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

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

The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

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New directions in the pursuit of Majorana fermions in solid state systems.

The 1937 theoretical discovery of Majorana fermions--whose defining property is that they are their own anti-particles--has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review article highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic `topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to `engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals, and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects, and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions--the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

/pdf/new-directions-in-the-pursuit-of-majorana-fermions-in-solid-5afwb64kak.pdf

New directions in the pursuit of Majorana fermions in solid state systems

The response of the worldwide scientific community to the discovery in 2008 of superconductivity at T c = 26 K in the Fe-based compound LaFeAsO1−x F x has been very enthusiastic. In short order, ot...

The puzzle of high temperature superconductivity in layered iron pnictides and chalcogenides

Bi2Se3 is one of a handful of known topological insulators. Here we show that copper intercalation in the van der Waals gaps between the Bi2Se3 layers, yielding an electron concentration of ?2×1020??cm-3, results in superconductivity at 3.8 K in CuxBi2Se3 for 0.12?x?0.15. This demonstrates that Cooper pairing is possible in Bi2Se3 at accessible temperatures, with implications for studying the physics of topological insulators and potential devices.

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Superconductivity in CuxBi2Se3 and its implications for pairing in the undoped topological insulator.

The recently discovered iron arsenide superconductors appear to display a universal set of characteristic features, including proximity to a magnetically ordered state and robustness of the superconductivity in the presence of disorder. Here we show that superconductivity in Fe1+?Se, which can be considered the parent compound of the superconducting arsenide family, is destroyed by very small changes in stoichiometry. Further, we show that nonsuperconducting Fe1+?Se is not magnetically ordered down to 5 K. These results suggest that robust superconductivity and immediate instability against an ordered magnetic state should not be considered as intrinsic characteristics of iron-based superconducting systems.

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Extreme sensitivity of superconductivity to stoichiometry in Fe 1+δ Se

In this Letter we show that superconducting ${\mathrm{Fe}}_{1.01}\mathrm{Se}$ undergoes a structural transition at 90 K from a tetragonal to an orthorhombic phase but that nonsuperconducting ${\mathrm{Fe}}_{1.03}\mathrm{Se}$ does not. High resolution electron microscopy at low temperatures further reveals an unexpected additional modulation of the crystal structure of the superconducting phase that involves displacements of the Fe atoms, and that the nonsuperconducting composition shows a different, complex nanometer-scale structural modulation. Finally, we show that magnetism is not the driving force for the phase transition in the superconducting phase.

Tetragonal-to-orthorhombic structural phase transition at 90 K in the superconductor Fe(1.01)Se.

We report the characterization of layered 2H-type CuxTaS2 for 0?x?0.12. The charge density wave (CDW), at 70 K for TaS2, is destabilized with Cu doping. The sub-1 K superconducting transition in undoped 2H-TaS2 jumps quickly to 2.5 K at low x, increases to 4.5 K at the optimal composition Cu0.04TaS2, and then decreases at higher x. The electronic contribution to the specific heat, first increasing and then decreasing as a function of Cu content, is 12 mJ mol?1 K?2 at Cu0.04TaS2. Electron-diffraction studies show that the CDW remains present at the optimal superconducting composition but with both a changed q vector and decreased coherence length. We present an electronic phase diagram for the system.

A. J. Williams

Papers

Superconductivity in CuxBi2Se3 and its implications for pairing in the undoped topological insulator.

Extreme sensitivity of superconductivity to stoichiometry in Fe 1+δ Se

Tetragonal-to-orthorhombic structural phase transition at 90 K in the superconductor Fe(1.01)Se.

Tuning the charge density wave and superconductivity in Cu x TaS 2

The stoichiometry of FeSe