Class Of Topological Materials Research Articles

Synthesis and characterisation of Cu2Ge, a new two-dimensional Dirac nodal line semimetal

Dirac nodal line (DNL) semimetals are a novel class of topological materials in which the valence and conduction bands touch along lines in the reciprocal space, with linear dispersion. These materials attract a growing attention, but the experimental realizations for two-dimensional systems are sparse. This article reports the first experimental realization of a two-dimensional hexagonal monolayer Cu2Ge, grown by evaporation of Ge on a Cu(111) substrate. Through a combination of low-energy electron diffraction XPS and ARPES measurements, it is shown that the surface presents all characteristics expected from calculations for a free-standing Cu2Ge monolayer. More specifically, the preservation of the two concentric nodal lines around the Γ point indicates weak interactions between the Cu2Ge surface and its Cu(111) substrate, making it an ideal system for the study of DNL materials.

Topology and Symmetry in Quantum Materials.

Interest in topological materials continues to grow unabated in view of their conceptual novelties as well as their potential as platforms for transformational new technologies. Electronic states in a topological material are robust against perturbations and support unconventional electromagnetic responses. The first-principles band-theory paradigm has been a key player in the field by providing successful prediction of many new classes of topological materials. This perspective presents a cross sectionthrough the recent work on understanding the role of geometry and topology in generating topological states and their responses to external stimuli, and as a basis for connecting theory and experiment within the band theory framework. In this work, effective strategies for topological materials discovery and impactful directions for future topological materials research are also commented.

Anomalous Hall signatures of nonsymmorphic nodal lines in the doped chromium chalcospinel CuCr2Se4

An emerging phase of matter among the class of topological materials is nodal line semimetal, possessing symmetry-protected one-dimensional gapless lines at the (or close to) the Fermi level in $k$-space. When the $k$-dispersion of the nodal line is weak, van Hove singularities generated by the almost flat nodal lines may be prone to instabilities introduced by additional perturbations such as spin-orbit coupling or magnetism. Here, we study Cr-based ferromagnetic chalcospinel compound CuCr$_2$Se$_4$ (CCS) via first-principles electronic structure methods and reveal the true origin of its dissipationless anomalous Hall conductivity, which was not well understood previously. We find that CCS hosts nodal lines protected by nonsymmorphic symmetries, located in the vicinity of Fermi level, and that such nodal lines are the origin of the previously observed distinct behavior of the anomalous Hall signature in the presence of electron doping. The splitting of nodal line via spin-orbit coupling produces a large Berry curvature, which leads to a significant response in anomalous Hall conductivity. Upon electron doping via chemical substitution or gating, or rotation of magnetization via external magnetic field, steep change of anomalous Hall behavior occurs, which makes CCS a promising compound for low energy spintronics applications.

Broadband circularly polarized thermal radiation from magnetic Weyl semimetals

We numerically demonstrate that a planar slab made of magnetic Weyl semimetal (a class of topological materials) can emit high-purity circularly polarized (CP) thermal radiation over a broad mid- and long-wave infrared wavelength range for a significant portion of its emission solid angle. This effect fundamentally arises from the strong infrared gyrotropy or nonreciprocity of these materials, which primarily depends on the momentum separation between Weyl nodes in the band structure. We clarify the dependence of this effect on the underlying physical parameters and highlight that the spectral bandwidth of CP thermal emission increases with increasing momentum separation between the Weyl nodes. We also demonstrate, using the recently developed thermal discrete dipole approximation (TDDA) computational method, that finite-size bodies of magnetic Weyl semimetals can emit spectrally broadband CP thermal light, albeit over smaller portion of the emission solid angle compared to the planar slabs. Our work identifies unique fundamental and technological prospects of magnetic Weyl semimetals for engineering thermal radiation and designing efficient CP light sources.

Evidence for higher order topology in Bi and Bi0.92Sb0.08

Higher order topological insulators (HOTIs) are a new class of topological materials which host protected states at the corners or hinges of a crystal. HOTIs provide an intriguing alternative platform for helical and chiral edge states and Majorana modes, but there are very few known materials in this class. Recent studies have proposed Bi as a potential HOTI, however, its topological classification is not yet well accepted. In this work, we show that the (110) facets of Bi and BiSb alloys can be used to unequivocally establish the topology of these systems. Bi and Bi0.92Sb0.08 (110) films were grown on silicon substrates using molecular beam epitaxy and studied by scanning tunneling spectroscopy. The surfaces manifest rectangular islands which show localized hinge states on three out of the four edges, consistent with the theory for the HOTI phase. This establishes Bi and Bi0.92Sb0.08 as HOTIs, and raises questions about the topological classification of the full family of BixSb1−x alloys.

Kramers nodal line metals

Recently, it was pointed out that all chiral crystals with spin-orbit coupling (SOC) can be Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta. In this work, we show that all achiral non-centrosymmetric materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there are doubly degenerate lines, which we call Kramers nodal lines (KNLs), connecting time-reversal invariant momenta. The KNLs create two types of Fermi surfaces, namely, the spindle torus type and the octdong type. Interestingly, all the electrons on octdong Fermi surfaces are described by two-dimensional massless Dirac Hamiltonians. These materials support quantized optical conductance in thin films. We further show that KNLMs can be regarded as parent states of KWSs. Therefore, we conclude that all non-centrosymmetric metals with SOC are topological, as they can be either KWSs or KNLMs.

Jacutingaite-family: A class of topological materials

Jacutingate, a recently discovered Brazilian naturally occurring mineral, has been shown to be an experimental realization of the Kane-Mele topological model. In this paper we present a class of materials, ${M}_{2}N{X}_{3}$ ($M=\mathrm{Ni}$, Pt, and Pd; $N=\mathrm{Zn}$, Cd, and Hg; and $X=\mathrm{S}$, Se, and Te), sharing jacutingaite's key features, i.e., high stability and a topological phase. By employing first-principles calculations we extensively characterize the energetic stability of this class while showing a common occurrence of the Kane-Mele topological phase. Here we present Pt-based materials surpassing jacutingaite's impressive topological gap and lower exfoliation barrier while retaining its stability.

Knitting topological bands in artificial sonic semimetals

Frontier investigations on a contemporary family of materials comprise a new class of topological materials that have been discovered in three dimensional (3D) semimetallic crystals. Beyond already unconventional topological quasiparticles in Dirac and Weyl semimetals, nodal-line semimetals provide an even richer platform encompassing robust band-touching manifolds and exotic transport properties. Classical configurations including artificial crystals have emerged as popular systems not only to replicate these new properties in wave-based scenarios, but particularly also to ease experimental complexities of electronic systems and to permit topological tuning via variable geometrical designs. Sonic crystals are one of such example, in which dissimilar fluid or rigid inclusions or channels are combined to tailor the acoustic material response at will. Here, we design a cubic lattice of guiding channels allowing us to map topological characteristics of quasi-particles excitations to audible sound properties. Simply by varying the cross section of these channels, we bring forward multiple phase transitions among four different interlaced nodal features, which resemble the knitting of 3D Bloch-bulk bands in momentum space. One nodal attribute appears to feature an acoustic version of directional massless Dirac fermions, which is experimentally characterized and displays linear crossing in one direction and flat bands in the perpendicular one, enabling strongly focused and collimated sound beams, thanks to this peculiar dispersion.

Selective control of surface spin current in topological pyrite-type OsX2 (X\u2009=\u2009Se, Te) crystals

Topological materials host robust surface states that could form the basis for future electronic devices. As such states have spins that are locked to the momentum, they are of particular interest for spintronic applications. Understanding spin textures of the surface states of topologically nontrivial materials, and being able to manipulate their polarization, is therefore essential if they are to be utilized in future technologies. Here we use first-principles calculations to show that pyrite-type crystals OsX2 (X = Se, Te) are a class of topological materials that can host surface states with spin polarization that can be either in-plane or out-of-plane. We show that the formation of low-energy states with symmetry-protected energy- and direction-dependent spin textures on the (001) surface of these materials is a consequence of a transformation from a topologically trivial to nontrivial state, induced by spin orbit interactions. The unconventional spin textures of these surface states feature an in-plane to out-of-plane spin polarization transition in the momentum space protected by local symmetries. Moreover, the surface spin direction and magnitude can be selectively filtered in specific energy ranges. Our demonstration of a new class of topological materials with controllable spin textures provides a platform for experimentalists to detect and exploit unconventional surface spin textures in future spin-based nanoelectronic devices.

Electromagnetic fields induced by an electric charge near a Weyl semimetal

Weyl semimetals (WSM) are a new class of topological materials that exhibit a bulk Hall effect due to time-reversal symmetry breaking, as well as a chiral magnetic effect due to inversion symmetry breaking. These unusual electromagnetic responses can be characterized by an axion term $\theta \textbf{E} \cdot \textbf{B}$ with space and time dependent axion angle $\theta (\textbf{r} ,t)$. In this paper we compute the electromagnetic fields produced by an electric charge near to a topological Weyl semimetal with two Weyl nodes in the bulk Brillouin zone. We find that, as in ordinary metals and dielectrics, outside the WSM the electric field is mainly determined by the optical properties of the material. The magnetic field is, on the contrary, of topological origin in nature due to the magnetoelectric effect of topological phases. We show that the magnetic field exhibits a particularly interesting behavior above the WSM: the field lines begin at the surface and then end at the surface (but not at the same point). This behavior is quite different from that produced by an electric charge near the surface of a topological insulator, where the magnetic field above the surface is generated by an image magnetic monopole beneath the surface, in which case, the magnetic field lines are straight rays. The unconventional behavior of the magnetic field is an experimentally observable signature of the anomalous Hall effect in the bulk of the WSM. We discuss a simple candidate material for testing our predictions, as well as two experimental setups which must be sensitive to the effects of the induced magnetic field.

Magnetoresistance Anomaly in Topological Kondo Insulator SmB6 Nanowires with Strong Surface Magnetism.

Topological Kondo insulators (TKIs) are a new class of topological materials in which topological surface states dominate the transport properties at low temperatures. They are also an ideal platform for studying the interplay between strong electron correlations and topological order. Here, hysteretic magnetoresistance (MR) is observed in TKI SmB6 thin nanowires at temperatures up to 8 K, revealing the strong magnetism at the surface of SmB6. It is also found that such MR anomaly exhibits an intriguing finite size effect and only appears in nanowires with diameter smaller than 58 nm. These nontrivial phenomena are discussed in terms of the latest Kondo breakdown model, which incorporates the RKKY magnetic interaction mediated by surface states with the strong electron correlation in SmB6. It would provide new insight into the nature of TKI surface states. Additionally, a non‐monotonically temperature dependent positive magnetoresistance is observed at intermediate temperatures, suggesting the possible impurity‐band conduction in SmB6, other than the surface state transport at low temperatures and the bulk‐band transport at high temperatures.

Observation of the Quantum Hall Effect in Confined Films of the Three-Dimensional Dirac Semimetal Cd_{3}As_{2}.

The magnetotransport properties of epitaxial films of Cd_{3}As_{2}, a paradigm three-dimensional Dirac semimetal, are investigated. We show that an energy gap opens in the bulk electronic states of sufficiently thin films and, at low temperatures, carriers residing in surface states dominate the electrical transport. The carriers in these states are sufficiently mobile to give rise to a quantized Hall effect. The sharp quantization demonstrates surface transport that is virtually free of parasitic bulk conduction and paves the way for novel quantum transport studies in this class of topological materials. Our results also demonstrate that heterostructuring approaches can be used to study and engineer quantum states in topological semimetals.

Research progress of single crystal growth for topological semimetals

Topological semimetals have attracted much attention and become a hot subject in condensed matter physics, and single crystal growth is the basis of the physical investigation on these materials. At present, the research of topological materials has formed a cooperation circle:presenting materials by theoretical calculation; single crystal growth; verification by experiments on single crystals. Single crystal growth has become a bridge between theory and experiment. Here in this paper, we introduce the single crystal growth of the topological semimetals presented in recent years, including topological Dirac semimetals, Weyl semimetals, Node-Line semimetals and other new classes of topological materials. The detailed growth methods are summarized in this paper for each material.

A simple and efficient criterion for ready screening of potential topological insulators

Topological materials are a new and rapidly expanding class of quantum matter. To date, identification of the topological nature of a given compound material demands specific determination of the appropriate topological invariant through detailed electronic structure calculations. Here we present an efficient criterion that allows ready screening of potential topological materials, using topological insulators as prototypical examples. The criterion is inherently tied to the band inversion induced by spin-orbit coupling, and is uniquely defined by a minimal number of two elemental physical properties of the constituent elements: the atomic number and Pauling electronegativity. The validity and predictive power of the criterion is demonstrated by rationalizing many known topological insulators and potential candidates in the tetradymite and half-Heusler families, and the underlying design principle is naturally also extendable to predictive discoveries of other classes of topological materials.

Topological materials discovery using electron filling constraints

Nodal semimetals are classes of topological materials that have nodal-point or nodal-line Fermi surfaces, which give them novel transport and topological properties. Despite being highly sought after, there are currently very few experimental realizations, and identifying new materials candidates has mainly relied on exhaustive database searches. Here we show how recent studies on the interplay between electron filling and nonsymmorphic space-group symmetries can guide the search for filling-enforced nodal semimetals. We recast the previously derived constraints on the allowed band-insulator fillings in any space group into a new form, which enables effective screening of materials candidates based solely on their space group, electron count in the formula unit, and multiplicity of the formula unit. This criterion greatly reduces the computation load for discovering topological materials in a database of previously synthesized compounds. As a demonstration, we focus on a few selected nonsymmorphic space groups which are predicted to host filling-enforced Dirac semimetals. Of the more than 30,000 entires listed, our filling criterion alone eliminates 96% of the entries before they are passed on for further analysis. We discover a handful of candidates from this guided search; among them, the monoclinic crystal Ca2Pt2Ga is particularly promising. Electron filling criterion can guide the search for new topological materials with nodal-point or nodal-line Fermi surfaces.

Electronic structure of SrSn2As2 near the topological critical point

Topological materials with exotic quantum properties are promising candidates for quantum spin electronics. Different classes of topological materials, including Weyl semimetal, topological superconductor, topological insulator and Axion insulator, etc., can be connected to each other via quantum phase transition. For example, it is believed that a trivial band insulator can be twisted into topological phase by increasing spin-orbital coupling or changing the parameters of crystal lattice. With the results of LDA calculation and measurement by angle-resolved photoemission spectroscopy (ARPES), we demonstrate in this work that the electronic structure of SrSn2As2 single crystal has the texture of band inversion near the critical point. The results indicate the possibility of realizing topological quantum phase transition in SrSn2As2 single crystal and obtaining different exotic quantum states.

Dirac-semimetal phase diagram of two-dimensional black phosphorus

Black phosphorus (BP), a layered van der Waals material, reportedly has a band gap sensitive to external perturbations and manifests a Dirac-semimetal phase when its band gap is closed. Previous studies were focused on effects of each perturbation, lacking a unified picture for the band-gap closing and the Dirac-semimetal phase. Here, using pseudospins from the glide-reflection symmetry, we study the electronic structures of mono- and bilayer BP and construct the phase diagram of the Dirac-semimetal phase in the parameter space related to pressure, strain, and electric field. We find that the Dirac-semimetal phase in BP layers is singly connected in the phase diagram, indicating the phase is topologically identical regardless of the gap-closing mechanism. Our findings can be generalized to the Dirac semimetal phase in anisotropic layered materials and can play a guiding role in search for a new class of topological materials and devices.

Majorana zero modes in spintronics devices

We show that topological phases should be realizable in readily available and well studied heterostructures. In particular we identify a new class of topological materials which are well known in spintronics: helical ferromagnet-superconducting junctions. We note that almost all previous work on topological heterostructures has focused on creating Majorana modes at the proximity interface in effectively two-dimensional or one-dimensional systems. The particular heterostructures we address exhibit finite range proximity effects leading to nodal superconductors with Majorana modes localized well away from this interface. To show this, we implement a Bogoliubov-de Gennes (BdG) proximity numerical scheme, which importantly, involves two finite dimensions in a three dimensional junction. Incorporating this level of numerical complexity serves to distinguish ours from alternative numerical BdG approaches which are limited by generally assuming translational invariance or periodic boundary conditions along multiple directions. With this access to the edges, we are then able to illustrate in a concrete fashion the wavefunctions of Majorana zero modes, and, moreover, address finite size effects. In the process we establish consistency with a simple analytical model.

Sinking into the bulk of a Weyl semimetal

Topological Matter![Figure][1] Surface properties of the material TaA. INOUE ET AL. A recently discovered class of topological materials, Weyl semimetals, have surface states in the form of so-called Fermi arcs. Inoue et al. used a high-resolution scanning tunneling microscope to explore

Tunable unconventional Kondo effect on topological insulator surfaces

We study Kondo physics of a spin-$\frac{1}{2}$ impurity in electronic matter with strong spin-orbit interaction, which can be realized by depositing magnetic adatoms on the surface of a three-dimensional topological insulator. We show that magnetic properties of topological surface states and the very existence of Kondo screening strongly depend on details of the bulk material, and specifics of surface preparation encoded in time-reversal preserving boundary conditions for electronic wavefunctions. When this tunable Kondo effect occurs, the impurity spin is screened by purely orbital motion of surface electrons. This mechanism gives rise to a transverse magnetic response of the surface metal, and spin textures that can be used to experimentally probe signatures of a Kondo resonance. Our predictions are particularly relevant for STM measurements in ${\rm Pb Te}$-class crystalline topological insulators, but we also discuss implications for other classes of topological materials.