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Herbertsmithite and Zn-doped barlowite are two compounds for experimental realization of twodimensional gapped kagome spin liquid. Theoretically, it has been proposed that charge doping a quantum spin liquid gives rise to exotic metallic states, such as high-temperature superconductivity. However, one recent experiment about herbertsmithite with successful Li-doping shows surprisingly the insulating state even under the heavy doped scenario, which can hardly be explained by many-body physics. Using first-principles calculation, we performed a comprehensive study about the Li intercalated doping effect of these two compounds. For the Li-doped herbertsmithite, we identified the optimized Li position at the Cl-(OH)$_3$-Cl pentahedron site instead of previously speculated Cl-(OH)$_3$ tetrahedral site. With the increase of Li doping concentration, the saturation magnetization decreases linearly due to the charge transfer from Li to Cu ions. Moreover, we found that Li forms chemical bonds with the nearby (OH)$^-$ and Cl$^-$ ions, which lowers the surrounding chemical potential and traps the electron, as evidenced by the localized charge distribution, explaining the insulating behavior measured experimentally. Though with different structure from herbertsmithite, Zn-doped Barlowite shows the same features upon Li doping. We conclude that Li doping this family of kagome spin liquid cannot realize exotic metallic states, other methods should be further explored, such as element substitution with different valence electrons., Comment: 6 figures

Topological semimetals have recently attracted extensive research interests as host materials to condensed matter physics counterparts of Dirac and Weyl fermions originally proposed in high energy physics. These fermions with linear dispersions near the Dirac or Weyl points obey Lorentz invariance, and the chiral anomaly leads to novel quantum phenomena such as negative magnetoresistance. The Lorentz invariance is, however, not necessarily respected in condensed matter physics, and thus Lorentz-violating type-II Dirac fermions with strongly tilted cones can be realized in topological semimetals. Here, we report the first experimental evidence of type-II Dirac fermions in bulk stoichiometric PtTe$_2$ single crystal. Angle-resolved photoemission spectroscopy (ARPES) measurements and first-principles calculations reveal a pair of strongly tilted Dirac cones along the $\Gamma$-A direction under the symmetry protection, confirming PtTe$_2$ as a type-II Dirac semimetal. The realization of type-II Dirac fermions opens a new door for exotic physical properties distinguished from type-I Dirac fermions in condensed matter materials., Comment: 12 pages, 4 figures

Topological crystalline insulators (TCIs) are usually described with topological protection imposed by the crystalline symmetry. In general, however, the existence of TCI states does not necessitate the periodicity of crystals as long as an essential lattice symmetry can be identified. Here we demonstrate the compatibility of TCIs with aperiodic systems, as exemplified by an octagonal quasicrystal. The aperiodic TCIs we proposed are attributed to a band inversion mechanism, which inverts states with the same parity but opposite eigenvalues of a specific symmetry (such as mirror reflection). The nontrivial topology is characterized by a nonzero integer ``mirror Bott index.'' Moreover, we demonstrate that the topological edge states and quantized conductance of the aperiodic TCI, which are robust against disorder, can be effectively manipulated by external electric fields. Our findings not only provide a better understanding of electronic topology in relation to symmetry but also extend the experimental realization of topological states to much broader material categories beyond crystals.

Following the discovery of topological insulators (TIs), topological Dirac/Weyl semimetal has attracted much recent interest. A prevailing mechanism for the formation of Weyl points is by breaking time-reversal symmetry (TRS) or spatial inversion symmetry of a Dirac point. Here we demonstrate a generic formation mechanism for Weyl points by breaking TRS of a three-dimensional (3D) TI featured with highly degenerate 3D flat bands (FBs). It is in direct contrast to the conventional view that breaking TRS of a 2D/3D TI leads to a Chern insulator exhibiting quantum anomalous Hall effect. Based on a tight-binding model of pyrochlore lattice, we show that this unusual 3D-FB-enabled Weyl state may contain only a minimum of two Weyl points. Furthermore, using first-principles calculations, we identify this Weyl state in a real material ${\mathrm{Sn}}_{2}{\mathrm{Nb}}_{2}{\mathrm{O}}_{7}$. The main features of the resulting Weyl points are analyzed with respect to symmetry, topological invariant and surface state. Our finding sheds new light on our fundamental understanding of topological physics and significantly extends the scope of Weyl semimetals to attract immediate experimental interest.

The kagome bands hosting exotic quantum phases generally and understandably pertain only to a kagome lattice. This has severely hampered the research of kagome physics due to the lack of real kagome-lattice materials. Interestingly, we discover that a coloring-triangle (CT) lattice, named after color-triangle tiling, also hosts kagome bands. We demonstrate first theoretically the equivalency between the kagome and CT lattices, and then computationally in photonic (waveguide lattice) and electronic (Au overlayer on electride $\mathrm{C}{\mathrm{a}}_{2}\mathrm{N}$ surface) systems by first-principles calculations. The theory can be generalized to even distorted kagome and CT lattices to exhibit ideal kagome bands. Our findings open an avenue to explore the alluding kagome physics.

Diamond-structure materials have been extensively studied for decades, which form the foundation for most semiconductors and their modern day electronic devices. Here, we discover a e$_g$-orbital ($d_{z^2}$,$d_{x^2-y^2}$ ) model within the diamond lattice (e$_g$-diamond model) that hosts novel topological states. Specifically, the e$_g$-diamond model yields a 3D nodal cage (3D-NC), which is characterized by a $d$-$d$ band inversion protected by two types of degenerate states (i.e., e$_g$-orbital and diamond-sublattice degeneracies). We demonstrate materials realization of this model in the well-known spinel compounds (AB$_2$X$_4$), where the tetrahedron-site cations (A) form the diamond sub-lattice. An ideal half metal with one metallic spin channel formed by well-isolated and half-filled e$_g$-diamond bands, accompanied by a large spin gap (4.36 eV) is discovered in one 4-2 spinel compound (VMg$_2$O$_4$), which becomes a magnetic Weyl semimetal when spin-orbit coupling effect is further considered. Our discovery greatly enriches the physics of diamond structure and spinel compounds, opening a door to their application in spintronics.

Numerous exotic properties have been discovered in Dirac Semimetals (DSMs) and Weyl Semimetals (WSMs). In a given DSM/WSM, the Dirac/Weyl nodes usually coexist with other bulk states, making their respective contribution elusive. In this work, we distinguish the role of bulk states from the tilted Dirac nodes on the transport properties in DSMs. Specifically, we applied pressure to a type-II DSM material, PtTe2, and studied its pressure modified electronic and lattice structure systematically by using in situ transport measurements and X-ray diffraction (XRD). A pressure-induced transition at about 20 GPa is revealed in the transport properties, while the layered lattice structure is robust against pressure as illustrated in XRD measurement results. Density functional theory (DFT) calculations suggest that this is originated from the Lifshitz transition in the bulk states. Our findings provide evidence to identify the bulk states’ influence on transport from the topologically-protected DSM states in the DSM material.

Despite the rapid progresses in the field of quantum spin Hall (QSH) effect, most of the QSH systems studied up to now are based on crystalline materials. Here we propose that the QSH effect can be realized in quasicrystal lattices (QLs). We show that the electronic topology of aperiodic and amorphous insulators can be characterized by a spin Bott index $B_s$. The nontrivial QSH state in a QL is identified by a nonzero spin Bott index $B_s=1$, associated with robust edge states and quantized conductance. We also map out a topological phase diagram in which the QSH state lies in between a normal insulator and a weak metal phase due to the unique wavefunctions of QLs. Our findings not only provide a better understanding of electronic properties of quasicrystals but also extend the search of QSH phase to aperiodic and amorphous materials that are experimentally feasible., 6 pages 3 figures

This is a joint publication with the Letter by H. Huang and F. Liu [Phys. Rev. Lett. 121, 126401 (2018)]. In this work, we propose the spin Bott index to identify the quantum spin Hall (QSH) state in both crystalline and non-periodic systems. The applicability of the spin Bott index is confirmed by analyzing the periodic and disorder Kane-Mele models. As an example of non-periodic systems, we systematically investigate the QSH effect in a Penrose-type quasicrystal lattice (QL). We characterized the nontrivial electronic topology of the QL by directly calculating the spin Bott index. In addition, the topological edge states, the localization of wavefunctions and quantized transport signatures are also studied in detail., 14 pages, 14 figures

Recently, realizing new fermions, such as type-I and type-II Dirac/Weyl fermions in condensed matter systems, has attracted considerable attention. Here, we show that the transition state from type-I to type-II Dirac fermions can be viewed as a ``type-III'' Dirac fermion, which exhibits unique characteristics, including a Dirac-line Fermi surface with a nontrivial topological invariant and critical chiral anomaly effect, distinct from previously known Dirac semimetals. Most importantly, we discover ${\mathrm{Zn}}_{2}{\mathrm{In}}_{2}{\mathrm{S}}_{5}$ is a type-III Dirac semimetal, characterized by a pair of Dirac points in the bulk and Fermi arcs on the surface. We further propose a solid-state realization of the black-hole-horizon analog in inhomogeneous ${\mathrm{Zn}}_{2}{\mathrm{In}}_{2}{\mathrm{In}}_{5}$ to simulate black-hole evaporation with a high Hawking temperature. We envision that our findings will stimulate researchers to study the physics of type-III Dirac fermions, as well as astronomical problems in a condensed matter analog.

A thickness dependent band gap is commonly found in layered two-dimensional (2D) materials. Here, using a C3N bilayer as a prototypical model, we systematically investigated the evolution of a band gap from a single layer to a bilayer using first principles calculations and tight binding modeling. We show that in addition to the widely known effect of interlayer hopping, de-charge transfer also plays an important role in tuning the band gap. The de-charge transfer is defined with reference to the charge states of atoms in the single layer without stacking, which shifts the energy level and modifies the band gap. Together with band edge splitting induced by the interlayer hopping, the energy level shifting caused by the de-charge transfer determines the size of the band gap in bilayer C3N. Our finding, applicable to other 2D semiconductors, provides an alternative approach for realizing band gap engineering in 2D materials.

We theoretically demonstrate that screw dislocation (SD), a 1D topological defect widely present in semiconductors, exhibits ubiquitously a new form of spin-orbit coupling (SOC) effect. Differing from the widely known conventional 2D Rashba-Dresselhaus (RD) SOC effect that typically exists at surfaces or interfaces, the deep-level nature of SD-SOC states in semiconductors readily makes it an ideal SOC. Remarkably, the spin texture of 1D SD-SOC, pertaining to the inherent symmetry of SD, exhibits a significantly higher degree of spin coherency than the 2D RD-SOC. Moreover, the 1D SD-SOC can be tuned by ionicity in compound semiconductors to ideally suppress spin relaxation, as demonstrated by comparative first-principles calculations of SDs in Si/Ge, GaAs, and SiC. Our findings therefore open a new door to manipulating spin transport in semiconductors by taking advantage of an otherwise detrimental topological defect.

The hunt for the benchmark topological superconductor (TSc) has been an extremely active research subject in condensed matter research, with quite a few candidates identified or proposed. However, low transition temperatures (Tc) and/or strong sensitivity to disorder and dopant levels in known TSc candidates have greatly hampered progress in this field. Here, we use Angle-resolved Photoemission Spectroscopy (ARPES) to show the presence of Dirac Nodal Lines (DNLs) and the corresponding topological surface states (TSS's) on the [010] faces of the Tc=39K s-wave BCS superconductor MgB2. Not only is this nearly triple the current record of superconducting Tc among all candidate TSc's, but the nature of these DNL states should make them highly tolerant against disorder and inadvertent doping variations. This makes MgB2 a promising high temperature platform for the study of topological superconductivity.

Dirac, triple-point, and Weyl fermions represent three topological semimetal phases, characterized with a descending degree of band degeneracy, which have been realized separately in specific crystalline materials with different lattice symmetries. Here we demonstrate an alloy engineering approach to realize all three types of fermions in one single material system of MgTa_{2-x}Nb_{x}N_{3}. Based on symmetry analysis and first-principles calculations, we map out a phase diagram of topological order in the parameter space of alloy concentration and crystalline symmetry, where the intrinsic MgTa_{2}N_{3} with the highest symmetry hosts the Dirac semimetal phase, which transforms into the triple-point and then the Weyl semimetal phases with increasing Nb concentration that lowers the crystalline symmetries. Therefore, alloy engineering affords a unique approach for the experimental investigation of topological transitions of semimetallic phases manifesting different fermionic behaviors.

Based on first-principles calculations and symmetry analysis, we discovery that the ${\mathrm{Ag}}_{2}\mathrm{S}$ with $Cmce$ symmetry is a topological nodal-line semimetal in the absence of spin-orbit coupling. A single nodal loop as protected by the glide symmetry exists around the center of the Brillouin zone, dispersing slightly in the momentum space to form both electron and hole pockets around the loop. Moreover, a nearly flat drumheadlike surface state appears on the (001) surface of this material. The nodal-line semimetal phase and its drumheadlike surface states are expected to be experimentally detectable in $Cmce$-phase ${\mathrm{Ag}}_{2}\mathrm{S}$ because spin-orbit coupling will only open a negligible gap comparing to the energy dispersion of the nodal loop. Our finding provides a different member to the growing family of nodal-line semimetals with a single nodal loop structure.

While a monolayer ${\mathrm{PtSe}}_{2}$ film is a semiconductor with interesting spin structure, bulk ${\mathrm{PtSe}}_{2}$ crystal has been predicted to be a topological Dirac semimetal that can host a new type of Lorentz-violating Dirac fermions. Despite the intriguing predictions, experimental progress on the electronic structure of bulk ${\mathrm{PtSe}}_{2}$ has been hindered due to the lack of large, high-quality single-crystal samples. Here we report the growth and characterization of high-quality ${\mathrm{PtSe}}_{2}$ single crystals and reveal the electronic structure to provide direct evidence for the existence of three-dimensional type-II Dirac fermions. A comparison of the crystal, vibrational, and electronic structure to a related compound, ${\mathrm{PtTe}}_{2}$, is also discussed. Our work provides an important platform for exploring the novel quantum phenomena associated with type-II Dirac fermions in the $1T\ensuremath{-}{\mathrm{PtSe}}_{2}$ class of transition-metal dichalcogenides.

The extremely stringent requirement on material quality has hindered the investigation and potential applications of exotic chiral magnetic effect in Dirac semimetals. Here, we propose that gray tin is a perfect candidate for observing the chiral anomaly effect and Shubnikov-de-Haas (SdH) oscillation at relatively low magnetic field. Based on effective $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ analysis and first-principles calculations, we discover that gray tin becomes a Dirac semimetal under tensile uniaxial strain, in contrast to a topological insulator under compressive uniaxial strain as known before. In this newly found Dirac semimetal state, two Dirac points which are tunable by tensile [001] strains lie in the ${k}_{z}$ axis and Fermi arcs appear in the (010) surface. Due to the low carrier concentration and high mobility of gray tin, a large chiral anomaly induced negative magnetoresistance and a strong SdH oscillation are anticipated in this half of the strain spectrum. Comparing to other Dirac semimetals, the proposed Dirac semimetal state in the nontoxic elemental gray tin can be more easily manipulated and accurately controlled. We envision that gray tin provides a perfect platform for strain engineering of chiral magnetic effects by sweeping through the strain spectrum from positive to negative and vice versa.

Pristine graphene is strongly diamagnetic. However, graphene with single carbon atom defects could exhibit paramagnetism. Theoretically, the $\ensuremath{\pi}$ magnetism induced by the monovacancy in graphene is characteristic of two spin-split density-of-states (DOS) peaks close to the Dirac point. Since its prediction, many experiments have attempted to study this $\ensuremath{\pi}$ magnetism in graphene, whereas only a notable resonance peak has been observed around the atomic defects, leaving the $\ensuremath{\pi}$ magnetism experimentally elusive. Here, we report direct experimental evidence of $\ensuremath{\pi}$ magnetism by using a scanning tunneling microscope. We demonstrate that the localized state of the atomic defects is split into two DOS peaks with energy separations of several tens of meV. Strong magnetic fields further increase the energy separations of the two spin-polarized peaks and lead to a Zeeman-like splitting. Unexpectedly, the effective $g$ factor around the atomic defect is measured to be about 40, which is about 20 times larger than the $g$ factor for electron spins.

Based on first-principles calculations and an effective Hamiltonian analysis, we systematically investigate the electronic and topological properties of alkaline-earth compounds $AX_2$ ($A$=Ca, Sr, Ba; $X$=Si, Ge, Sn). Taking BaSn$_2$ as an example, we find that when spin-orbit coupling is ignored, these materials are three-dimensional topological nodal-line semimetals characterized by a snake-like nodal loop in three-dimensional momentum space. Drumhead-like surface states emerge either inside or outside the loop circle on the (001) surface depending on surface termination, while complicated double-drumhead-like surface states appear on the (010) surface. When spin-orbit coupling is included, the nodal line is gapped and the system becomes a topological insulator with Z$_2$ topological invariants (1;001). Since spin-orbit coupling effects are weak in light elements, the nodal-line semimetal phase is expected to be achievable in some alkaline-earth germanides and silicides., 13 pages, 5 figures

Weyl semimetal is a new quantum state of matter [1-12] hosting the condensed matter physics counterpart of relativisticWeyl fermion [13] originally introduced in high energy physics. The Weyl semimetal realized in the TaAs class features multiple Fermi arcs arising from topological surface states [10, 11, 14-16] and exhibits novel quantum phenomena, e.g., chiral anomaly induced negative mag-netoresistance [17-19] and possibly emergent supersymmetry [20]. Recently it was proposed theoretically that a new type (type-II) of Weyl fermion [21], which does not have counterpart in high energy physics due to the breaking of Lorentz invariance, can emerge as topologically-protected touching between electron and hole pockets. Here, we report direct spectroscopic evidence of topological Fermi arcs in the predicted type-II Weyl semimetal MoTe2 [22-24]. The topological surface states are confirmed by directly observing the surface states using bulk-and surface-sensitive angle-resolved photoemission spectroscopy (ARPES), and the quasi-particle interference (QPI) pattern between the two putative Fermi arcs in scanning tunneling microscopy (STM). Our work establishes MoTe2 as the first experimental realization of type-II Weyl semimetal, and opens up new opportunities for probing novel phenomena such as exotic magneto-transport [21] in type-II Weyl semimetals., Comment: submitted on 01/29/2016. Nature Physics, in press. Spectroscopic evidence of the Fermi arcs from two complementary surface sensitive probes - ARPES and STS. A comparison of the calculated band structure for T_d and 1T' phase to identify the topological Fermi arcs in the T_d phase is also included in the supplementary information

Recently, a new "type-II" Weyl fermion, which exhibits exotic phenomena such as angle-dependent chiral anomaly, was discovered in a new phase of matter where electron and hole pockets contact at isolated Weyl points. [Nature \textbf{527}, 495 (2015)] This raises an interesting question whether its counterpart, i.e., type-II \textit{Dirac} fermion, exists in real materials. Here, we predict the existence of symmetry-protected type-II Dirac fermions in a class of transition metal dichalcogenide materials. Our first-principles calculations on PtSe$_2$ reveal its bulk type-II Dirac fermions which are characterized by strongly tilted Dirac cones, novel surface states, and exotic doping-driven Lifshitz transition. Our results show that the existence of type-II Dirac fermions in PtSe$_2$-type materials is closely related to its structural $P\bar{3}m1$ symmetry, which provides useful guidance for the experimental realization of type-II Dirac fermions and intriguing physical properties distinct from those of the standard Dirac fermions known before., Comment: 12 pages, 3 figures

The rise of topological insulators in recent years has broken new ground both in the conceptual cognition of condensed matter physics and the promising revolution of the electronic devices. It also stimulates the explorations of more topological states of matter. Topological crystalline insulator is a new topological phase, which combines the electronic topology and crystal symmetry together. In this article, we review the recent progress in the studies of SnTe-class topological crystalline insulator materials. Starting from the topological identifications in the aspects of the bulk topology, surface states calculations and experimental observations, we present the electronic properties of topological crystalline insulators under various perturbations, including native defect, chemical doping, strain, and thickness-dependent confinement effects, and then discuss their unique quantum transport properties, such as valley-selective filtering and helicity-resolved functionalities for Dirac fermions. The rich properties and high tunability make SnTe-class materials promising candidates for novel quantum devices., Comment: 15 pages, 15 figures, invited review

Bismuth iodide Bi4I4, composed of quasi-one-dimensional molecular chains, was theoretically predicted and now has been experimentally verified to be a novel strong topological insulator.

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY).-- et al., From density functional theory within the generalized gradient approximation we predict a structure of stanene with dumbbell units (DBs), and show that it is a two-dimensional topological insulator with an inverted band gap which can be tuned by compressive strain. Furthermore, we propose that the boron nitride sheet and reconstructed (2x2) InSb(111) surfaces are ideal substrates for the experimental realization of DB stanene, maintaining its nontrivial topology. Combined with standard semiconductor technologies, such as magnetic doping and electrical gating, the quantum anomalous Hall effect, Chern half metallicity, and topological superconductivity can be realized in DB stanene on those substrates. These properties make the two-dimensional supported stanene a good platform for the study of quantum spin Hall insulators as well as other exotic quantum states of matter., We acknowledge support from the Ministry of Science and Technology of China (Grants No. 2011CB606405 and No. 2011CB921901) and the National Natural Science Foundation of China (Grant No. 11334006). A.R., S.C., and L.X. acknowledge financial support from the European Research Council Grant DYNamo (ERC-2010-AdG No. 267374) Spanish Grants (FIS2010-21282-C02-01), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13), and EC project CRONOS (280879-2 CRONOS CP-FP7.

Inspired by the discovery of graphene, various two-dimensional (2D) materials have been experimentally realized, which exhibit novel physical properties and support promising applications. Exotic topological states in 2D materials (including quantum spin Hall and quantum anomalous Hall insulators), which are characterized by nontrivial metallic edge states within the insulating bulk gap, have attracted considerable attentions in the past decade due to their great importance for fundamental research and practical applications. They also create a surge of research activities and attract extensive efforts to search for new topological materials in realistic 2D/quasi-2D systems. This review presents a comprehensive survey of recent progress in designing of topological states in quasi-2D materials, including various quantum well heterostructures and 2D atomic lattice structures. In particular, the possibilities of constructing topological nontrivial states from commonly used materials are discussed and the ways of enlarging energy gaps of topological states and realizing different topological states in a single material are presented. WIREs Comput Mol Sci 2017, 7:e1296. doi: 10.1002/wcms.1296 For further resources related to this article, please visit the WIREs website.

We report thermoelectric transport studies on Bi2Se3 topological insulator thin films with varied thickness grown by molecular beam epitaxy. We find that the Seebeck coefficient and thermoelectric power factor decrease systematically with the reduction of film thickness. These experimental observations can be explained quantitatively by theoretical calculations based on realistic electronic band structure of the Bi2Se3 thin films. Lastly, this work illustrates the crucial role played by the topological surface states on the thermoelectric transport of topological insulators, and sheds new light on further improvement of their thermoelectric performance.

The generally accepted view that spin polarization in non-magnetic solids is induced by the asymmetry of the global crystal space group has limited the search for spintronics materials mainly to non-centrosymmetric materials. In recent times it has been suggested that spin polarization originates fundamentally from local atomic site asymmetries and therefore centrosymmetric materials may exhibit previously overlooked spin polarizations. Here, by using spin- and angle-resolved photoemission spectroscopy, we report the observation of helical spin texture in monolayer, centrosymmetric and semiconducting PtSe2 film without the characteristic spin splitting in conventional Rashba effect (R-1). First-principles calculations and effective analytical model analysis suggest local dipole induced Rashba effect (R-2) with spin-layer locking: opposite spins are degenerate in energy, while spatially separated in the top and bottom Se layers. These results not only enrich our understanding of the spin polarization physics but also may find applications in electrically tunable spintronics., Spin polarization in non-magnetic solids has mainly been limited to non-centrosymmetric materials. Here, the authors identify a helical spin texture in the centrosymmetric semiconductor platinum diselenide, and suggest it arises from a local dipole induced Rashba effect rather than the usual spin-splitting.