Liang Fu

Quantum spin Hall effect in two-dimensional transition metal dichalcogenides

Quantum spin Hall (QSH) effect materials feature edge states that are topologically protected from backscattering. However, the small band gap in materials that have been identified as QSH insulators limits applications. We use first-principles calculations to predict a class of large-gap QSH insulators in two-dimensional transition metal dichalcogenides with 1T′ structure, namely, 1T′-MX2 with M = (tungsten or molybdenum) and X = (tellurium, selenium, or sulfur). A structural distortion causes an intrinsic band inversion between chalcogenide-p and metal-d bands. Additionally, spin-orbit coupling opens a gap that is tunable by vertical electric field and strain. We propose a topological field effect transistor made of van der Waals heterostructures of 1T′-MX2 and two-dimensional dielectric layers that can be rapidly switched off by electric field through a topological phase transition instead of carrier depletion. First-principles calculations are used to predict an exotic effect in a particular structure of WTe2 and related materials. Predicting an exotic state of matter Much like graphene, twodimensional flakes of transition metal dichalcogenides have appealing electronic properties. Qian et al. now find that certain structures of these materials may also exhibit the so-called spin Hall effect. The spin Hall effect represents an exotic state of matter in which a 2D material conducts electricity along its edge in a way that drastically reduces dissipation. To show this, the researchers used first-principle calculations and found that the materials also feature a large band gap, which reduces undesirable conduction through the bulk. Their proposed device could be switched on and off quickly using an electric field. Science, this issue p. 1344We report a new class of large-gap quantum spin Hall insulators in two-dimensional transition metal dichalcogenides, namely, MX

Quantum Spin Hall Effect and Topological Field Effect Transistor in Two-Dimensional Transition Metal Dichalcogenides

_2

Topological crystalline insulators in the SnTe material class

with M=(Mo, W) and X=(S, Se, and Te), whose topological electronic properties are highly tunable by external electric field. We propose a novel topological field effect transistor made of these atomic layer materials and their van der Waals heterostructures. Our device exhibits parametrically enhanced charge-spin conductance through topologically protected transport channels, and can be rapidly switched off by electric field through topological phase transition instead of carrier depletion. Our work provides a practical material platform and device architecture for topological quantum electronics.

Experimental observation of Weyl points

Quantum spin Hall (QSH) effect materials feature edge states that are topologically protected from backscattering. However, the small band gap in materials that have been identified as QSH insulators limits applications. We use first-principles calculations to predict a class of large-gap QSH insulators in two-dimensional transition metal dichalcogenides with 1T′ structure, namely, 1T′-MX2 with M = (tungsten or molybdenum) and X = (tellurium, selenium, or sulfur). A structural distortion causes an intrinsic band inversion between chalcogenide-p and metal-d bands. Additionally, spin-orbit coupling opens a gap that is tunable by vertical electric field and strain. We propose a topological field effect transistor made of van der Waals heterostructures of 1T′-MX2 and two-dimensional dielectric layers that can be rapidly switched off by electric field through a topological phase transition instead of carrier depletion. First-principles calculations are used to predict an exotic effect in a particular structure of WTe2 and related materials. Predicting an exotic state of matter Much like graphene, twodimensional flakes of transition metal dichalcogenides have appealing electronic properties. Qian et al. now find that certain structures of these materials may also exhibit the so-called spin Hall effect. The spin Hall effect represents an exotic state of matter in which a 2D material conducts electricity along its edge in a way that drastically reduces dissipation. To show this, the researchers used first-principle calculations and found that the materials also feature a large band gap, which reduces undesirable conduction through the bulk. Their proposed device could be switched on and off quickly using an electric field. Science, this issue p. 1344We report a new class of large-gap quantum spin Hall insulators in two-dimensional transition metal dichalcogenides, namely, MX

Probing Neutral Majorana Fermion Edge Modes with Charge Transport

_2

Odd-Parity Topological Superconductors: Theory and Application to CuxBi2Se3

with M=(Mo, W) and X=(S, Se, and Te), whose topological electronic properties are highly tunable by external electric field. We propose a novel topological field effect transistor made of these atomic layer materials and their van der Waals heterostructures. Our device exhibits parametrically enhanced charge-spin conductance through topologically protected transport channels, and can be rapidly switched off by electric field through topological phase transition instead of carrier depletion. Our work provides a practical material platform and device architecture for topological quantum electronics.

Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction

Topological crystalline insulators are new states of matter in which the topological nature of electronic structures arises from crystal symmetries. Here we predict the first material realization of topological crystalline insulator in the semiconductor SnTe by identifying its non-zero topological index. We predict that as a manifestation of this non-trivial topology, SnTe has metallic surface states with an even number of Dirac cones on high-symmetry crystal surfaces such as {001}, {110} and {111}. These surface states form a new type of high-mobility chiral electron gas, which is robust against disorder and topologically protected by reflection symmetry of the crystal with respect to {110} mirror plane. Breaking this mirror symmetry via elastic strain engineering or applying an in-plane magnetic field can open up a continuously tunable band gap on the surface, which may lead to wide-ranging applications in thermoelectrics, infra-red detection and tunable electronics. Closely related semiconductors PbTe and PbSe also become topological crystalline insulators after band inversion by pressure, strain and alloying.

Topological nodal line semimetals with and without spin-orbital coupling

Weyl physics emerges in the laboratory Weyl fermions—massless particles with half-integer spin—were once mistakenly thought to describe neutrinos. Although not yet observed among elementary particles, Weyl fermions may exist as collective excitations in so-called Weyl semimetals. These materials have an unusual band structure in which the linearly dispersing valence and conduction bands meet at discrete “Weyl points.” Xu et al. used photoemission spectroscopy to identify TaAs as a Weyl semimetal capable of hosting Weyl fermions. In a complementary study, Lu et al. detected the characteristic Weyl points in a photonic crystal. The observation of Weyl physics may enable the discovery of exotic fundamental phenomena. Science, this issue p. 613 and 622 Microwave measurements are used to identify Weyl points in a double-gyroid photonic crystal. [Also see Research Article by Xu et al.] The massless solutions to the Dirac equation are described by the so-called Weyl Hamiltonian. The Weyl equation requires a particle to have linear dispersion in all three dimensions while being doubly degenerate at a single momentum point. These Weyl points are topological monopoles of quantized Berry flux exhibiting numerous unusual properties. We performed angle-resolved microwave transmission measurements through a double-gyroid photonic crystal with inversion-breaking where Weyl points have been theoretically predicted to occur. The excited bulk states show two linear dispersion bands touching at four isolated points in the three-dimensional Brillouin zone, indicating the observation of Weyl points. This work paves the way to a variety of photonic topological phenomena in three dimensions.

Valley-selective optical Stark effect in monolayer WS2

We propose two experiments to probe the Majorana fermion edge states that occur at a junction between a superconductor and a magnet deposited on the surface of a topological insulator. Combining two Majorana fermions into a single Dirac fermion on a magnetic domain wall allows the neutral Majorana fermions to be probed with charge transport. We will discuss a novel interferometer for Majorana fermions, which probes their Z2 phase. This setup also allows the transmission of neutral Majorana fermions through a point contact to be measured. We introduce a point contact formed by a superconducting junction and show that its transmission can be controlled by the phase difference across the junction. We discuss the feasibility of these experiments using the recently discovered topological insulator Bi2Se3.

Spin-filtered edge states with an electrically tunable gap in a two-dimensional topological crystalline insulator

Topological superconductors have a full pairing gap in the bulk and gapless surface Andreev bound states. In this Letter, we provide a sufficient criterion for realizing time-reversal-invariant topological superconductors in centrosymmetric superconductors with odd-parity pairing. We next study the pairing symmetry of the newly discovered superconductor CuxBi2Se3 within a two-orbital model, and find that a novel spin-triplet pairing with odd parity is favored by strong spin-orbit coupling. Based on our criterion, we propose that CuxBi2Se3 is a good candidate for a topological superconductor. We close by discussing experimental signatures of this new topological phase.