Symmetry-protected ideal Weyl semimetal in HgTe-class materials

Electric, thermal, and thermoelectric magnetoconductivity for Weyl/multi-Weyl semimetals in planar Hall set-ups induced by the combined effects of topology and strain

We continue our investigation of the response tensors in planar Hall (or planar thermal Hall) configurations where a three-dimensional Weyl/multi-Weyl semimetal is subjected to the combined influence of an electric field E (and/or temperature gradient∇ r T ) and an effective magnetic field B χ , generalizing the considerations of Phys. Rev. B 108 (2023) 155132 and Physica E 159 (2024) 115914. The electromagnetic fields are oriented at a generic angle with respect to each other, thus leading to the possibility of having collinear components, which do not arise in a Hall set-up. The net effective magnetic field B χ consists of two parts-(a) an actual/physical magnetic field B applied externally; and (b) an emergent magnetic field B 5 which quantifies the elastic deformations of the sample. B 5 is an axial pseudomagnetic field because it couples to conjugate nodal points with opposite chiralities with opposite signs. Using a semiclassical Boltzmann formalism, we derive the generic expressions for the response tensors, including the effects of the Berry curvature (BC) and the orbital magnetic moment (OMM), which arise due to a nontrivial topology of the bandstructures. We elucidate the interplay of the BC-only and the OMM-dependent parts in the longitudinal and transverse (or Hall) components of the electric, thermal, and thermoelectric response tensors. Especially, for the co-planar transverse components of the response tensors, the OMM part acts exclusively in opposition (sync) with the BC-only part for the Weyl (multi-Weyl) semimetals.

Thermoelectric transport in Weyl semimetals under a uniform concentration of torsional dislocations

In this article, we present an effective continuum model for a Weyl semimetal, to calculate its thermal and thermoelectric transport coefficients in the presence of a uniform concentration of torsional dislocations. We model each dislocation as a cylindrical region of finite radius a, where the corresponding elastic strain is described as a gauge field leading to a local pseudo-magnetic field. The transport coefficients are obtained by a combination of scattering theory, Green's functions and the Kubo formulae in the linear response regime. We applied our theoretical results to predict the electrical and thermal conductivities as well as the Seebeck coefficient for several transition metal monopnictides, i.e. TaAs, TaP, NbAs and NbP.

Direction-dependent conductivity in planar Hall set-ups with tilted Weyl/multi-Weyl semimetals

We compute the magnetoelectric conductivity tensors in planar Hall set-ups, which are built with tilted Weyl semimetals (WSMs) and multi-Weyl semimetals (mWSMs), considering all possible relative orientations of the electromagnetic fields (EandB) and the direction of the tilt. The non-Drude part of the response arises from a nonzero Berry curvature in the vicinity of the WSM/mWSM node under consideration. Only in the presence of a nonzero tilt do we find linear-in-|B|terms in set-ups where the tilt-axis is not perpendicular to the plane spanned byEandB. The advantage of the emergence of the linear-in-|B|terms is that, unlike the various|B|2-dependent terms that can contribute to experimental observations, they have purely a topological origin, and they dominate the overall response-characteristics in the realistic parameter regimes. The important signatures of these terms are that they (1) change the periodicity of the response fromπto 2π, when we consider their dependence on the angleθbetweenEandB; and (2) lead to an overall change in sign of the conductivity depending onθ, when measured with respect to theB=0case.

Light-Induced Ideal Weyl Semimetal in HgTe via Nonlinear Phononics

Interactions between light and matter allow the realization of out-of-equilibrium states in quantum solids. In particular, nonlinear phononics is one of the most efficient approaches to realizing the stationary electronic state in nonequilibrium. Herein, by an extended ab initio molecular dynamics method, we identify that long-lived light-driven quasistationary geometry could stabilize the topological nature in the material family of HgTe compounds. We show that coherent excitation of the infrared-active phonon mode results in a distortion of the atomic geometry with a lifetime of several picoseconds. We show that four Weyl points are located exactly at the Fermi level in this nonequilibrium geometry, making it an ideal long-lived metastable Weyl semimetal. We propose that such a metastable topological phase can be identified by photoelectron spectroscopy of the Fermi arc surface states or ultrafast pump-probe transport measurements of the nonlinear Hall effect.

Fluctuations in Planar Magnetotransport Due to Tilted Dirac Cones in Topological Materials

Fluctuations in planar magnetotransport are ubiquitous in topological HgTe structures, in both tensile (topological insulator) and compressively strained layers (Weyl semimetal phase). We show that the common reason for the fluctuations is the presence of tilted Dirac cones combined with the formation of charge puddles. The origin of the tilted Dirac cones is the mix of the Zeeman term due to the in-plane magnetic field and quadratic contributions to the dispersion relation. We develop a network model that mimics the transport of tilted Dirac fermions in the landscape of charge puddles. The model captures the essential features of the experimental data. It should be relevant for the interpretation of planar magnetotransport in a variety of topological and small band gap materials.

Two step I to II type transitions in layered Weyl semi-metals and their impact on superconductivity

Novel "quasi two dimensional" typically layered (semi) metals offer a unique opportunity to control the density and even the topology of the electronic matter. Along with doping and gate voltage, a robust tuning is achieved by application of the hydrostatic pressure. In Weyl semi-metals the tilt of the dispersion relation cones, [Formula: see text] increases with pressure, so that one is able to reach type II ([Formula: see text]starting from the more conventional type I Weyl semi-metals [Formula: see text]. The microscopic theory of such a transition is constructed. It is found that upon increasing pressure the I to II transition occurs in two continuous steps. In the first step the cones of opposite chirality coalesce so that the chiral symmetry is restored, while the second transition to the Fermi surface extending throughout the Brillouin zone occurs at higher pressures. Flattening of the band leads to profound changes in Coulomb screening. Superconductivity observed recently in wide range of pressure and chemical composition in Weyl semi-metals of both types. The phonon theory of pairing including the Coulomb repulsion for a layered material is constructed and applied to recent extensive experiments on [Formula: see text].

Positive longitudinal magnetoconductivity induced by chiral magnetic effect in mercury selenide

A negative longitudinal magnetoresistance without any sign of saturation was found in a non-centrosymmetric Weyl semimetal (WSM) candidate mercury selenide in an electron concentration range of 5.5 × 10¹⁵-1.7 × 10¹⁷cm^-3and a temperature range of 0.33-150 K. The magnitude of the effect varies with a sample from≈10% up to≈30% in a magnetic field of 12 T atT= 150 K. Moreover, the positive contribution to magnetoconductivity has a characteristic quadratic dependence on the magnetic field, increasing with a charged center concentration atT= 150 K. The most likely explanation for the discovered longitudinal magnetoconductivity feature lies in the chiral magnetic effect, which is inherent to WSMs. The role of the Dyakonov-Perel mechanism in inter-nodal spin relaxation is discussed in regard to HgSe.

Photonic Weyl semimetals in pseudochiral metamaterials

We investigate the photonic topological phases in pseudochiral metamaterials characterized by the magnetoelectric tensors with symmetric off-diagonal chirality components. The underlying medium is considered a photonic analogue of the type-II Weyl semimetal featured with two pairs of tilted Weyl cones in the frequency-wave vector space. As the ’spin’-degenerate condition is satisfied, the photonic system consists of two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in terms of the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between vacuum and the pseudochiral metamaterial exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, the surface modes are tangent to both the vacuum light cone and the Weyl cones, which form two pairs of crossing surface sheets that are symmetric about the transverse axes. At the Weyl frequency, the surface modes that connect the Weyl points form four Fermi arc-like states as line segments. Topological features of the pseudochiral metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.

Electronic Transport in Weyl Semimetals with a Uniform Concentration of Torsional Dislocations

In this article, we consider a theoretical model for a type I Weyl semimetal, under the presence of a diluted uniform concentration of torsional dislocations. By means of a mathematical analysis for partial wave scattering (phase-shift) for the T-matrix, we obtain the corresponding retarded and advanced Green's functions that include the effects of multiple scattering events with the ensemble of randomly distributed dislocations. Combining this analysis with the Kubo formalism, and including vertex corrections, we calculate the electronic conductivity as a function of temperature and concentration of dislocations. We further evaluate our analytical formulas to predict the electrical conductivity of several transition metal monopnictides, i.e., TaAs, TaP, NbAs, and NbP.

Superconductivity in Crystallographically Disordered LaHg6.4

The influence of structural disorder on superconductivity is not yet fully understood. A concurrent examination of crystallographic and physical properties of LaHg_6.4 reveals that this material enters a superconducting state below T_c = 2.4 K while showing crystallographic disorder in one dimension. Lanthanum mercuride, which crystallizes in a new structure type (space group Cmcm, a = 9.779(2) Å, b = 28.891(4) Å, c = 5.0012(8) Å, Z = 8), has remained out of reach for nearly 50 years. In this crystal structure, strong disorder is present in the channels that propagate along the [001] direction. By implementing a combination of cutting-edge synthesis and characterization techniques, we were able to circumvent the complexity associated with the low formation temperature and chemical reactivity of this substance and study the superconductivity of LaHg_6.4 in detail.

Superconductivity in Mo-P compounds under pressure and in double-Weyl semimetal Hex-MoP2

Based on first-principles calculations, we predict five global stable molybdenum phosphorus compounds in the pressure range of 0-300 GPa. All of them display superconductivity with different transition temperatures. Meanwhile, we find that a metastable crystal hex-MoP₂, crystallized in a noncentrosymmetric structure, is a double-Weyl semimetal and the Weyl point is in the H-K path. The long Fermi arcs and the topological surface states, which can be observed by angle-resolved photoemission spectroscopy, emerge at the (100) surface below the Fermi level. Furthermore, we find that the superconductivity in hex-MoP₂ can be enhanced by carrier doping. Due to the breaking of inversion symmetry, the unconventional spin-triplet pairing coexists with spin-singlet pairing in channel . Based on our theoretical model, there are the superconducting band gaps in both pairings. Our work provides a new platform of hex-MoP₂ for studying both topological double-Weyl semimetal and superconductivity.

Elemental Topological Dirac Semimetal α-Sn with High Quantum Mobility

α-Sn provides an ideal avenue to investigate novel topological properties owing to its rich diagram of topological phases and simple elemental material structure. Thus far, however, the realization of high-quality α-Sn remains a challenge, which limits the understanding of its quantum transport properties and device applications. Here, epitaxial growth of α-Sn on InSb (001) with the highest quality thus far is presented. The studied samples exhibit unprecedentedly high quantum mobilities of both the surface state (30 000 cm² V^-1 s^-1 ), which is ten times higher than the previously reported values, and the bulk heavy-hole state (1800 cm² V^-1 s^-1 ), which is never obtained experimentally. These excellent features allow quantitative characterization of the nontrivial interfacial and bulk band structure of α-Sn via a thorough investigation of Shubnikov-de Haas oscillations combined with first-principles calculations. The results firmly identify that α-Sn grown on InSb (001) is a topological Dirac semimetal (TDS). Furthermore, a crossover from the TDS to a 2D topological insulator and a subsequent phase transition to a trivial insulator when varying the thickness of α-Sn are demonstrated. This work indicates that α-Sn is an excellent model system to study novel topological phases and a prominent material candidate for topological devices.

Thermo-Magneto-Electric Transport through a Torsion Dislocation in a Type I Weyl Semimetal

Herein, we study electronic and thermoelectric transport in a type I Weyl semimetal nanojunction, with a torsional dislocation defect, in the presence of an external magnetic field parallel to the dislocation axis. The defect is modeled in a cylindrical geometry, as a combination of a gauge field accounting for torsional strain and a delta-potential barrier for the lattice mismatch effect. In the Landauer formalism, we find that due to the combination of strain and magnetic field, the electric current exhibits chiral valley-polarization, and the conductance displays the signature of Landau levels. We also compute the thermal transport coefficients, where a high thermopower and a large figure of merit are predicted for the junction.

Ideal type-II Weyl points in topological circuits

Weyl points (WPs), nodal degenerate points in three-dimensional (3D) momentum space, are said to be 'ideal' if they are symmetry-related and well-separated, and reside at the same energy and far from nontopological bands. Although type-II WPs have unique spectral characteristics compared with type-I counterparts, ideal type-II WPs have not yet been reported because of a lack of an experimental platform with enough flexibility to produce strongly tilted dispersion bands. Here, we experimentally realize a topological circuit that hosts only topological bands with a minimal number of four ideal type-II WPs. By stacking two-dimensional (2D) layers of inductor-capacitor (LC) resonator dimers with the broken parity inversion symmetry (P), we achieve a strongly tilted band structure with two group velocities in the same direction, and topological surface states in an incomplete bandgap. Our results establish an ideal system for the further study of Weyl physics and other exotic topological phenomena.

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.

A Raman probe of phonons and electron-phonon interactions in the Weyl semimetal NbIrTe4

There is tremendous interest in measuring the strong electron-phonon interactions seen in topological Weyl semimetals. The semimetal NbIrTe4 has been proposed to be a Type-II Weyl semimetal with 8 pairs of opposite Chirality Weyl nodes which are very close to the Fermi energy. We show using polarized angular-resolved micro-Raman scattering at two excitation energies that we can extract the phonon mode dependence of the Raman tensor elements from the shape of the scattering efficiency versus angle. This van der Waals semimetal with broken inversion symmetry and 24 atoms per unit cell has 69 possible phonon modes of which we measure 19 modes with frequencies and symmetries consistent with Density Functional Theory calculations. We show that these tensor elements vary substantially in a small energy range which reflects a strong variation of the electron-phonon coupling for these modes.

Controlling magnetoresistance by tuning semimetallicity through dimensional confinement and heteroepitaxy

Controlling electronic properties via band structure engineering is at the heart of modern semiconductor devices. Here, we extend this concept to semimetals where, using LuSb as a model system, we show that quantum confinement lifts carrier compensation and differentially affects the mobility of the electron and hole-like carriers resulting in a strong modification in its large, nonsaturating magnetoresistance behavior. Bonding mismatch at the heteroepitaxial interface of a semimetal (LuSb) and a semiconductor (GaSb) leads to the emergence of a two-dimensional, interfacial hole gas. This is accompanied by a charge transfer across the interface that provides another avenue to modify the electronic structure and magnetotransport properties in the ultrathin limit. Our work lays out a general strategy of using confined thin-film geometries and heteroepitaxial interfaces to engineer electronic structure in semimetallic systems, which allows control over their magnetoresistance behavior and simultaneously provides insights into its origin.

Fully spin-polarized Weyl fermions and in/out-of-plane quantum anomalous Hall effects in a two-dimensional d0 ferromagnet

The quantum anomalous Hall effect (QAHE) in intrinsic ferromagnets has attracted considerable attention recently. Previously, studies of the QAHE have mostly focused on the default assumption of out-of-plane magnetization. In fact, the QAHE can also be achieved via in-plane magnetization, but such candidate materials are very scarce. Here, we find that two-dimensional (2D) YN₂ not only possesses the previously reported out-of-plane QAHE, but it also possesses a tunable in-plane QAHE. More importantly, unlike the previously reported in-plane QAHE in d/f-type ferromagnets, here we report the effect in a 2D d⁰ ferromagnet, namely YN₂, for the first time. In the ground state, a YN₂ monolayer has a half-metal band structure, and manifests six pairs of fully spin-polarized Weyl points at the Fermi level. When spin-orbit coupling is included, the YN₂ monolayer can realize multiple topological phases, determined based on the magnetization direction. Under in-plane magnetization, the YN₂ monolayer shows either the Weyl state or in-plane QAHE state. Remarkably, the Chern number (±1) and the propagating direction of QAHE edge channels can be continuously switched via shifting the direction of the in-plane magnetic field. When magnetization is applied out-of-plane, the YN₂ monolayer realizes an out-of-plane QAHE phase with a high Chern number of 3. The nontrivial edge states for all the topological phases in the YN₂ monolayer have been clearly identified. This work suggests that 2D YN₂ is an excellent candidate for investigating in-plane QAHE phases in d⁰ ferromagnets.

Emergence of -s, -p-dband inversion in zincblende gold iodide topological insulator and its thermoelectric properties

We employfirst-principlescalculations to investigate the topological states (TS) and thermoelectric (TE) transport properties of three dimensional (3D) gold iodide (AuI) which belongs to the zincblende family. We explore, semi-metal (SM) to topological conductor (TC) and topological insulator (TI) phase transitions. Under pristine conditions, AuI exhibits Dirac SM nature but, under the influence of mild isotropic compressive pressure the system undergoes electronic quantum phase transition driving it into non-trivial topological state. This state exhibits Dresselhaus like band spin splitting leading to a TC state. In order to realize TI state from the SM state, we break the cubic symmetry of the system by introducing a compressive pressure along (001) crystal direction. The non-trivial TI nature of the system is characterized by the emergence of robust surface states and theZ2invariantν0= 1 which indicates a strong TI nature. A novel facet of the phase transition discussed here is, the -sand -p, -dorbital band inversion mechanism which is unconventional as compared to previously explored TI families. This mechanism unravels new path by which TI materials can be predicted. Also, we investigated the lattice and electronic contributions to the TE transport properties. We characterize the TE performance by calculating the figure of merit (zT) and find that, at room temperature (300 K) and for a fixed doping concentration (i.e.,n= 1 × 1019 cm-3) the zT is 0.55 and 0.53 for electrons and holes respectively. This is quite remarkable since, higher values of zT are generally predicted at higher temperature scales whereas, zT values as in the present case are desired at room temperatures for various energy applications. The manifestation of non-trivial TS governed by the unconventional band inversion mechanism and the TE properties of AuI make it a unique multi-functional candidate with probable thermoelectric and spintronic applications.

Weyl Fermions in VI3 Monolayer

We report the presence of a Weyl fermion in VI₃ monolayer. The material shows a sandwich-like hexagonal structure and stable phonon spectrum. It has a half-metal band structure, where only the bands in one spin channel cross the Fermi level. There are three pairs of Weyl points slightly below the Fermi level in spin-up channel. The Weyl points show a clean band structure and are characterized by clear Fermi arcs edge state. The effects of spin-orbit coupling, electron correlation, and lattice strain on the electronic band structure were investigated. We find that the half-metallicity and Weyl points are robust against these perturbations. Our work suggests VI₃ monolayer is an excellent Weyl half-metal.

Ideal Unconventional Weyl Point in a Chiral Photonic Metamaterial

Unconventional Weyl points (WPs), carrying topological charge 2 or higher, possess interesting properties different from ordinary charge-1 WPs, including multiple Fermi arcs that stretch over a large portion of the Brillouin zone. Thus far, such WPs have been observed in chiral materials and acoustic metamaterials, but there has been no clean demonstration in photonics in which the unconventional photonic WPs are separated from trivial bands. We experimentally realize an ideal symmetry-protected photonic charge-2 WP in a three-dimensional topological chiral microwave metamaterial. We use field mapping to directly observe the projected bulk dispersion, as well as the two long surface arcs that form a noncontractible loop wrapping around the surface Brillouin zone. The surface states span a record-wide frequency window of around 22.7% relative bandwidth. We demonstrate that the surface states exhibit a novel topological self-collimation property and are robust against disorder. This work provides an ideal photonic platform for exploring fundamental physics and applications of unconventional WPs.

Observation of Dirac state in half-Heusler material YPtBi

The prediction of non-trivial topological electronic states in half-Heusler compounds makes these materials good candidates for discovering new physics and devices as half-Heusler phases harbour a variety of electronic ground states, including superconductivity, antiferromagnetism, and heavy-fermion behaviour. Here, we report a systematic studies of electronic properties of a superconducting half-Heusler compound YPtBi, in its normal state, investigated using angle-resolved photoemission spectroscopy. Our data reveal the presence of a Dirac state at the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma$$\end{document}Γ point of the Brillouin zone at 500 meV below the Fermi level. We observe the presence of multiple Fermi surface pockets, including two concentric hexagonal and six half-oval shaped pockets at the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma$$\end{document}Γ and K points of the Brillouin zone, respectively. Furthermore, our measurements show Rashba-split bands and multiple surface states crossing the Fermi level, this is also supported by the first-principles calculations. Our findings of a Dirac state in YPtBi contribute to the establishing of half-Heusler compounds as a potential platform for novel topological phases.

Coexistence of type-I and critical-type nodal line states in intermetallic compounds ScM (M = Cu, Ag, Au)

In recent years, topological semimetals such as Weyl, Dirac, and nodal-line semimetals have been a hot topic in the field of condensed matter physics. Depending on the orientation of band crossing in momentum space, topological semimetals and metals can be identified as type-I or type-II. Here, we report the coexistence of two new types of topological metal phase in the ScM (M = Cu, Ag, Au) intermetallic compounds (IMCs): (1) multi-nodal-lines semimetals (above Fermi energy), (2) critical-type nodal-lines (lower than Fermi energy). The first case has already been investigated. So, in this paper, we focus on the second case. We find that these IMCs can be an existing topological metal lower than Fermi energy, which are characterized with type-I (for ScCu and ScAu) and critical-type (for ScAg) nodal-lines in the bulk and drumhead liked surface states in the absence of the spin-orbit coupling (SOC). It has also been shown that when SOC is included, these compounds are converted into topological metal materials.

Ternary compound HfCuP: An excellent Weyl semimetal with the coexistence of type-I and type-II Weyl nodes

In most Weyl semimetal (WSMs), the Weyl nodes with opposite chiralities usually have the same type of band dispersions (either type-I or type-II), whereas realistic candidate materials hosting different types of Weyl nodes have not been identified to date. Here we report for the first time that, a ternary compound HfCuP, is an excellent WSM with the coexistence of type-I and type-II Weyl nodes. Our results show that, HfCuP totally contains six pairs of type-I and six pairs of type-II Weyl nodes in the Brillouin zone, all locating at the H-K path. These Weyl nodes situate slightly below the Fermi level, and do not coexist with other extraneous bands. The nontrivial band structure in HfCuP produces clear Fermi arc surface states in the (1 0 0) surface projection. Moreover, we find the Weyl nodes in HfCuP can be effectively tuned by strain engineering. These characteristics make HfCuP a potential candidate material to investigate the novel properties of type-I and type-II Weyl fermions, as well as the potential entanglements between them.

Ideal Type-II Weyl Phase and Topological Transition in Phononic Crystals

Ideal Weyl points, which are related by symmetry and thus reside at the same frequency, could offer further insight into the Weyl physics. The ideal type-I Weyl points have been observed in photonic crystals, but the ideal type-II Weyl points with tilted conelike band dispersions are still not realized. Here we present the observation of the ideal type-II Weyl points of the minimal number in three-dimensional phononic crystals and, in the meantime, the topological phase transition from the Weyl semimetal to the valley insulators of two distinct types. The Fermi-arc surface states are shown to exist on the surfaces of the Weyl phase, and the Fermi-circle surface states are also observed, but on the interface of the two distinct valley phases. Intriguing wave partition of the Fermi-circle surface states is demonstrated.

Hybridization of topological surface states with a flat band

We address the problem of hybridization between topological surface states and a non-topological flat bulk band. Our model, being a mixture of three-dimensional Bernevig-Hughes-Zhang and two-dimensional pseudospin-1 Hamiltonian, allows explicit treatment of the topological surface state evolution by continuously changing the hybridization between the inverted bands and an additional 'parasitic' flat band in the bulk. We show that the hybridization with a flat band lying below the edge of the conduction band converts the initial Dirac-like surface states into a branch below and one above the flat band. Our results univocally demonstrate that the upper branch of the topological surface states is formed by Dyakonov-Khaetskii surface states, known for HgTe since the 1980s. Additionally we explore an evolution of the surface states and the arising of Fermi arcs in Dirac semimetals when the flat band crosses the conduction band.

Electronic stopping power for slow ions in the low-hardness semimetal HgTe using first-principles calculations

The electronic stopping power for low-velocity ions (including protons, [Formula: see text]-particles, and [Formula: see text]) is investigated in a novel semimetal HgTe system, where the data are obtained with the aid of Ehrenfest dynamics combined with time-dependent density functional theory. For the light projectile ions (protons and [Formula: see text]-particles), the linear and nonlinear behaviors of electronic stopping power in three different channel directions are analyzed in detail. In the case where the projectile ion is a proton, the linear results for the threshold velocity are correlated with an indirect band gap; the direction of the electronic stopping power depends on the radial drag force, the channeling electronic density and the trapped charge. More notably, we report an interesting channel-geometry fact, i.e. that the electronic stopping power of HgTe is powerfully modulated by the impact parameters. The parallel off-center tracks increase the electronic stopping power, making it more consistent with the SRIM data. In the case of an [Formula: see text]-particle as the projectile ion, nonlinear behavior that varies with velocity can be ascribed to the charge transfer, which is another mode of energy dissipation. In addition, when the slightly heavier projectile [Formula: see text] travels through the medium HgTe, the projectile [Formula: see text] can capture more free charges than the protons and [Formula: see text]-particles under the same circumstances. Especially, for the projectile in the off-channel, the electronic stopping power is close to the SRIM data with the decrease of the impact parameter. These results extend the study of radiation damage to a new field of materials.

A type of novel Weyl semimetal candidate: layered transition metal monochalcogenides Mo2XY (X, Y = S, Se, Te, X ≠ Y)

Based on ab initio calculations and the Wannier-based tight-binding method, we studied the topological electronic properties and strain modulation of transition metal monochalcogenides (TMM) Mo₂XY (X, Y = S, Se, Te, X ≠ Y). These materials are nodal line semimetals in the absence of spin-orbit coupling (SOC). The presence of SOC turns them into Weyl semimetals with 24 Weyl nodes located in the k_z≠ 0 planes and related by time-reversal, rotation C_3z, and mirror symmetries. The maximal separation between two neighboring Weyl points with opposite chirality is of the order of magnitude of 0.10 Å^-1, which can be readily accessed by angle-resolved photoemission spectroscopy (ARPES). The Weyl semimetal phase shows great robustness and demonstrates different responses under uniaxial and biaxial strain. Intriguingly, the location of the Weyl point changes significantly, resulting in a striking modulation of topological properties under in-plane biaxial strain. Our finding provides a realistic and promising platform for studying and manipulating the behavior of Weyl fermions in experiments.

Lasing with Topological Weyl Semimetal

Lasing behavior of optically active planar topological Weyl semimetal (TWS) is investigated in view of the Kerr and Faraday rotations. Robust topological character of TWS is revealed by the presence of Weyl nodes and relevant surface conductivities. We focus our attention on the surfaces where no Fermi arcs are formed, and thus Maxwell equations contain topological terms. We explicitly demonstrate that two distinct lasing modes arise because of the presence of effective refractive indices which lead to the birefringence phenomena. Transfer matrix is constructed in such a way that reflection and transmission amplitudes involve 2 × 2 matrix-valued components describing the bimodal character of the TWS laser. We provide associated parameters of the topological laser system yielding the optimal impacts. We reveal that gain values corresponding to the lasing threshold display a quantized behavior, which occurs due to topological character of the system. Our proposal is supported by the corresponding graphical demonstrations. Our observations and predictions suggest a concrete way of forming TWS laser and coherent perfect absorber; and are awaited to be confirmed by an experimental realization based on our computations.

Observation of quantum topological Hall effect in the Weyl semimetal candidate HgSe

The magnetoresistance (MR) and Hall effect of a single HgSe crystal with an extremely low electron concentration of 8.8  ×  10¹⁵ cm^-3 were studied in a quantising magnetic field applied both along and across the direction of the electric current. As the result, a broad plateau was discovered in the ordinary (transverse) Hall resistance in the quantum limit. Within a framework of quantum spin Hall effect for an inversion breaking Weyl semimetal, we associate this plateau with a contribution to Hall conductivity from Chern insulator edge states when only a zero Landau level is occupied. In addition to the plateau in the quantum limit, we also detected a well-developed plateau-like behaviour in a phenomenologically-introduced 'longitudinal' Hall resistivity. In the 'longitudinal' Hall conductivity, a step-like behaviour was revealed, which we identify with the discovery of half-integer quantum spin Hall effect in HgSe. This effect, being purely topological in origin, supplements the non-trivial Weyl semimetal physics and may serve as a promising magnetotransport method for the detection of Weyl nodes in a studied material.

Intrinsic magnetic topological insulator phases in the Sb doped MnBi2Te4 bulks and thin flakes

Magnetic topological insulators (MTIs) offer a combination of topologically nontrivial characteristics and magnetic order and show promise in terms of potentially interesting physical phenomena such as the quantum anomalous Hall (QAH) effect and topological axion insulating states. However, the understanding of their properties and potential applications have been limited due to a lack of suitable candidates for MTIs. Here, we grow two-dimensional single crystals of Mn(SbxBi(1-x))2Te4 bulk and exfoliate them into thin flakes in order to search for intrinsic MTIs. We perform angle-resolved photoemission spectroscopy, low-temperature transport measurements, and first-principles calculations to investigate the band structure, transport properties, and magnetism of this family of materials, as well as the evolution of their topological properties. We find that there exists an optimized MTI zone in the Mn(SbxBi(1-x))2Te4 phase diagram, which could possibly host a high-temperature QAH phase, offering a promising avenue for new device applications.

Bandgap engineering of PbTe ultra-thin layers by surface passivations

We calculate the electronic structures of the PbTe (1 1 1) ultra-thin films by performing the first-principles calculations. The PbTe (1 1 1) ultra-thin films possess direct or indirect band gaps depending sensitively on surface passivations with hydrogen or halogen atoms, and the band gaps depend sensitively on the passivation elements. The bandgaps of PbTe (1 1 1) ultra-thin films with hydrogen passivations can be tuned from 15 meV to 65 meV by applying external strains, making PbTe ultra-thin films promising candidates for optoelectronic device applications in terahertz regime.

Topological Axion States in the Magnetic Insulator MnBi_{2}Te_{4} with the Quantized Magnetoelectric Effect

Topological states of quantum matter have attracted great attention in condensed matter physics and materials science. The study of time-reversal-invariant topological states in quantum materials has made tremendous progress. However, the study of magnetic topological states falls much behind due to the complex magnetic structures. Here, we predict the tetradymite-type compound MnBi_{2}Te_{4} and its related materials host topologically nontrivial magnetic states. The magnetic ground state of MnBi_{2}Te_{4} is an antiferromagetic topological insulator state with a large topologically nontrivial energy gap (∼0.2  eV). It presents the axion state, which has gapped bulk and surface states, and the quantized topological magnetoelectric effect. The ferromagnetic phase of MnBi_{2}Te_{4} might lead to a minimal ideal Weyl semimetal.

Topological Semimetals in the SnTe Material Class: Nodal Lines and Weyl Points

We theoretically show that IV-VI semiconducting compounds with low-temperature rhombohedral crystal structure represent a new potential platform for topological semimetals. By means of minimal k·p models, we find that the two-step structural symmetry reduction of the high-temperature rocksalt crystal structure, comprising a rhombohedral distortion along the [111] direction followed by a relative shift of the cation and anion sublattices, gives rise to topologically protected Weyl semimetal and nodal line semimetal phases. We derive general expressions for the nodal features and apply our results to SnTe, showing explicitly how Weyl points and nodal lines emerge in this system. Experimentally, the topological semimetals could potentially be realized in the low-temperature ferroelectric phase of SnTe, GeTe, and related alloys.

Nontrivial topology of bulk HgSe from the study of cyclotron effective mass, electron mobility and phase shift of Shubnikov-de Haas oscillations

In this paper, the authors report the results of an experimental study of effective mass, electron mobility and phase shift of Shubnikov-de Haas oscillations of transverse magnetoresistance in an extended electron concentration region from 8.8  ×  10¹⁵ cm^-3 to 4.3  ×  10¹⁸ cm^-3 in single crystals of mercury selenide. The revealed features indicate that Weyl semimetal phase may exist in HgSe at low electron density. The most significant result is the discovery of an abrupt change of Berry phase [Formula: see text] at electron concentration [Formula: see text] 2  ×  10¹⁸ cm^-3, which we explain in terms of a manifestation of topological Lifshitz transition in HgSe that occurs by tuning Fermi energy via doping.

Electrically tunable valley polarization in Weyl semimetals with tilted energy dispersion

Tunneling transport across electrical potential barriers in Weyl semimetals with tilted energy dispersion is investigated. We report that the electrons around different valleys experience opposite direction refractions at the barrier interface when the energy dispersion is tilted along one of the transverse directions. Chirality dependent refractions at the barrier interface polarize the Weyl fermions in angle-space according to their valley index. A real magnetic barrier configuration is used to select allowed transmission angles, which results in electrically controllable and switchable valley polarization. Our findings may pave the way for experimental investigation of valley polarization, as well as valleytronic and electron optic applications in Weyl semimetals.

Inter-node superconductivity in strained Weyl semimetals

The effects of a strain-induced pseudomagnetic field on inter-node spin-triplet superconducting states in Weyl semimetals are studied by using the quasiclassical Eilenberger formalism. It is found that the Cooper pairing with spins parallel to the pseudomagnetic field has the lowest energy among the spin-triplet states and its gap does not depend on the strength of the field. In such a state, both electric and chiral superconducting currents are absent. This is in contrast to the superconducting states with the spins of Cooper pairs normal to the field, which support a nonzero chiral current and are inhibited by the strain-induced pseudomagnetic field. The corresponding critical value of the field, which separates the normal and superconducting phases, is estimated.

Chirality Josephson Current Due to a Novel Quantum Anomaly in Inversion-Asymmetric Weyl Semimetals

We study Josephson junctions based on inversion-asymmetric but time-reversal symmetric Weyl semimetals under the influence of Zeeman fields. We find that, due to distinct spin textures, the Weyl nodes of opposite chirality respond differently to an external magnetic field. Remarkably, a Zeeman field perpendicular to the junction direction results in a phase shift of opposite sign in the current-phase relations of opposite chirality. This leads to a finite chirality Josephson current (CJC) even in the absence of a phase difference across the junction. This feature could allow for applications in chiralitytronics. In the long junction and zero temperature limit, the CJC embodies a novel quantum anomaly of Goldstone bosons at π phase difference which is associated with a Z_{2} symmetry at low energies. It can be detected experimentally via an anomalous Fraunhofer pattern.

In Situ Strain Tuning of the Dirac Surface States in Bi2Se3 Films

Elastic strain has the potential for a controlled manipulation of the band gap and spin-polarized Dirac states of topological materials, which can lead to pseudomagnetic field effects, helical flat bands, and topological phase transitions. However, practical realization of these exotic phenomena is challenging and yet to be achieved. Here we show that the Dirac surface states of the topological insulator Bi₂Se₃ can be reversibly tuned by an externally applied elastic strain. Performing in situ X-ray diffraction and in situ angle-resolved photoemission spectroscopy measurements during tensile testing of epitaxial Bi₂Se₃ films bonded onto a flexible substrate, we demonstrate elastic strains of up to 2.1% and quantify the resulting changes in the topological surface state. Our study establishes the functional relationship between the lattice and electronic structures of Bi₂Se₃ and, more generally, demonstrates a new route toward momentum-resolved mapping of strain-induced band structure changes.

Conversion Rules for Weyl Points and Nodal Lines in Topological Media

According to a widely held paradigm, a pair of Weyl points with opposite chirality mutually annihilate when brought together. In contrast, we show that such a process is strictly forbidden for Weyl points related by a mirror symmetry, provided that an effective two-band description exists in terms of orbitals with opposite mirror eigenvalue. Instead, such a pair of Weyl points convert into a nodal loop inside a symmetric plane upon the collision. Similar constraints are identified for systems with multiple mirrors, facilitating previously unreported nodal-line and nodal-chain semimetals that exhibit both Fermi-arc and drumhead surface states. We further find that Weyl points in systems symmetric under a π rotation composed with time reversal are characterized by an additional integer charge that we call helicity. A pair of Weyl points with opposite chirality can annihilate only if their helicities also cancel out. We base our predictions on topological crystalline invariants derived from relative homotopy theory, and we test our predictions on simple tight-binding models. The outlined homotopy description can be directly generalized to systems with multiple bands and other choices of symmetry.

Strain-induced topological magnon phase transitions: applications to kagome-lattice ferromagnets

A common feature of topological insulators is that they are characterized by topologically invariant quantity such as the Chern number and the [Formula: see text] index. This quantity distinguishes a nontrivial topological system from a trivial one. A topological phase transition may occur when there are two topologically distinct phases, and it is usually defined by a gap closing point where the topologically invariant quantity is ill-defined. In this paper, we show that the magnon bands in the strained (distorted) kagome-lattice ferromagnets realize an example of a topological magnon phase transition in the realistic parameter regime of the system. When spin-orbit coupling (SOC) is neglected (i.e. no Dzyaloshinskii-Moriya interaction), we show that all three magnon branches are dispersive with no flat band, and there exists a critical point where tilted Dirac and semi-Dirac point coexist in the magnon spectra. The critical point separates two gapless magnon phases as opposed to the usual phase transition. Upon the inclusion of SOC, we realize a topological magnon phase transition point at the critical strain [Formula: see text], where D and J denote the perturbative SOC and the Heisenberg spin exchange interaction respectively. It separates two distinct topological magnon phases with different Chern numbers for [Formula: see text] and for [Formula: see text]. The associated anomalous thermal Hall conductivity develops an abrupt change at [Formula: see text], due to the divergence of the Berry curvature in momentum space. The proposed topological magnon phase transition is experimentally feasible by applying external perturbations such as uniaxial strain or pressure.

Zitterbewegung in time-reversal Weyl semimetals

We perform a systematic study of the Zitterbewegung effect of fermions, which are described by a Gaussian wave with broken spatial-inversion symmetry in a three-dimensional low-energy Weyl semimetal. Our results show that the motion of fermions near the Weyl points is characterized by rectilinear motion and Zitterbewegung oscillation. The ZB oscillation is affected by the width of the Gaussian wave packet, the position of the Weyl node, and the chirality and anisotropy of the fermions. By introducing a one-dimensional cosine potential, the new generated massless fermions have lower Fermi velocities, which results in a robust relativistic oscillation. Modulating the height and periodicity of periodic potential demonstrates that the ZB effect of fermions in the different Brillouin zones exhibits quasi-periodic behavior. These results may provide an appropriate system for probing the Zitterbewegung effect experimentally.

Fermi arcs connect topological degeneracies

Surface or bulk Fermi arcs are engineered in photonic structures to connect ideal Weyl points or exceptional points

Universality and Stability of the Edge States of Chiral-Symmetric Topological Semimetals and Surface States of the Luttinger Semimetal

We theoretically demonstrate that the chiral structure of the nodes of nodal semimetals is responsible for the existence and universal local properties of the edge states in the vicinity of the nodes. We perform a general analysis of the edge states for an isolated node of a 2D semimetal, protected by chiral symmetry and characterized by the topological winding number N. We derive the asymptotic chiral-symmetric boundary conditions and find that there are N+1 universal classes of them. The class determines the numbers of flatband edge states on either side off the node in the 1D spectrum and the winding number N gives the total number of edge states. We then show that the edge states of chiral nodal semimetals are robust: they persist in a finite-size stability region of parameters of chiral-asymmetric terms. This significantly extends the notion of 2D and 3D topological nodal semimetals. We demonstrate that the Luttinger model with a quadratic node for j=3/2 electrons is a 3D topological semimetal in this new sense and predict that α-Sn, HgTe, possibly Pr_{2}Ir_{2}O_{7}, and many other semimetals described by it are topological and exhibit surface states.

Topological states of condensed matter

Topological states of quantum matter have been investigated intensively in recent years in materials science and condensed matter physics. The field developed explosively largely because of the precise theoretical predictions, well-controlled materials processing, and novel characterization techniques. In this Perspective, we review recent progress in topological insulators, the quantum anomalous Hall effect, chiral topological superconductors, helical topological superconductors and Weyl semimetals.

Topological semimetal in honeycomb lattice LnSI

Recognized as elementary particles in the standard model, Weyl fermions in condensed matter have received growing attention. However, most of the previously reported Weyl semimetals exhibit rather complicated electronic structures that, in turn, may have raised questions regarding the underlying physics. Here, we report promising topological phases that can be realized in specific honeycomb lattices, including ideal Weyl semimetal structures, 3D strong topological insulators, and nodal-line semimetal configurations. In particular, we highlight a semimetal featuring both Weyl nodes and nodal lines. Guided by this model, we showed that GdSI, the long-perceived ideal Weyl semimetal, has two pairs of Weyl nodes residing at the Fermi level and that LuSI (YSI) is a 3D strong topological insulator with the right-handed helical surface states. Our work provides a mechanism to study topological semimetals and proposes a platform for exploring the physics of Weyl semimetals as well as related device designs.

Prediction of Triple Point Fermions in Simple Half-Heusler Topological Insulators

We predict the existence of triple point fermions in the band structure of several half-Heusler topological insulators by ab initio calculations and the Kane model. We find that many half-Heusler compounds exhibit multiple triple points along four independent C_{3} axes, through which the doubly degenerate conduction bands and the nondegenerate valence band cross each other linearly nearby the Fermi energy. When projected from the bulk to the (111) surface, most of these triple points are located far away from the surface Γ[over ¯] point, as distinct from previously reported triple point fermion candidates. These isolated triple points give rise to Fermi arcs on the surface, that can be readily detected by photoemission spectroscopy or scanning tunneling spectroscopy.

3D Quantum Hall Effect of Fermi Arcs in Topological Semimetals

The quantum Hall effect is usually observed in 2D systems. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. Via a "wormhole" tunneling assisted by the Weyl nodes, the Fermi arcs at opposite surfaces can form a complete Fermi loop and support the quantum Hall effect. The edge states of the Fermi arcs show a unique 3D distribution, giving an example of (d-2)-dimensional boundary states. This is distinctly different from the surface-state quantum Hall effect from a single surface of topological insulator. As the Fermi energy sweeps through the Weyl nodes, the sheet Hall conductivity evolves from the 1/B dependence to quantized plateaus at the Weyl nodes. This behavior can be realized by tuning gate voltages in a slab of topological semimetal, such as the TaAs family, Cd_{3}As_{2}, or Na_{3}Bi. This work will be instructive not only for searching transport signatures of the Fermi arcs but also for exploring novel electron gases in other topological phases of matter.

Generic Coexistence of Fermi Arcs and Dirac Cones on the Surface of Time-Reversal Invariant Weyl Semimetals

The hallmark of Weyl semimetals is the existence of open constant-energy contours on their surface-the so-called Fermi arcs-connecting Weyl points. Here, we show that, for time-reversal symmetric realizations of Weyl semimetals, these Fermi arcs, in many cases, coexist with closed Fermi pockets originating from surface Dirac cones pinned to time-reversal invariant momenta. The existence of Fermi pockets is required for certain Fermi-arc connectivities due to additional restrictions imposed by the six Z_{2} topological invariants characterizing a generic time-reversal invariant Weyl semimetal. We show that a change of the Fermi-arc connectivity generally leads to a different topology of the surface Fermi surface and identify the half-Heusler compound LaPtBi under in-plane compressive strain as a material that realizes this surface Lifshitz transition. We also discuss universal features of this coexistence in quasiparticle interference spectra.