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

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.

Cubic Stuffed-Diamond Semiconductors LiCu3TiQ4 (Q = S, Se, and Te)

Lithium chalcogenides have been understudied, owing to the difficulty in managing the chemical reactivity of lithium. These materials are of interest as potential ion conductors and thermal neutron detectors. In this study, we describe three new cubic lithium copper chalcotitanates that crystallize in the P4̅3m space group. LiCu₃TiS₄, a = 5.5064(6) Å, and LiCu₃TiSe₄, a = 5.7122(7) Å, represent two members of a new stuffed diamond-type crystal structure, while LiCu₃TiTe₄, a = 5.9830(7) Å crystallized into a similar structure exhibiting lithium and copper mixed occupancy. These structures can be understood as hybrids of the zinc-blende and sulvanite structure types. In situ powder X-ray diffraction was utilized to construct a "panoramic" reaction map for the preparation of LiCu₃TiTe₄, facilitating the design of a rational synthesis and uncovering three new transient phases. LiCu₃TiS₄ and LiCu₃TiSe₄ are thermally stable up to 1000 °C under vacuum, while LiCu₃TiTe₄ partially decomposes when slowly cooled to 400 °C. Density functional theory calculations suggest that these compounds are indirect band gap semiconductors. The measured work functions are 4.77(5), 4.56(5), and 4.69(5) eV, and the measured band gaps are 2.23(5), 1.86(5), and 1.34(5) eV for the S, Se, and Te analogues, respectively.

Experimental and Theoretical Investigations of Fe-Doped Hexagonal MnNiGe

We report a comprehensive investigation of MnNi_0.7Fe_0.3Ge Heusler alloy to explore its magnetic, caloric, and electrical transport properties. The alloy undergoes a ferromagnetic transition across T _C ∼ 212 K and a weak-antiferromagnetic transition across T _t ∼ 180 K followed by a spin-glass transition below T _f ∼ 51.85 K. A second-order phase transition across T _C with mixed short and long-range magnetic interactions is confirmed through the critical exponent study and universal scaling of magnetic entropy and magnetoresistance. A weak first-order phase transition is evident across T _t from magnetization and specific heat data. The frequency dependent cusp in χ_AC(T) along with the absence of a clear magnetic transition in specific heat C(T) and resistivity ρ(T) establish the spin glass behavior below T _f. Mixed ferromagnetic and antiferromagnetic interactions with dominant ferromagnetic coupling, as revealed by density functional calculations, are experimentally evident from the large positive Weiss temperature, magnetic saturation, and negative magnetic-entropy and magnetoresistance.

First principle based investigation of topological insulating phase in half-Heusler family NaYO (Y= Ag, Au, and Cu)

The ternary half-Heusler compounds have shown great potential for realizing new 3D topological insulators. With band gap tuning and spin orbit coupling these compounds may undergo topological phase transitions. In present work, we explore the possibility of realizing a topological insulating phase in half-Heusler family NaYO (Y= Ag, Au, and Cu). We find that for NaAgO, external strain (∼19%) along with spin-orbit coupling (SOC), is required to achieve band-inversion at Γ high-symmetry point and leads to phase transition from trivial to non-trivial topological insulating phase. In case of NaAuO and NaCuO, non-trivial phase appears in their equilibrium lattice constant, hence only SOC is enough to achieve band-inversion leading to non-trivial topology. The non-centrosymmetric nature of crystal geometry leads to the formation of two twofold degenerate point nodes near the Fermi level.

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.

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.

Epitaxy, exfoliation, and strain-induced magnetism in rippled Heusler membranes

Single-crystalline membranes of functional materials enable the tuning of properties via extreme strain states; however, conventional routes for producing membranes require the use of sacrificial layers and chemical etchants, which can both damage the membrane and limit the ability to make them ultrathin. Here we demonstrate the epitaxial growth of the cubic Heusler compound GdPtSb on graphene-terminated Al2O3 substrates. Despite the presence of the graphene interlayer, the Heusler films have epitaxial registry to the underlying sapphire, as revealed by x-ray diffraction, reflection high energy electron diffraction, and transmission electron microscopy. The weak Van der Waals interactions of graphene enable mechanical exfoliation to yield free-standing GdPtSb membranes, which form ripples when transferred to a flexible polymer handle. Whereas unstrained GdPtSb is antiferromagnetic, measurements on rippled membranes show a spontaneous magnetic moment at room temperature, with a saturation magnetization of 5.2 bohr magneton per Gd. First-principles calculations show that the coupling to homogeneous strain is too small to induce ferromagnetism, suggesting a dominant role for strain gradients. Our membranes provide a novel platform for tuning the magnetic properties of intermetallic compounds via strain (piezomagnetism and magnetostriction) and strain gradients (flexomagnetism).

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.

Heusler alloys for spintronic devices: review on recent development and future perspectives

Heusler alloys are theoretically predicted to become half-metals at room temperature (RT). The advantages of using these alloys are good lattice matching with major substrates, high Curie temperature above RT and intermetallic controllability for spin density of states at the Fermi energy level. The alloys are categorised into half- and full-Heusler alloys depending upon the crystalline structures, each being discussed both experimentally and theoretically. Fundamental properties of ferromagnetic Heusler alloys are described. Both structural and magnetic characterisations on an atomic scale are typically carried out in order to prove the half-metallicity at RT. Atomic ordering in the films is directly observed by X-ray diffraction and is also indirectly probed via the temperature dependence of electrical resistivity. Element specific magnetic moments and spin polarisation of the Heusler alloy films are directly measured using X-ray magnetic circular dichroism and Andreev reflection, respectively. By employing these ferromagnetic alloy films in a spintronic device, efficient spin injection into a non-magnetic material and large magnetoresistance are also discussed. Fundamental properties of antiferromagnetic Heusler alloys are then described. Both structural and magnetic characterisations on an atomic scale are shown. Atomic ordering in the Heusler alloy films is indirectly measured by the temperature dependence of electrical resistivity. Antiferromagnetic configurations are directly imaged by X-ray magnetic linear dichroism and polarised neutron reflection. The applications of the antiferromagnetic Heusler alloy films are also explained. The other non-magnetic Heusler alloys are listed. A brief summary is provided at the end of this review.

Topological Quantum Materials from the Viewpoint of Chemistry

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space, namely atoms, valence electrons, bonds, and orbitals, and reciprocal space, namely bands and Fermi surfaces, via symmetry and topology, classifying topological materials within a single-particle picture is possible. Currently, most materials are classified as trivial insulators, semimetals, and metals or as topological insulators, Dirac and Weyl nodal-line semimetals, and topological metals. The key ingredients for topology are certain symmetries, the inert pair effect of the outer electrons leading to inversion of the conduction and valence bands, and spin-orbit coupling. This review presents the topological concepts related to solids from the viewpoint of a solid-state chemist, summarizes techniques for growing single crystals, and describes basic physical property measurement techniques to characterize topological materials beyond their structure and provide examples of such materials. Finally, a brief outlook on the impact of topology in other areas of chemistry is provided at the end of the article.

One Structure, Two Elements-LuGe2 Superconductor vs Ordinary Metallic Conductor LuSn2. A Case Study on How Site-Selective Germanium for Tin Atom Substitution Leads to Modulating of the Charge Distribution

The substitution of chemically similar elements in a given crystal structure is an effective way to enhance physical properties, but the understanding on such improvements is usually impeded because the substitutions are random, and the roles of the different atoms cannot be distinguished by crystallographic symmetry. Herein, we provide a detailed crystallographic analysis and property measurements for the continuous solid solutions LuGe_xSn_2-x (0 < x < 2). The results show that there is no apparent change of the global symmetry, with the end-members LuGe₂ and LuSn₂, as well as the intermediate LuGe_xSn_2-x compositions adopting the ZrSi₂ type structure (space group Cmcm, Pearson index oC12). Yet, the refinements of the crystal structures from single-crystal X-ray diffraction data show that Ge-Sn atom substitutions are not random, but occur preferentially at the zigzag chain. The patterned distribution of two group 14 elements leads to a significant variation in chemical bonding and charge ordering within the other structural fragment, the 2D square nets, thereby resulting in tuned electron transport. The enhancement is greater than that for the typical Bloch-Gruneisen model and more akin to that for the parallel-resistor model. Magnetization measurements on single crystals show bulk superconductivity in all LuGe_xSn_2-x samples with shielding fractions as high as 90%. Specific heat data confirm the effect to originate from residual metallic tin in the material, indicating that Sn atom substitutions in the 2D square nets cause disruptions of the hypervalent bonding and local anisotropy, which ultimately leads to vanishing of the superconducting state in the end-member LuGe₂. This work sheds light on how the complexity in chemical interactions by two different carbon congeners leads to changes in the physical properties and how they can be correlated with the induced charge distribution. These studies also provide a general approach to modulation of charge density and. thus, of emerging physical properties in other classes of intermetallic systems based on the main-group elements of groups 13 to 15.

Prediction of topological nontrivial semimetals and pressure-induced Lifshitz transition in 1T'-MoS2 layered bulk polytypes

Recently, bulk MoS2 crystals stacked by 1T'-MoS2 monolayers have been synthesized successfully, but little is known about their stacking sequences and topological properties. Based on first-principles calculations and symmetry-based indicator theory, we discovered that three predicted bulk structures of MoS2 (named 2M-, 1T'- and β-MoS2) stacked by 1T' monolayers are topological insulators and nodal line semimetals with and without spin-orbit coupling. Their stacking stability, electronic structure and the topology origin were systematically investigated. Further research proves that in the absence of SOC the open- and closed-type nodal lines can coexist in the momentum space of 2M-MoS2, which also possesses drumhead-like surface state. Moreover, we predicted a pressure-induced Lifshitz transition at about 1.3 GPa in 2M-MoS2. Our findings greatly enrich the topological phases of MoS2 and probably bring MoS2 to the rapidly growing family of layered topological semimetals.

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.

The topological properties of Dp-wave superconductors in the mixed Rashba/Dresselhaus systems

We investigate the effect of mixing Rashba/Dresselhaus spin-orbit couplings (SOCs) on the topological properties of D + p-wave superconductors. It is known that the nodal D + p-wave Rashba superconductors become gapful under a Zeeman magnetic field. We extend this gap-generation mechanism to mixed Rashba/Dresselhaus systems and find that the induced energy gaps are strongly modified by the Dresselhaus component in the second quadrant of the Brillion zone (BZ). We further calculate the Chern number numerically and obtain the topological phase diagram. It is shown that the Dresselhaus SOCs have a negative effect on the topological properties; the topological nontrivial region withC= -4 in the phase diagram shrinks as the amplitude of the Dresselhaus component increases. In the Dresselhaus-dominated regime, the contributions of gapped nodes from different quadrants of the BZ cancel each other, resulting in zero Chern number in most of the phase diagram. The numerical results are well explained by an approximate analytical formula for Chern number.

Reliable Prediction of New Quantum Materials for Topological and Renewable-Energy Applications: A High-Throughput Screening

Half-Heusler (HH) alloys provide a general platform for searching candidate materials for various energy applications. Here, we present a high-throughput first-principles calculation of a set of 960 eight valence-electron HH alloys to search potential candidates for thermoelectric (TE), solar harvesting (SH), topological insulator (TI), and transparent conductor (TC) applications. The initial screening parameters (such as stability, bandgap (E_g), band-inversion strength) followed by application specific descriptors are used to predict promising compounds. 121 out of 960 compounds were found to be dynamically and chemically stable. Of them, 31 compounds (with E_g < 1.5 eV) were studied for TE application, 30 (with 1 < E_g < 1.8 eV) for SH application, 21 for TI application, and 29 (with E_g > 2 eV) for TC applications. Some of the compounds show reasonably high thermoelectric figure of merit (ZT ∼ 1.6) and solar efficiency (SLME) > 20%, comparable to existing state-of-the-art materials. Surface band structure and topological Z2 index reconfirms the robustness of topological behavior. We strongly believe that our calculations should leverage useful insights to experimentalists.

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.

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.

Emergence of intrinsic superconductivity below 1.178 K in the topologically non-trivial semimetal state of CaSn3

Topological materials which are also superconducting are of great current interest, since they may exhibit a non-trivial topologically-mediated superconducting phase. Although there have been many reports of pressure-tuned or chemical-doping-induced superconductivity in a variety of topological materials, there have been few examples of intrinsic, ambient pressure superconductivity in a topological system having a stoichiometric composition. Here, we report that the pure intermetallic CaSn₃ not only exhibits topological fermion properties, but also has a superconducting phase at ~1.178 K under ambient pressure. The topological fermion properties, including the nearly zero quasi-particle mass and the non-trivial Berry phase accumulated in cyclotron motions, were revealed from the de Haas-van Alphen (dHvA) quantum oscillation studies of this material. Although CaSn₃ was previously reported to be superconducting with T _c  =  4.2 K, our studies show that the T _c  =  4.2 K superconductivity is extrinsic and caused by Sn on the degraded surface, whereas its intrinsic bulk superconducting transition occurs at 1.178 K. These findings make CaSn₃ a promising candidate for exploring new exotic states arising from the interplay between non-trivial band topology and superconductivity, e.g. topological superconductivity (TSC).

Linear-in-Frequency Optical Conductivity in GdPtBi due to Transitions near the Triple Points

The complex optical conductivity of the half-Heusler compound GdPtBi is measured in a frequency range from 20 to 22 000  cm^{-1} (2.5 meV-2.73 eV) at temperatures down to 10 K in zero magnetic field. We find the real part of the conductivity, σ_{1}(ω), to be almost perfectly linear in frequency over a broad range from 50 to 800  cm^{-1} (∼6-100  meV) for T≤50  K. This linearity strongly suggests the presence of three-dimensional linear electronic bands with band crossings (nodes) near the chemical potential. Band-structure calculations show the presence of triple points, where one doubly degenerate and one nondegenerate band cross each other in close vicinity of the chemical potential. From a comparison of our data with the optical conductivity computed from the band structure, we conclude that the observed nearly linear σ_{1}(ω) originates as a cumulative effect from all the transitions near the triple points.

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.

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.

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

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

Topological Phase Transitions in Multicomponent Superconductors

We study the phase transition between a trivial and a time-reversal-invariant topological superconductor in a single-band system. By analyzing the interplay of symmetry, topology, and energetics, we show that for a generic normal state band structure, the phase transition occurs via extended intermediate phases in which even- and odd-parity pairing components coexist. For inversion-symmetric systems, the coexistence phase spontaneously breaks time-reversal symmetry. For noncentrosymmetric superconductors, the low-temperature intermediate phase is time-reversal breaking, while the high-temperature phase preserves time-reversal symmetry and has topologically protected line nodes. Furthermore, with approximate rotational invariance, the system has an emergent U(1)×U(1) symmetry, and novel topological defects, such as half vortex lines binding Majorana fermions, can exist. We analytically solve for the dispersion of the Majorana fermion and show that it exhibits small and large velocities at low and high energies. Relevance of our theory to superconducting pyrochlore oxide Cd_{2}Re_{2}O_{7} and half-Heusler materials is discussed.

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.

Angle-dependent magnetoresistance and quantum oscillations in high-mobility semimetal LuPtBi

The recent discovery of ultrahigh mobility and large positive magnetoresistance in the topologically non-trivial half-Heusler semimetal LuPtBi provides a unique playground for studying exotic physics and significant perspective for device applications. As an fcc-structured electron-hole-compensated semimetal, LuPtBi theoretically exhibits six symmetrically arranged anisotropic electron Fermi pockets and two nearly-spherical hole pockets, offering the opportunity to explore the physics of Fermi surfaces with simple angle-related magnetotransport properties. In this work, through angle-dependent transverse magnetoresistance measurements, in combination with high-field SdH quantum oscillations, we aimed to map out a Fermi surface with six anisotropic pockets in the high-temperature and low-field regime, and furthermore, identify a possible magnetic field driven Fermi surface change at lower temperatures. Reasons account for the Fermi surface change in LuPtBi are discussed in terms of the field-induced electron evacuation due to Landau quantization.

Multiple Dirac cones at the surface of the topological metal LaBi

The rare-earth monopnictide LaBi exhibits exotic magneto-transport properties, including an extremely large and anisotropic magnetoresistance. Experimental evidence for topological surface states is still missing although band inversions have been postulated to induce a topological phase in LaBi. In this work, we have revealed the existence of surface states of LaBi through the observation of three Dirac cones: two coexist at the corners and one appears at the centre of the Brillouin zone, by employing angle-resolved photoemission spectroscopy in conjunction with ab initio calculations. The odd number of surface Dirac cones is a direct consequence of the odd number of band inversions in the bulk band structure, thereby proving that LaBi is a topological, compensated semimetal, which is equivalent to a time-reversal invariant topological insulator. Our findings provide insight into the topological surface states of LaBi's semi-metallicity and related magneto-transport properties.

The magnetoresistance suggests an exotic topological phase in LaBi, but the evidence is still missing. Here, Nayak et al. report the existence of surface states of LaBi through the observation of three Dirac cones, confirming it a topological semimetal.