Spin-Resolved Electronic Response to the Phase Transition in MoTe_{2}

Spin-resolved topology and partial axion angles in three-dimensional insulators

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ([Formula: see text]-) invariant (helical) 3D TCIs-termed higher-order TCIs (HOTIs)-the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), "spin-Weyl" semimetals, and [Formula: see text]-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that β-MoTe2 realizes a spin-Weyl state and that α-BiBr hosts both 3D QSHI and T-DAXI regimes.

Geometry-Induced Spin Filtering in Photoemission Maps from WTe_{2} Surface States

We demonstrate that an important quantum material WTe_{2} exhibits a new type of geometry-induced spin filtering effect in photoemission, stemming from low symmetry that is responsible for its exotic transport properties. Through the laser-driven spin-polarized angle-resolved photoemission Fermi surface mapping, we showcase highly asymmetric spin textures of electrons photoemitted from the surface states of WTe_{2}. Such asymmetries are not present in the initial state spin textures, which are bound by the time-reversal and crystal lattice mirror plane symmetries. The findings are reproduced qualitatively by theoretical modeling within the one-step model photoemission formalism. The effect could be understood within the free-electron final state model as an interference due to emission from different atomic sites. The observed effect is a manifestation of time-reversal symmetry breaking of the initial state in the photoemission process, and as such it cannot be eliminated, but only its magnitude influenced, by special experimental geometries.

Origin of the Anomalous Electrical Transport Behavior in Fe-Intercalated Weyl Semimetal Td -MoTe2

Weyl semimetal T_d -MoTe₂ has recently attracted much attention due to its intriguing electronic properties and potential applications in spintronics. Here, Fe-intercalated T_d -Fe_x MoTe₂ single crystals (0 < x < 0.15 ) are grown successfully. The electrical and thermoelectric transport results consistently demonstrate that the phase transition temperature T_S is gradually suppressed with increasing x. Theoretical calculation suggests that the increased energy of the T_d phase, enhanced transition barrier, and more occupied bands in 1T' phase is responsible for the suppression in T_S . In addition, a ρ^α -lnT behavior induced by Kondo effect is observed with x ≥ 0.08, due to the coupling between conduction carriers and the local magnetic moments of intercalated Fe atoms. For T_d -Fe_0.15 MoTe₂ , a spin-glass transition occurs at ≈10 K. The calculated band structure of T_d -Fe_0.25 MoTe₂ shows that two flat bands exist near the Fermi level, which are mainly contributed by the d_yz and d x 2 - y 2 ${{\rm{d}}_{{x^2} - {y^2}}}$ orbitals of the Fe atoms. Finally, the electronic phase diagram of T_d -Fe_x MoTe₂ is established for the first time. This work provides a new route to control the structural instability and explore exotic electronic states for transition-metal dichalcogenides.

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.

Engineering Weyl Phases and Nonlinear Hall Effects in T_{d}-MoTe_{2}

MoTe_{2} has recently attracted much attention due to the observation of pressure-induced superconductivity, exotic topological phase transitions, and nonlinear quantum effects. However, there has been debate on the intriguing structural phase transitions among various observed phases of MoTe_{2} and their connection to the underlying topological electronic properties. In this work, by means of density-functional theory calculations, we investigate the structural phase transition between the polar T_{d} and nonpolar 1T^{'} phases of MoTe_{2} in reference to a hypothetical high-symmetry T_{0} phase that exhibits higher-order topological features. In the T_{d} phase we obtain a total of 12 Weyl points, which can be created/annihilated, dynamically manipulated, and switched by tuning a polar phonon mode. We also report the existence of a tunable nonlinear Hall effect in T_{d}-MoTe_{2} and propose the use of this effect as a probe for the detection of polarity orientation in polar (semi)metals. By studying the role of dimensionality, we identify a configuration in which a nonlinear surface response current emerges. The potential technological applications of the tunable Weyl phase and the nonlinear Hall effect are discussed.

Coexistence of large conventional and planar spin Hall effect with long spin diffusion length in a low-symmetry semimetal at room temperature

The spin Hall effect (SHE) is usually observed as a bulk effect in high-symmetry crystals with substantial spin-orbit coupling (SOC), where the symmetric spin-orbit field imposes a widely encountered trade-off between spin Hall angle (θ_SH) and spin diffusion length (L_sf), and spin polarization, spin current and charge current are constrained to be mutually orthogonal. Here, we report a large θ_SH of 0.32 accompanied by a long L_sf of 2.2 μm at room temperature in a low-symmetry few-layered semimetal MoTe₂, thus identifying it as an excellent candidate for simultaneous spin generation, transport and detection. In addition, we report that longitudinal spin current with out-of-plane polarization can be generated by both transverse and vertical charge current, due to the conventional and a newly observed planar SHE, respectively. Our study suggests that manipulation of crystalline symmetries and strong SOC opens access to new charge-spin interconversion configurations and spin-orbit torques for spintronic applications.

Detection of Hole Pockets in the Candidate Type-II Weyl Semimetal MoTe_{2} from Shubnikov-de Haas Quantum Oscillations

The bulk electronic structure of T_{d}-MoTe_{2} features large hole Fermi pockets at the Brillouin zone center (Γ) and two electron Fermi surfaces along the Γ-X direction. However, the large hole pockets, whose existence has important implications for the Weyl physics of T_{d}-MoTe_{2}, has never been conclusively detected in quantum oscillations. This raises doubt about the realizability of Majorana states in T_{d}-MoTe_{2}, because these exotic states rely on the existence of Weyl points, which originated from the same band structure predicted by density functional theory (DFT). Here, we report an unambiguous detection of these elusive hole pockets via Shubnikov-de Haas (SdH) quantum oscillations. At ambient pressure, the quantum oscillation frequencies for these pockets are 988 and 1513 T, when the magnetic field is applied along the c axis. The quasiparticle effective masses m^{*} associated with these frequencies are 1.50 and 2.77 m_{e}, respectively, indicating the importance of Coulomb interactions in this system. We further measure the SdH oscillations under pressure. At 13 kbar, we detected a peak at 1798 T with m^{*}=2.86m_{e}. Relative to the oscillation data at a lower pressure, the amplitude of this peak experienced an enhancement, which can be attributed to the reduced curvature of the hole pockets under pressure. Combining our experimental data with DFT+U calculations, where U is the Hubbard parameter, our results shed light on why these important hole pockets have not been detected until now.

Transport evidence of asymmetric spin-orbit coupling in few-layer superconducting 1Td-MoTe2

Two-dimensional transition metal dichalcogenides MX₂ (M = W, Mo, Nb, and X = Te, Se, S) with strong spin-orbit coupling possess plenty of novel physics including superconductivity. Due to the Ising spin-orbit coupling, monolayer NbSe₂ and gated MoS₂ of 2H structure can realize the Ising superconductivity, which manifests itself with in-plane upper critical field far exceeding Pauli paramagnetic limit. Surprisingly, we find that a few-layer 1T_d structure MoTe₂ also exhibits an in-plane upper critical field which goes beyond the Pauli paramagnetic limit. Importantly, the in-plane upper critical field shows an emergent two-fold symmetry which is different from the isotropic in-plane upper critical field in 2H transition metal dichalcogenides. We show that this is a result of an asymmetric spin-orbit coupling in 1T_d transition metal dichalcogenides. Our work provides transport evidence of a new type of asymmetric spin-orbit coupling in transition metal dichalcogenides which may give rise to novel superconducting and spin transport properties.