also explored, along with strategies to improve charge carrier mobility, high frequency operation and the use of strain engineering to tailor their properties. 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.

2D transition metal dichalcogenides

Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

The magnetoresistance effect in WTe2, a layered semimetal, is extremely large: the electrical resistance can be changed by more than 13 million per cent at very high magnetic fields and low temperatures. Apply a magnetic field to a magnetoresistive material and its electrical resistance changes — a technologically useful phenomenon that is harnessed, for example, in the data-reading sensors of hard drives. Mazhar Ali and colleagues have now identified a material (tungsten ditelluride or WTe2) in which the magnetoresistance effect is unusually large: the electrical resistance can be changed by more than 13 million per cent. Its remarkable magnetoresitance is evident at very high magnetic fields and at extremely low temperatures, so practical applications are not yet in prospect. But this finding suggests new directions in the study of magnetoresistivity that could ultimately lead to new uses of this effect. Magnetoresistance is the change in a material’s electrical resistance in response to an applied magnetic field. Materials with large magnetoresistance have found use as magnetic sensors1, in magnetic memory2, and in hard drives3 at room temperature, and their rarity has motivated many fundamental studies in materials physics at low temperatures4. Here we report the observation of an extremely large positive magnetoresistance at low temperatures in the non-magnetic layered transition-metal dichalcogenide WTe2: 452,700 per cent at 4.5 kelvins in a magnetic field of 14.7 teslas, and 13 million per cent at 0.53 kelvins in a magnetic field of 60 teslas. In contrast with other materials, there is no saturation of the magnetoresistance value even at very high applied fields. Determination of the origin and consequences of this effect, and the fabrication of thin films, nanostructures and devices based on the extremely large positive magnetoresistance of WTe2, will represent a significant new direction in the study of magnetoresistivity.

Large, non-saturating magnetoresistance in WTe2.

Dirac semimetals and Weyl semimetals are 3D analogs of graphene in which crystalline symmetry protects the nodes against gap formation [1-3]. Na$_3$Bi and Cd$_3$As$_2$ were predicted to be Dirac semimetals [4,5], and recently confirmed to be so by photoemission [6-8]. Several novel transport properties in a magnetic field $\bf H$ have been proposed for Dirac semimetals [2,9-11]. Here we report an interesting property in Cd$_3$As$_2$ that was unpredicted, namely a remarkable protection mechanism that strongly suppresses back-scattering in zero $\bf H$. In single crystals, the protection results in a very high mobility that exceeds $>10^7$ cm$^2$/Vs below 4 K. Suppression of backscattering results in a transport lifetime 10$^4\times$ longer than the quantum lifetime. The lifting of this protection by $\bf H$ leads to an unusual giant $\bf H$-linear magnetoresistance that violates Kohler's rule. We discuss how this may relate to changes to the Fermi surface induced by $\bf H$.

Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd$_3$As$_2$

Charge density waves (CDWs) are periodic modulations of the density of conduction electrons in solids. They are collective states that arise from intrinsic instabilities often present in low-dimensional electronic systems. The most well-studied examples are the layered dichalcogenides–an example of which is TiSe2, one of the first CDW-bearing materials to be discovered. At low temperatures, a widely held belief is that the CDW competes with another collective electronic state, superconductivity. But despite much exploration, a detailed study of this competition is lacking. Here we report how, on controlled intercalation of TiSe2 with Cu to yield CuxTiSe2, the CDW transition can be continuously suppressed, and a new superconducting state emerges near x=0.04, with a maximum transition temperature Tc of 4.15 K at x=0.08. CuxTiSe2 thus provides the first opportunity to study the CDW to superconductivity transition in detail through an easily controllable chemical parameter, and will provide fundamental insight into the behaviour of correlated electron systems.

Superconductivity in CuxTiSe2

The growth and elementary properties of $p$-type ${\text{Bi}}_{2}{\text{Se}}_{3}$ single crystals are reported. Based on a hypothesis about the defect chemistry of ${\text{Bi}}_{2}{\text{Se}}_{3}$, the $p$-type behavior has been induced through low-level substitutions (1% or less) of Ca for Bi. Scanning tunneling microscopy is employed to image the defects and establish their charge. Tunneling and angle-resolved photoemission spectra show that the Fermi level has been lowered into the valence band by about 400 meV in ${\text{Bi}}_{1.98}{\text{Ca}}_{0.02}{\text{Se}}_{3}$ relative to the $n$-type material. $p$-type single crystals with $ab$-plane Seebeck coefficients of $+180\text{ }\ensuremath{\mu}\text{V}/\text{K}$ at room temperature are reported. These crystals show an anomalous peak in the Seebeck coefficient at low temperatures, reaching $+120\text{ }\ensuremath{\mu}\text{V}\text{ }{\text{K}}^{\ensuremath{-}1}$ at 7 K, giving them a high thermoelectric power factor at low temperatures. In addition to its interesting thermoelectric properties, $p$-type ${\text{Bi}}_{2}{\text{Se}}_{3}$ is of substantial interest for studies of technologies and phenomena proposed for topological insulators.

p -type Bi 2 Se 3 for topological insulator and low-temperature thermoelectric applications

In the cuprate superconductors, Nernst and torque magnetization experiments have provided evidence that the disappearance of the Meissner effect at ${T}_{c}$ is caused by the loss of long-range phase coherence, rather than the vanishing of the pair condensate. Here we report a series of torque magnetization measurements on single crystals of ${\text{La}}_{2\ensuremath{-}x}{\text{Sr}}_{x}{\text{CuO}}_{4}$ (LSCO), ${\text{Bi}}_{2}{\text{Sr}}_{2\ensuremath{-}y}{\text{La}}_{y}{\text{CuO}}_{6}$ (Bi 2201), ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$, and optimal ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{7}$. Some of the measurements were taken to fields as high as 45 T. Focusing on the magnetization above ${T}_{c}$, we show that the diamagnetic term ${M}_{d}$ appears at an onset temperature ${T}_{onset}^{M}$ high above ${T}_{c}$. We construct the phase diagram of both LSCO and Bi 2201 and show that ${T}_{onset}^{M}$ agrees with the onset temperature of the vortex Nernst signal ${T}_{onset}^{\ensuremath{\nu}}$. Our results provide thermodynamic evidence against a recent proposal that the high-temperature Nernst signal in LSCO arises from a quasiparticle contribution in a charge-ordered state.

https://physics.aps.org/featured-article-pdf/10.1103/PhysRevB.81.054510

N. P. Ong

Papers

Large, non-saturating magnetoresistance in WTe2.

Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd$_3$As$_2$

Superconductivity in CuxTiSe2

p -type Bi 2 Se 3 for topological insulator and low-temperature thermoelectric applications

Diamagnetism and Cooper pairing above T c in cuprates