Topological RPdBi half-Heusler semimetals: A new family of noncentrosymmetric magnetic superconductors

Large Spin Hall Efficiency and Current-Induced Magnetization Switching in Ferromagnetic Heusler Alloy Co2MnAl-Based Magnetic Trilayers

The spin Hall efficiency (ξ) is a crucial parameter that evaluates the charge-to-spin conversion capability of a material, and thus materials with higher ξ are highly desirable in spin-orbit torque (SOT) devices. Recent studies have highlighted the use of ferromagnetic materials as robust spin sources, paving the way for the development of more efficient SOT devices. To accelerate this innovation, it is essential to pursue ferromagnetic materials of high ξ. Here the experimental observation of a large spin Hall efficiency is reported in ferromagnetic Heusler alloy Co2MnAl (CMA)-based magnetic trilayers. Utilizing the current-induced hysteresis loop shift technique, the spin Hall efficiency is determined to be 0.077 for the B2-phase and 0.029 for the disordered CMA. Notably, magnetization switching both with and without the application of an external auxiliary magnetic field were achieved in these trilayers. The enhancement of ξ is attributed to the formation of chemical ordering in CMA. These findings provide new avenues for the development of ferromagnet-based SOT devices.

Helical Topological Superconducting Pairing at Finite Excitation Energies

We propose helical topological superconductivity away from the Fermi surface in three-dimensional time-reversal-symmetric odd-parity multiband superconductors. In these systems, pairing between electrons originating from different bands is responsible for the corresponding topological phase transition. Consequently, a pair of helical topological Dirac surface states emerges at finite excitation energies. These helical Dirac surface states are tunable in energy by chemical potential and strength of band splitting. They are protected by time-reversal symmetry combined with crystalline twofold rotation symmetry. We suggest concrete materials in which this phenomenon could be observed.

Colossal negative magnetoresistance in field-induced Weyl semimetal of magnetic half-Heusler compound

The discovery of topological insulators and semimetals triggered enormous interest in exploring emergent electromagnetic responses in solids. Particular attention has been focused on ternary half-Heusler compounds, whose electronic structure bears analogy to the topological zinc-blende compounds while also including magnetic rare-earth ions coupled to conduction electrons. However, most of the research in this system has been in band-inverted zero-gap semiconductors such as GdPtBi, which still does not fully exhaust the large potential of this material class. Here, we report a less-studied member of half-Heusler compounds, HoAuSn, which we show is a trivial semimetal or narrow-gap semiconductor at zero magnetic field but undergoes a field-induced transition to a Weyl semimetal, with a negative magnetoresistance exceeding four orders of magnitude at low temperatures. The combined study of Shubnikov-de Haas oscillations and first-principles calculation suggests that the exchange field from Ho 4f moments reconstructs the band structure to induce Weyl points which play a key role in the strong suppression of large-angle carrier scattering. Our findings demonstrate the unique mechanism of colossal negative magnetoresistance and provide pathways towards realizing topological electronic states in a large class of magnetic half-Heusler compounds.

Topological Superconductors from a Materials Perspective

Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (nonuniversal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this Perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSCs, focusing on how a system is identified as a TSC candidate and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.

Antiferromagnetic Spin Fluctuations and Unconventional Superconductivity in Topological Superconductor Candidate YPtBi Revealed by ^{195}Pt-NMR

We report ^{195}Pt nuclear magnetic resonance (NMR) measurements on topological superconductor candidate YPtBi, which has broken inversion symmetry and topological nontrivial band structures due to the strong spin-orbit coupling. In the normal state, we find that Knight shift K is field- and temperature independent, suggesting that the contribution from the topological bands is very small at low temperatures. However, the spin-lattice relaxation rate 1/T_{1} divided by temperature (T), 1/T_{1}T, increases with decreasing T, implying the existence of antiferromagnetic spin fluctuations. In the superconducting state, no Hebel-Slichter coherence peak is seen below T_{c} and 1/T_{1} follows T^{3} variation, indicating the unconventional superconductivity. The finite spin susceptibility at zero-temperature limit and the anomalous increase of the NMR linewidth below T_{c} point to a mixed state of spin-singlet and spin-triplet (or spin-septet) pairing.

Topological superconducting vortex from trivial electronic bands

Superconducting vortices are promising traps to confine non-Abelian Majorana quasi-particles. It has been widely believed that bulk-state topology, of either normal-state or superconducting ground-state wavefunctions, is crucial for enabling Majorana zero modes in solid-state systems. This common belief has shaped two major search directions for Majorana modes, in either intrinsic topological superconductors or trivially superconducting topological materials. Here we show that Majorana-carrying superconducting vortex is not exclusive to bulk-state topology, but can arise from topologically trivial quantum materials as well. We predict that the trivial bands in superconducting HgTe-class materials are responsible for inducing anomalous vortex topological physics that goes beyond any existing theoretical paradigms. A feasible scheme of strain-controlled Majorana engineering and experimental signatures for vortex Majorana modes are also discussed. Our work provides new guidelines for vortex-based Majorana search in general superconductors.

Common Topological Features in Band Structure of RNiSb and RSb Compounds for R = Tb, Dy, Ho

The electronic and band structures of ternary RNiSb and binary RSb compounds for R = Tb, Dy, Ho, have been investigated using an ab initio method accounting for strong electron correlations in the 4f shell of the rare-earth metals. These ternary compounds are found to be semiconductors with the indirect gap of 0.21, 0.21, and 0.26 eV for Tb, Dy, and Ho(NiSb), respectively. In contrast, in all binary RSb compounds, bands near the Fermi energy at the Г and X points are shifted relatively to RNiSb and form hole and electron pockets, so the energy gap is closed in RSb. The band structure typical for semimetals is formed in all RSb compounds for R = Tb, Dy, Ho. For the first time, we identify similar features near the Fermi level in the considered binary semimetals, namely, the presence of the hole and electron pockets in the vicinity of the Г and X points, the nonsymmetric electron pocket along Γ-X-W direction and hole pockets along the L-Γ-X direction, which were previously found experimentally in the other compound of this series GdSb. The magnetic moment of all considered compounds is fully determined by magnetic moments of the rare earth elements, the calculated effective magnetic moments of these ions have values close to the experimental values for all ternary compounds.

Pressure induced topological and topological crystalline insulators

Research on topological and topological crystalline insulators (TCIs) is one of the most intense and exciting topics due to its fascinating fundamental science and potential technological applications. Pressure (strain) is one potential pathway to induce the non-trivial topological phases in some topologically trivial (normal) insulating or semiconducting materials. In the last ten years, there have been substantial theoretical and experimental efforts from condensed-matter scientists to characterize and understand pressure-induced topological quantum phase transitions (TQPTs). In particular, a promising enhancement of the thermoelectric performance through pressure-induced TQPT has been recently realized; thus evidencing the importance of this subject in society. Since the pressure effect can be mimicked by chemical doping or substitution in many cases, these results have opened a new route to develop more efficient materials for harvesting green energy at ambient conditions. Therefore, a detailed understanding of the mechanism of pressure-induced TQPTs in various classes of materials with spin-orbit interaction is crucial to improve their properties for technological implementations. Hence, this review focuses on the emerging area of pressure-induced TQPTs to provide a comprehensive understanding of this subject from both theoretical and experimental points of view. In particular, it covers the Raman signatures of detecting the topological transitions (under pressure), some of the important pressure-induced topological and TCIs of the various classes of spin-orbit coupling materials, and provide future research directions in this interesting field.

Flux Growth, Crystal Structures, and Electronic Properties of the Ternary Intermetallic Compounds Ca3Pd4Bi8 and Ca3Pt4Bi8

Reaction of the elements yielded Ca₃Pt₄Bi₈ and CaPtBi, which are, to the best of our knowledge, the first reported ternary Ca–Pt–Bi compounds. The compounds crystallize isostructural to the Pd analogs Ca₃Pd₄Bi₈ (own structure type) and CaPdBi (TiNiSi structure type), respectively. Employing a multistep temperature treatment allows for the growth of mm-sized single crystals of Ca₃Pd₄Bi₈ and Ca₃Pt₄Bi₈ from a Bi self-flux. Their crystal structures can be visualized as consisting of a three-dimensional extended polyanion [M₄Bi₈]^6– (M = Pd, Pt), composed of interlinked M–Bi chains propagating along the c direction, and Ca²⁺ cations residing in one-dimensional channels between the chains. First-principles calculations reveal quasi-one-dimensional electronic behavior with reduced effective electron masses along [001]. Bader analysis points to a strong anionic character of the M species (M = Pd, Pt) in Ca₃M₄Bi₈. Thus, it is more appropriate to address the compounds Ca₃Pd₄Bi₈ and Ca₃Pt₄Bi₈ as a palladide and platinide, respectively. Magnetization measurements indicate diamagnetic behavior with no indications for superconductivity down to 2 K. Electrical resistivity data are consistent with metallic behavior and suggest predominant electron–phonon scattering.

Reaction of the elements yielded Ca₃Pt₄Bi₈ and CaPtBi, which are, to the best of our knowledge, the first reported ternary Ca−Pt−Bi compounds.

Effect of Strain on the Electronic Structure and Phonon Stability of SrBaSn Half Heusler Alloy

This paper presents the strain effects on the structural, electronic and phonon properties of a newly proposed SrBaSn half Heusler compound. Since it is stable considering chemical thermodynamics, we tested its strength against uniform strain w.r.t phonon spectrum and it produces a direct bandgap of 0.7 eV. The direct bandgap reduces to 0.19 eV at -12% strain beyond which the structure is unstable. However, an indirect gap of 0.63 eV to 0.39 eV is observed in the range of +5% to +8% strain and afterwards the strain application destabilizes the structure. From elastic parameters, the ductile nature of this material is observed.

Review on crystal structures and magnetic properties ofRTX3materials

The structural and compositional diversity of theRTX₃family of materials offers various magnetic and thermodynamic properties such as complex magnetic structure, vibronic bound states, heavy-fermions, valence fluctuations, metamagnetism, spin glass behavior, quantum criticality, and unconventional superconductivity. Here we present an overview of the crystal structures, crystal growth and magnetic properties ofRTX₃compounds as well as a discussion of the relevant physics. The magnetic properties of several compounds of theRTX₃family still remain unexplored. The compounds with a complex magnetic structure could potentially host exotic topological phases. This review article may help explore exotic magnetic properties such as the vibron state and topological spin textures.

An ideal Weyl nodal ring with a large drumhead surface state in the orthorhombic compound TiS2

Topological metals or semimetals have attracted great research attention and interest in condensed matter physics and chemistry due to their exotic properties. Different from the conventional topological insulators, topological metals or semimetals are characterized by distinct topological surface states, such as a Fermi arc or a drumhead surface state, which are often used in experiments to verify the corresponding topological properties. However, the current study in this field is strongly limited in the experimental characterization because of the extreme lack of perfect material candidates with a clean band structure and clear surface states. In this work, based on theoretical calculations, we propose a new topological semimetal TiS₂, which has an orthorhombic structure and exhibits excellent stability. Calculated electronic band structures reveal that there is a single Weyl nodal ring in the k_y = 0 plane. A detailed symmetry analysis is provided and the corresponding surface state is calculated, which exhibits both a large energy variation of 1.5 eV and wide space distribution without and with the spin orbit coupling effect. Besides, the surface states are well separated from the bulk state. These ideal features together make TiS₂ a promising nodal line semimetal for experimental investigation. In combination with the other two isostructural compounds TiSe₂ and TiTe₂ with similar properties, their further experimental synthesis and characterization can be highly expected and the corresponding study for the topological nodal line state can thus be greatly facilitated.

Efficient spin current source using a half-Heusler alloy topological semimetal with back end of line compatibility

Topological materials, such as topological insulators (TIs), have great potential for ultralow power spintronic devices, thanks to their giant spin Hall effect. However, the giant spin Hall angle (θ_SH > 1) is limited to a few chalcogenide TIs with toxic elements and low melting points, making them challenging for device integration during the silicon Back-End-of-Line (BEOL) process. Here, we show that by using a half-Heusler alloy topological semi-metal (HHA-TSM), YPtBi, it is possible to achieve both a giant θ_SH up to 4.1 and a high thermal budget up to 600 °C. We demonstrate magnetization switching of a CoPt thin film using the giant spin Hall effect of YPtBi by current densities lower than those of heavy metals by one order of magnitude. Since HHA-TSM includes a group of three-element topological materials with great flexibility, our work opens the door to the third-generation spin Hall materials with both high θ_SH and high compatibility with the BEOL process that would be easily adopted by the industry.

Using Disorder to Identify Bogoliubov Fermi-Surface States

We argue that a superconducting state with a Fermi surface of Bogoliubov quasiparticles, a Bogoliubov Fermi surface (BG-FS), can be identified by the dependence of physical quantities on disorder. In particular, we show that a linear dependence of the residual density of states at weak disorder distinguishes a BG-FS state from other nodal superconducting states. We further demonstrate the stability of supercurrent against impurities and a characteristic Drude-like behavior of the optical conductivity. Our results can be directly applied to electron irradiation experiments on candidate materials of BG-FSs, including Sr_{2}RuO_{4}, FeSe_{1-x}S_{x}, and UBe_{13}.

Ferromagnetic Cr4PtGa17: A Half-Heusler-Type Compound with a Breathing Pyrochlore Lattice

We describe the crystal structure and elementary magnetic properties of a previously unreported ternary intermetallic compound, Cr₄PtGa₁₇, which crystallizes in a rhombohedral unit cell in the noncentrosymmetric space group R3m. The crystal structure is closely related to those of XYZ half-Heusler compounds, where X, Y, and Z are reported to be single elements only, occupying three different face-centered-cubic sublattices. The new material, Cr₄PtGa₁₇, can be most straightforwardly illustrated by writing the formula as (PtGa₂)(Cr₄Ga₁₄)Ga (X = PtGa₂, Y = Cr₄Ga₁₄, Z = Ga); that is, the X and Y sites are occupied by clusters instead of single elements. The magnetic Cr occupies a breathing pyrochlore lattice. Ferromagnetic ordering is found below T_C ∼ 61 K, by both neutron diffraction and magnetometer studies, with a small, saturated moment of ∼0.25 μ_B/Cr observed at 2 K, making Cr₄PtGa₁₇ the first ferromagnetically ordered material with a breathing pyrochlore lattice. A magnetoresistance of ∼140% was observed at 2 K. DFT calculations suggest that the material has a nearly half-metallic electronic structure. The new material, Cr₄PtGa₁₇, the first realization of both a half-Heusler-type structure and a breathing pyrochlore lattice, might pave a new way to achieve novel types of half-Heusler compounds.

Anomalous magnetoresistance and magneto-thermal properties of the half-Heuslers,RPdSi (RY, Gd-Er)

Here, we present a detailed study on the magnetic, magneto-transport, and magneto-thermal properties of the equiatomic half-Heusler compounds with the general formula,RPdSi (R= Y and rare-earth, Gd-Er). These materials crystallize in two different superstructures of the TiNiSi-type orthorhombic unit cell with the space groupsPnmaandPmmn. Our magnetic and heat capacity measurements reveal the onset of an antiferromagnetic (AFM) ordering in the temperature range 3-16 K for all the local moments bearingRPdSi compounds, while the non-magnetic analog, YPdSi exhibits a Pauli-paramagnetic behaviour. The AFM state of these compounds can be tuned by magnetic field and temperature as demonstrated by the magnetic measurements below the Neel temperature (T_N). Most importantly, this tuning of the magnetic structure is well documented in the complex temperature and field dependence of magnetoresistance (MR) and magnetocaloric effect (MCE). Our study establishes a striking correlation of the commensurate/incommensurate AFM structure with that of positive/negative MR and MCE in this series of compounds. We emphasize that such a framework applies to a large number of AFM intermetallic systems.

Strain-tunable triple point Fermions in diamagnetic rare-earth half-Heusler alloys

Topologically non-trivial electronic structure is a feature of many rare-earth half-Heusler alloys, which host atoms with high spin-orbit coupling bringing in the non-triviality. In this article, using the first-principles simulations, rare-earth half-Heusler YPdBi, ScPdBi, LaPdBi, LuPdBi, YPtBi and LuPtBi alloys are studied under strain to reveal multiple band inversions associated with topological phase transitions. From our simulations we find that, as a result of first band-inversion, the Brillouin zone of the diamagnetic half-Heusler alloys hosts eight triple points whereas, the second band inversion causes the emergence of sixteen more triple points. These band-inversions are observed to be independent of the spin-orbit coupling and are the reason behind increasing occupation of bismuth 7s orbitals as volume of the unit cell increases. The surface electronic transport in different triple point semi-metallic phases is found to evolve under strain, as the number of Fermi arcs change due to multiple band inversions. Once the second band inversion occurs, further application of tensile strain does not increase the number of triple points and Fermi arcs. However, increasing tensile strain (or decreasing compressive strain) pushes the triple point crossing to higher momenta, making them more effective as source of highly mobile electrons. These observations make a pathway to tune the bulk as well as surface transport through these semi-metals by application of tensile or compressive strain depending on the unstrained relative band-inversion strength of the material.

Unusual upper critical fields of the topological nodal-line semimetal candidate SnxNbSe2-δ

We report superconductivity in Sn_xNbSe_2-δ, a topological nodal-line semimetal candidate with a noncentrosymmetric crystal structure. The superconducting transition temperatureT_cof this compound is extremely sensitive to Sn concentrationxand Se deficiencyδ, 5.0 K for Sn_0.13NbSe_1.70and 8.6 K for Sn_0.14NbSe_1.71and Sn_0.15NbSe_1.69. In all samples, the temperature dependence of the upper critical fieldH_c2(T) differs from the prediction of the Werthamer-Helfand-Hohenberg theory. While the zero-temperature value of the in-plane upper critical field of Sn_xNbSe_2-δwith the higherT_cis lower than the BCS Pauli paramagnetic limitH_P, that of the lowerT_csample exceedsH_Pby a factor of ∼2. Our observations suggest that a possible odd-parity contribution dominates the superconducting gap function of Sn_xNbSe_2-δ, and it can be fine-tuned by the Sn concentration and Se deficiency.

Fermi surfaces of the topological semimetal CaSn3probed through de Haas van Alphen oscillations

In the search of topological superconductors, nailing down the Fermiology of the normal state is as crucial a prerequisite as unraveling the superconducting pairing symmetry. In particular, the number of time-reversal-invariant momenta (TRIM) in the Brillouin zone enclosed by Fermi surfaces is closely linked to the topological class of time-reversal-invariant systems, and can experimentally be investigated. We report here a detailed study of de Haas van Alphen quantum oscillations in single crystals of the topological semimetal CaSn₃with torque magnetometry in high magnetic fields up to 35 T. In conjunction with density functional theory based calculations, the observed quantum oscillations frequencies indicate that the Fermi surfaces of CaSn₃enclose an odd number of TRIM, satisfying one of the proposed criteria to realize topological superconductivity. Nonzero Berry phases extracted from the magnetic oscillations also support the nontrivial topological nature of CaSn₃.

Strain driven emergence of topological non-triviality in YPdBi thin films

Half-Heusler compounds exhibit a remarkable variety of emergent properties such as heavy-fermion behaviour, unconventional superconductivity and magnetism. Several of these compounds have been predicted to host topologically non-trivial electronic structures. Remarkably, recent theoretical studies have indicated the possibility to induce non-trivial topological surface states in an otherwise trivial half-Heusler system by strain engineering. Here, using magneto-transport measurements and first principles DFT-based simulations, we demonstrate topological surface states on strained [110] oriented thin films of YPdBi grown on (100) MgO. These topological surface states arise in an otherwise trivial semi-metal purely driven by strain. Furthermore, we observe the onset of superconductivity in these strained films highlighting the possibility of engineering a topological superconducting state. Our results demonstrate the critical role played by strain in engineering novel topological states in thin film systems for developing next-generation spintronic devices.

Anisotropic gapping of topological Weyl rings in the charge-density-wave superconductor InxTaSe2

Topological materials and topological phases have recently become a hot topic in condensed matter physics. In this work, we report an In-intercalated transition-metal dichalcogenide In_xTaSe₂ (named 112 system), a topological nodal-line semimetal in the presence of both charge density wave (CDW) and superconductivity. In the x = 0.58 sample, the 2×3 commensurate CDW (CCDW) and the 2×2 CCDW are observed below 116 and 77 K, respectively. Consistent with theoretical calculations, the spin-orbital coupling gives rise to two twofold-degenerate nodal rings (Weyl rings) connected by drumhead surface states, confirmed by angle-resolved photoemission spectroscopy. Our results suggest that the 2×2 CCDW ordering gaps out one Weyl ring in accordance with the CDW band folding, while the other Weyl ring remains gapless with intact surface states. In addition, superconductivity emerges at 0.91 K, with the upper critical field deviating from the s-wave behavior at low temperature, implying possibly unconventional superconductivity. Therefore, we think this type of the 112 system may possess abundant physical states and offer a platform to investigate the interplay between CDW, nontrivial band topology and superconductivity.

Thickness-dependent magneto-transport properties of topologically nontrivial DyPdBi thin films

DyPdBi (DPB) is a topological semimetal which belongs to the rare-earth-based half-Heusler alloy family. In this work, we studied the thickness-dependent structural and magneto-transport properties of DPB thin films (20 to 60 nm) grown using pulsed laser deposition. The DPB thin films show (110) oriented growth on MgO(100) single crystal substrates. Longitudinal resistance data indicate metallic surface states dominated carrier transport and the suppression of semiconducting bulk state carriers for films ≤40 nm. We observe the weak antilocalization (WAL) effect and Shubnikov-de Hass (SdH) oscillations in the magneto-transport data. The presence of a single coherent transport channel (α∼ -0.50) is observed in the Hikami-Larkin-Nagaoka (HLN) fitting of WAL data. The power law temperature dependence of phase coherence length (L_Ø ) ∼ T^-0.50 indicates the observation of the 2D WAL effect and the presence of topological nontrivial surface states for films ≤40 nm. The 60 nm sample shows semiconducting resistivity behavior at higher temperature (>180 K) and HLN fitting results (α∼ -0.72, L_Ø ∼ T^-0.68 ) indicate the presence of partial decoupled top and bottom surface states. The Berry phase ∼π is extracted for thin films ≤40 nm, which further demonstrates the presence of Dirac fermions and nontrivial surface states. Band structure parameters are extracted by fitting SdH data to the standard Lifshitz-Kosevich formula. The sheet carrier concentration and cyclotron effective mass of carriers decrease with increasing thickness (20 nm to 60 nm) from ∼1.35 × 10¹² cm^-2 to 0.68 × 10¹² cm^-2 and from ∼0.26 m_e to 0.12 m_e, respectively. Our observations suggest that samples with a thickness ≤40 nm have transport properties dominated by surface states and samples with a thickness ≥60 nm have contributions from both bulk and surface states.

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.

DFT Investigation on the Electronic, Magnetic, Mechanical Properties and Strain Effects of the Quaternary Compound Cu2FeSnS4

The electronic, magnetic and mechanical properties of the quaternary compound Cu2FeSnS4 have been investigated with first principle calculations. Its half-metallicity has been identified with spin polarized band structures and its magnetic origination is caused by the strong spin splitting effect in the d orbitals of Fe atoms. The total magnetic moment of 4 μB is mainly contributed by the Fe atoms and the spatial distribution of the magnetic spin density and charge density difference have also been examined. Moreover, several mechanical properties of Cu2FeSnS4 have been derived and its mechanical stability is also verified. The directional dependent Young’s modulus exhibits relatively small anisotropy yet the shear modulus shows strong directional anisotropy. At last, the tetragonal strain effects have been evaluated and their impact on the electronic and magnetic properties are provided. Results show the total magnetic moment stays almost unchanged while the half-metallicity can only be maintained under relatively small variations for both strains. This study can provide comprehensive information about the various properties of Cu2FeSnS4 compound and serve as a helpful reference for its future applications.

Magneto-conductivity of Weyl semimetals: the roles of inter-valley scattering and high-order Feynman diagrams

Within the theoretical framework of Kubo formula and self-consistent Born approximation, we theoretically study the transversal and longitudinal magneto-conductivity of a type-I Weyl semimetal. We focus mainly on the peculiar role of inter-valley scattering on linear transversal magnetoresistance (LTMR) and negative longitudinal magnetoresistance (NLMR). At first, we find that the contributions of high-order Feynman diagrams to the transversal magneto-conductivity play the distinct roles between the cases of intra- and inter-valley scatterings. The former suppresses the transversal conductivity whereas the latter enhances it. Then, with the increase of scattering strength, the LTMR is destroyed, accompanying a sizable increase of transversal conductivity, in particular, in the case of the tilted cone. For longitudinal magneto-transport, inter-valley scattering contributes only trivial magnetoresistance. In contrast, intra-valley scattering is invalid for longitudinal magneto-transport which means a very large NLMR. In addition, the high-order Feynman diagrams always play the nontrivial role on the longitudinal conductivity even in the weak scattering limit. Finally, when altering the Fermi energy among low-lying Landau level, the peaks of transversal conductivity just correspond to the valleys of the longitudinal conductivity.

Electronic structure of the PrNiBi half-Heusler system based on the σGGA + U method

In this works, we study the electronic structure and magnetic properties of the Pr-Ni-Bi half-Heusler systems based on density functional theory. We use the σ GGA + U scheme to consider the effects of on-site electron-electron interactions. Results show that in contrast to the rough estimation of the total magnetic moment of the unit cell, based on the Slater-Pauling behavior in the half-Heusler systems, this system has an antiferromagnetic ground state because of the localized Pr-f electrons. By increasing the magnitude of the effective U parameter, band-inversion occurs in the band structure of this system, which shows the possibility of topological state occurrence.

Crystalline electric field study in a putative topologically trivial rare-earth doped YPdBi compound

Topological states of matter have attracted a lot of attention recently due to their intriguing physical properties and potential applications. In particular, the family of half-Heusler compounds [Formula: see text] (R  =  rare earth, M  =  Pt, Pd or Au, and T  =  Bi, Sb, Pb or Sn) has been predicted to display tunable topological properties via their cubic unit cell volume and/or the charges of the M and T atoms. In this work, we report electron spin resonance (ESR), along with complementary macroscopic experiments, in the putative topologically trivial rare-earth doped (Gd, Nd and Er) YPdBi. From magnetic susceptibility data analysis constrained by ESR results, we were able to extract the fourth (A ₄) and sixth (A ₆) order crystal field parameters (CFP) for YPdBi and compared them with those already reported to YPtBi, which is known as a topologically non-trivial compound. We observed that the sign of the CFP changes systematically from YPdBi to YPtBi, possibly due to the inversion of the valence and conduction bands at the Fermi level. The enhanced spin-orbit coupling in YPtBi, when compared to YPdBi, induces the band inversion that drives the system to a non-trivial topological state. This band inversion likely has an effect on the effective charges surrounding the magnetic dopants that are probed by the CFP.

Theoretical Study of the Electronic and Magnetic Properties and Phase Stability of the Full Heusler Compound Pd2CoAl

Based on first principles calculation, a systematical investigation has been performed to study the electronic, magnetic, dynamic, and mechanical properties of the full Heusler compound Pd2CoAl. It is found that the L21-type structure is energetically more stable than the XA-type due to the lower total energy. The obtained lattice constant in cubic ground state is 6.057 Å, which matches well with previous study. The calculated electronic band structure reveals the metallic nature of Pd2CoAl and its total magnetic moment of 1.78 μB is mainly contributed by Co atom from strong spin splitting effect, as indicated with the distinctive distributions of the density of states in two spin directions. Under uniform strains from −5% to +5%, the variation of total magnetic moment has been obtained and it is still caused by the much larger change from Co atom, compared with Pd and Al atoms. The tetragonal structure has further been analyzed and we found that there is possible martensitic phase transformation because the total energy can be further reduced when the cubic structure is varied into the tetragonal one. The large energy difference of 0.165 eV between the tetragonal and cubic phases is found at the c/a ratio of 1.30. The total density of states has been compared between the cubic and tetragonal phases for Pd2CoAl and results show tetragonal phase transformation could reduce the states at the Fermi energy level in both directions. In addition, the dynamic and mechanical stabilities have also been evaluated for Pd2CoAl in both cubic and tetragonal structures and results confirm that the tetragonal phase shows good stability against the cubic phase, which further verifies that the tetragonal phase transformation is highly expected. In the end, the strong elastic anisotropy in the tetragonal structure has been clearly shown with the calculated directional dependence of the Young’s modulus and shear modulus.

Site preference and tetragonal distortion in palladium-rich Heusler alloys

In this work, two kinds of competition between different Heusler structure types are considered, one is the competition between XA and L21 structures based on the cubic system of full-Heusler alloys, Pd2 YZ (Y = Co, Fe, Mn; Z = B, Al, Ga, In, Tl, Si, Ge, Sn, Pb, P, As, Sb). Most alloys prefer the L21 structure; that is, Pd atoms tend to occupy the a (0, 0, 0) and c (0.5, 0.5, 0.5) Wyckoff sites, the Y atom is generally located at site b (0.25, 0.25, 0.25), and the main group element Z has a preference for site d (0.75, 0.75, 0.75), meeting the well known site-preference rule. The difference between these two cubic structures in terms of their magnetic and electronic properties is illustrated further by their phonon dispersion and density-of-states curves. The second type of competition that was subjected to systematic study was the competitive mechanism between the L21 cubic system and its L10 tetragonal system. A series of potential tetragonal distortions in cubic full-Heusler alloys (Pd2 YZ) have been predicted in this work. The valley-and-peak structure at, or in the vicinity of, the Fermi level in both spin channels is mainly attributed to the tetragonal ground states according to the density-of-states analysis. ΔE M is defined as the difference between the most stable energy values of the cubic and tetragonal states; the larger the value, the easier the occurrence of tetragonal distortion, and the corresponding tetragonal structure is stable. Compared with the ΔE M values of classic Mn2-based tetragonal Heusler alloys, the ΔE M values of most Pd2CoZ alloys in this study indicate that they can overcome the energy barriers between cubic and tetragonal states, and possess possible tetragonal transformations. The uniform strain has also been taken into consideration to further investigate the tetragonal distortion of these alloys in detail. This work aims to provide guidance for researchers to further explore and study new magnetic functional tetragonal materials among the full-Heusler alloys.

Magnetic Properties and Carrier Transport of Ir0.9Mn1-xSn1.1+x

The nonstoichiometric Ir_0.9Mn_1−xSn_1.1+x (x = 0.1, 0.05, and −0.05) are crystallized in half-Heusler alloys. The magnetic transition is observed at 77 K for x = 1.05, and it decreases with the decreasing Mn content. It is proven to be a ferromagnetic transition with a nonlinear magnetic moment alignment, as the magnetization is not saturated at 70 kOe. The different magnetic behavior than a typical ferromagnet (FM is due to the Ir ions with strong spin orbital coupling (SOC). The different hysteresis loops reflect that the ionic distribution is not completely homogeneous. The high coercivity observed in the cubic compound is due to the strong single-ion anisotropy of the Ir ions. A metallic-semiconducting transition at 130 K is observed in Ir_0.9Mn_1.05Sn_1.05. A negative magnetoresistance is observed at 2 K and 14 T with the value as −2.6%.

Anomalous Hall effect in Weyl semimetal half-Heusler compounds RPtBi (R = Gd and Nd)

Topological materials ranging from topological insulators to Weyl and Dirac semimetals form one of the most exciting current fields in condensed-matter research. Many half-Heusler compounds, RPtBi (R = rare earth), have been theoretically predicted to be topological semimetals. Among various topological attributes envisaged in RPtBi, topological surface states, chiral anomaly, and planar Hall effect have been observed experimentally. Here, we report an unusual intrinsic anomalous Hall effect (AHE) in the antiferromagnetic Heusler Weyl semimetal compounds GdPtBi and NdPtBi that is observed over a wide temperature range. In particular, GdPtBi exhibits an anomalous Hall conductivity of up to 60 Ω-1⋅cm-1 and an anomalous Hall angle as large as 23%. Muon spin-resonance (μSR) studies of GdPtBi indicate a sharp antiferromagnetic transition (TN) at 9 K without any noticeable magnetic correlations above TN Our studies indicate that Weyl points in these half-Heuslers are induced by a magnetic field via exchange splitting of the electronic bands at or near the Fermi energy, which is the source of the chiral anomaly and the AHE.

Weak Antilocalization and Quantum Oscillations of Surface States in Topologically Nontrivial DyPdBi(110)Half Heusler alloy

Recently, a number of ternary half-Heusler compounds have been predicted independently by several research groups as candidates for 3D topological insulators. In this work, we report the observation of a two-dimensional (2D) weak antilocalization (WAL) effect, one of the hall-marks of topological surface states, and Shubnikov-de Hass (SdH) quantum oscillations in <110> oriented DyPdBi (DPB) thin films grown on MgO (100) substrates. The films prepared by pulsed laser deposition technique under the optimized conditions, showed a textured structure with (110) planes parallel to the (100) plane of MgO. The measured WAL effect follows the Hikami-Larkin-Nagaoka (HLN) model and the extracted values of phase coherence length (l_ϕ) and α are ~420 nm and ~−0.52 respectively. The power law variation of l_ϕ (~T^−0.46) indicates the presence of the 2D surface states in DPB film. The Dirac nature of the surface states is further confirmed by Landau-level fan diagram analysis of SdH oscillations of the magneto-transport data. This analysis shows a finite Berry phase of 0.90π ± 0.16, reasonably close to the expected π value. Sheet Carrier density, n_s ~ 2.56 × 10¹² cm⁻², calculated from the SdH oscillations (f_SdH ~ 106 T) and Hall measurements agree well with each other. These findings demonstrate that the half Heusler DPB thin films (~15–20 nm) can be used as a suitable material for investigating the novel intrinsic quantum transport properties of surface Dirac fermions.

A simple electron counting model for half-Heusler surfaces

Heusler compounds are a ripe platform for discovery and manipulation of emergent properties in topological and magnetic heterostructures. In these applications, the surfaces and interfaces are critical to performance; however, little is known about the atomic-scale structure of Heusler surfaces and interfaces or why they reconstruct. Using a combination of molecular beam epitaxy, core-level and angle-resolved photoemission, scanning tunneling microscopy, and density functional theory, we map the phase diagram and determine the atomic and electronic structures for several surface reconstructions of CoTiSb (001), a prototypical semiconducting half-Heusler. At low Sb coverage, the surface is characterized by Sb-Sb dimers and Ti vacancies, while, at high Sb coverage, an adlayer of Sb forms. The driving forces for reconstruction are charge neutrality and minimizing the number of Sb dangling bonds, which form metallic surface states within the bulk bandgap. We develop a simple electron counting model that explains the atomic and electronic structure, as benchmarked against experiments and first-principles calculations. We then apply the model to explain previous experimental observations at other half-Heusler surfaces, including the topological semimetal PtLuSb and the half-metallic ferromagnet NiMnSb. The model provides a simple framework for understanding and predicting the surface structure and properties of these novel quantum materials.

Beyond triplet: Unconventional superconductivity in a spin-3/2 topological semimetal

In all known fermionic superfluids, Cooper pairs are composed of spin-1/2 quasi-particles that pair to form either spin-singlet or spin-triplet bound states. The "spin" of a Bloch electron, however, is fixed by the symmetries of the crystal and the atomic orbitals from which it is derived and, in some cases, can behave as if it were a spin-3/2 particle. The superconducting state of such a system allows pairing beyond spin-triplet, with higher spin quasi-particles combining to form quintet or septet pairs. We report evidence of unconventional superconductivity emerging from a spin-3/2 quasi-particle electronic structure in the half-Heusler semimetal YPtBi, a low-carrier density noncentrosymmetric cubic material with a high symmetry that preserves the p-like j = 3/2 manifold in the Bi-based Γ₈ band in the presence of strong spin-orbit coupling. With a striking linear temperature dependence of the London penetration depth, the existence of line nodes in the superconducting order parameter Δ is directly explained by a mixed-parity Cooper pairing model with high total angular momentum, consistent with a high-spin fermionic superfluid state. We propose a k ⋅ p model of the j = 3/2 fermions to explain how a dominant J = 3 septet pairing state is the simplest solution that naturally produces nodes in the mixed even-odd parity gap. Together with the underlying topologically nontrivial band structure, the unconventional pairing in this system represents a truly novel form of superfluidity that has strong potential for leading the development of a new series of topological superconductors.

Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State

We investigate unconventional superconductivity in three-dimensional electronic systems with the chemical potential close to a quadratic band touching point in the band dispersion. Short-range interactions can lead to d-wave superconductivity, described by a complex tensor order parameter. We elucidate the general structure of the corresponding Ginzburg-Landau free energy and apply these concepts to the case of an isotropic band touching point. For a vanishing chemical potential, the ground state of the system is given by the superconductor analogue of the uniaxial nematic state, which features line nodes in the excitation spectrum of quasiparticles. In contrast to the theory of real tensor order in liquid crystals, however, the ground state is selected here by the sextic terms in the free energy. At a finite chemical potential, the nematic state has an additional instability at weak coupling and low temperatures. In particular, the one-loop coefficients in the free energy indicate that at weak coupling genuinely complex orders, which break time-reversal symmetry, are energetically favored. We relate our analysis to recent measurements in the half-Heusler compound YPtBi and discuss the role of cubic crystal symmetry.

Superconductivity and spin-orbit coupling in non-centrosymmetric materials: a review

In non-centrosymmetric superconductors, where the crystal structure lacks a centre of inversion, parity is no longer a good quantum number and an electronic antisymmetric spin-orbit coupling (ASOC) is allowed to exist by symmetry. If this ASOC is sufficiently large, it has profound consequences on the superconducting state. For example, it generally leads to a superconducting pairing state which is a mixture of spin-singlet and spin-triplet components. The possibility of such novel pairing states, as well as the potential for observing a variety of unusual behaviors, led to intensive theoretical and experimental investigations. Here we review the experimental and theoretical results for superconducting systems lacking inversion symmetry. Firstly we give a conceptual overview of the key theoretical results. We then review the experimental properties of both strongly and weakly correlated bulk materials, as well as two dimensional systems. Here the focus is on evaluating the effects of ASOC on the superconducting properties and the extent to which there is evidence for singlet-triplet mixing. This is followed by a more detailed overview of theoretical aspects of non-centrosymmetric superconductivity. This includes the effects of the ASOC on the pairing symmetry and the superconducting magnetic response, magneto-electric effects, superconducting finite momentum pairing states, and the potential for non-centrosymmetric superconductors to display topological superconductivity.

The chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi

The Dirac and Weyl semimetals are unusual materials in which the nodes of the bulk states are protected against gap formation by crystalline symmetry. The chiral anomaly, predicted to occur in both systems, was recently observed as a negative longitudinal magnetoresistance (LMR) in Na₃Bi (ref. ) and in TaAs (ref. ). An important issue is whether Weyl physics appears in a broader class of materials. We report evidence for the chiral anomaly in the half-Heusler GdPtBi. In zero field, GdPtBi is a zero-gap semiconductor with quadratic bands. In a magnetic field, the Zeeman energy leads to Weyl nodes. We have observed a large negative LMR with the field-steering properties specific to the chiral anomaly. The chiral anomaly also induces strong suppression of the thermopower. We report a detailed study of the thermoelectric response function α_xx of Weyl fermions. The scheme of creating Weyl nodes from quadratic bands suggests that the chiral anomaly may be observable in a broad class of semimetals.

Observation of unusual topological surface states in half-Heusler compounds LnPtBi (Ln=Lu, Y)

Topological quantum materials represent a new class of matter with both exotic physical phenomena and novel application potentials. Many Heusler compounds, which exhibit rich emergent properties such as unusual magnetism, superconductivity and heavy fermion behaviour, have been predicted to host non-trivial topological electronic structures. The coexistence of topological order and other unusual properties makes Heusler materials ideal platform to search for new topological quantum phases (such as quantum anomalous Hall insulator and topological superconductor). By carrying out angle-resolved photoemission spectroscopy and ab initio calculations on rare-earth half-Heusler compounds LnPtBi (Ln=Lu, Y), we directly observe the unusual topological surface states on these materials, establishing them as first members with non-trivial topological electronic structure in this class of materials. Moreover, as LnPtBi compounds are non-centrosymmetric superconductors, our discovery further highlights them as promising candidates of topological superconductors.

Heusler compounds have been predicted to host topological order with other emergent properties, which yet awaits for experimental evidence. Here, Liu et al. report a direct observation of topological surface states on half-Heusler compounds LnPtBi.

Rotational symmetry breaking in the topological superconductor SrxBi2Se3 probed by upper-critical field experiments

Recently it was demonstrated that Sr intercalation provides a new route to induce superconductivity in the topological insulator Bi2Se3. Topological superconductors are predicted to be unconventional with an odd-parity pairing symmetry. An adequate probe to test for unconventional superconductivity is the upper critical field, Bc2. For a standard BCS layered superconductor Bc2 shows an anisotropy when the magnetic field is applied parallel and perpendicular to the layers, but is isotropic when the field is rotated in the plane of the layers. Here we report measurements of the upper critical field of superconducting SrxBi2Se3 crystals (Tc = 3.0 K). Surprisingly, field-angle dependent magnetotransport measurements reveal a large anisotropy of Bc2 when the magnet field is rotated in the basal plane. The large two-fold anisotropy, while six-fold is anticipated, cannot be explained with the Ginzburg-Landau anisotropic effective mass model or flux flow induced by the Lorentz force. The rotational symmetry breaking of Bc2 indicates unconventional superconductivity with odd-parity spin-triplet Cooper pairs (Δ4-pairing) recently proposed for rhombohedral topological superconductors, or might have a structural nature, such as self-organized stripe ordering of Sr atoms.

Pairing of j=3/2 Fermions in Half-Heusler Superconductors

We theoretically consider the superconductivity of the topological half-Heusler semimetals YPtBi and LuPtBi. We show that pairing occurs between j=3/2 fermion states, which leads to qualitative differences from the conventional theory of pairing between j=1/2 states. In particular, this permits Cooper pairs with quintet or septet total angular momentum, in addition to the usual singlet and triplet states. Purely on-site interactions can generate s-wave quintet time-reversal symmetry-breaking states with topologically nontrivial point or line nodes. These local s-wave quintet pairs reveal themselves as d-wave states in momentum space. Furthermore, due to the broken inversion symmetry in these materials, the s-wave singlet state can mix with a p-wave septet state, again with topologically stable line nodes. Our analysis lays the foundation for understanding the unconventional superconductivity of the half-Heuslers.

Unconventional Superconductivity in YPtBi and Related Topological Semimetals

YPtBi, a topological semimetal with a very low carrier density, was recently found to be superconducting below T_{c}=0.77  K. In conventional theory, the nearly vanishing density of states around the Fermi level would imply a vanishing electron-phonon coupling and would, therefore, not allow for superconductivity. Based on relativistic density-functional theory calculations of the electron-phonon coupling in YPtBi, it is found that carrier concentrations of more than 10^{21}  cm^{-3} are required to explain the observed critical temperature with the conventional pairing mechanism, which is several orders of magnitude larger than experimentally observed. It is very likely that an unconventional pairing mechanism is responsible for the superconductivity in YPtBi and related topological semimetals with half-Heusler structure.

Antiferromagnetism and superconductivity in the half-Heusler semimetal HoPdBi

We observed the coexistence of superconductivity and antiferromagnetic order in the single-crystalline ternary pnictide HoPdBi, a plausible topological semimetal. The compound orders antiferromagnetically at TN = 1.9 K and exhibits superconductivity below Tc = 0.7 K, which was confirmed by magnetic, electrical transport and specific heat measurements. The specific heat shows anomalies corresponding to antiferromagnetic ordering transition and crystalline field effect, but not to superconducting transition. Single-crystal neutron diffraction indicates that the antiferromagnetic structure is characterized by the propagation vector. Temperature variation of the electrical resistivity reveals two parallel conducting channels of semiconducting and metallic character. In weak magnetic fields, the magnetoresistance exhibits weak antilocalization effect, while in strong fields and temperatures below 50 K it is large and negative. At temperatures below 7 K Shubnikov-de Haas oscillations with two frequencies appear in the resistivity. These oscillations have non-trivial Berry phase, which is a distinguished feature of Dirac fermions.

Magnetic and superconducting phase diagram of the half-Heusler topological semimetal HoPdBi

We report a study of the magnetic and electronic properties of the non-centrosymmetric half-Heusler antiferromagnet HoPdBi (TN = 2.0 K). Magnetotransport measurements show HoPdBi has a semimetallic behavior with a carrier concentration n = 3.7 × 10(18) cm(-3) extracted from the Shubnikov-de Haas effect. The magnetic phase diagram in the field-temperature plane has been determined by transport, magnetization, and thermal expansion measurements: magnetic order is suppressed at BM ~ 3.6 T for T --> 0. Superconductivity with Tc ~ 1.9 K is found in the antiferromagnetic phase. Ac-susceptibility measurements provide solid evidence for bulk superconductivity below Tc = 0.75 K with a screening signal close to a volume fraction of 100%. The upper critical field shows an unusual linear temperature variation with Bc2(T --> 0) = 1.1 T. We also report electronic structure calculations that classify HoPdBi as a new topological semimetal, with a non-trivial band inversion of 0.25 eV.