Directional massless Dirac fermions in a layered van der Waals material with one-dimensional long-range order

Br-Vacancies Induced Variable Ranging Hopping Conduction in High-Order Topological Insulator Bi4Br4

The defects have a remarkable influence on the electronic structures and the electric transport behaviors of the matter, providing the additional means to engineering their physical properties. In this work, a comprehensive study on the effect of Br-vacancies on the electronic structures and transport behaviors in the high-order topological insulator Bi4Br4 is performed by the combined techniques of the scanning tunneling microscopy (STM), angle-resolved photoemission spectroscopy (ARPES), and physical properties measurement system along with the first-principle calculations. The STM results show the defects on the cleaved surface of a single crystal and reveal that the defects are correlated to the Br-vacancies with the support of the simulated STM images. The role of the Br-vacancies in the modulation of the band structures has been identified by ARPES spectra and the calculated energy-momentum dispersion. The relationship between the Br-vacancies and the semiconducting-like transport behaviors at low temperature has been established, implying a Mott variable ranging hopping conduction in Bi4Br4. The work not only resolves the unclear transport behaviors in this matter, but also paves a way to modulate the electric conduction path by the defects engineering.

Two-dimensional quadratic Weyl points, nodal loops, and spin-orbit Dirac points in PtS, PtSe, and PtTe monolayers

Topological quasiparticles have garnered significant research attention in condensed matter physics. However, they are exceedingly rare in two-dimensional systems, particularly those hosting unconventional topological quasiparticles. In this work, employing first-principles calculations and symmetry analysis, we demonstrate that PtS, PtSe, and PtTe monolayers serve as high-quality two-dimensional topological semimetal materials. These materials exhibit multiple types of topological quasiparticles around the Fermi level in the absence of spin-orbit coupling, such as conventional linear Weyl points and unconventional quadratic Weyl points in the PtS monolayer, as well as nodal loops in PtSe and PtTe monolayers. When spin-orbit coupling (SOC) is introduced, a tiny gap opens, transforming the systems into quantum spin hall insulators. Simultaneously, three spin-orbit Dirac points, robust against SOC, appear at the X, Y, and M points. We illustrate the symmetry protection, low-energy effective model, and edge states of these topological states. Our work provides an excellent material platform for studying novel two-dimensional topological quasiparticles and topological insulators.

Robust Luttinger Liquid State of 1D Dirac Fermions in a Van der Waals System Nb9Si4Te18

We report on the Tomonaga-Luttinger liquid (TLL) behavior in fully degenerate 1D Dirac Fermions. A ternary van der Waals material Nb9Si4Te18 incorporates in-plane NbTe2 chains, which produce a 1D Dirac band crossing Fermi energy. Tunneling conductance of electrons confined within NbTe2 chains is found to be substantially suppressed at Fermi energy, which follows a power law with a universal temperature scaling, hallmarking a TLL state. The obtained Luttinger parameter of ∼0.15 indicates a strong electron-electron interaction. The TLL behavior is found to be robust against atomic-scale defects, which might be related to the Dirac electron nature. These findings, combined with the tunability of the compound and the merit of a van der Waals material, offer a robust, tunable, and integrable platform to exploit non-Fermi liquid physics.

Experimental Realization of a Three-Dimensional Dirac Semimetal Phase with a Tunable Lifshitz Transition in Au_{2}Pb

Three-dimensional Dirac semimetals are an exotic state of matter that continue to attract increasing attention due to the unique properties of their low-energy excitations. Here, by performing angle-resolved photoemission spectroscopy, we investigate the electronic structure of Au_{2}Pb across a wide temperature range. Our experimental studies on the (111)-cleaved surface unambiguously demonstrate that Au_{2}Pb is a three-dimensional Dirac semimetal characterized by the presence of a bulk Dirac cone projected off-center of the bulk Brillouin zone (BZ), in agreement with our theoretical calculations. Unusually, we observe that the bulk Dirac cone is significantly shifted by more than 0.4 eV to higher binding energies with reducing temperature, eventually going through a Lifshitz transition. The pronounced downward shift is qualitatively reproduced by our calculations indicating that an enhanced orbital overlap upon compression of the lattice, which preserves C_{4} rotational symmetry, is the main driving mechanism for the Lifshitz transition. These findings not only broaden the range of currently known materials exhibiting three-dimensional Dirac phases, but also show a viable mechanism by which it could be possible to switch on and off the contribution of the degeneracy point to electron transport without external doping.

Dirac Nodal Line in Hourglass Semimetal Nb3SiTe6

Glide-mirror symmetry in nonsymmorphic crystals can foster the emergence of novel hourglass nodal loop states. Here, we present spectroscopic signatures from angle-resolved photoemission of a predicted topological hourglass semimetal phase in Nb₃SiTe₆. Linear band crossings are observed at the zone boundary of Nb₃SiTe₆, which could be the origin of the nontrivial Berry phase and are consistent with a predicted glide quantum spin Hall effect; such linear band crossings connect to form a nodal loop. Furthermore, the saddle-like Fermi surface of Nb₃SiTe₆ observed in our results helps unveil linear band crossings that could be missed. In situ alkali-metal doping of Nb₃SiTe₆ also facilitated the observation of other band crossings and parabolic bands at the zone center correlated with accidental nodal loop states. Overall, our results complete the system's band structure, help explain prior Hall measurements, and suggest the existence of a nodal loop at the zone center of Nb₃SiTe₆.

Influence of Orbital Character on the Ground State Electronic Properties in the van Der Waals Transition Metal Iodides VI3 and CrI3

Two-dimensional van der Waals magnetic semiconductors display emergent chemical and physical properties and hold promise for novel optical, electronic and magnetic "few-layers" functionalities. Transition-metal iodides such as CrI₃ and VI₃ are relevant for future electronic and spintronic applications; however, detailed experimental information on their ground state electronic properties is lacking often due to their challenging chemical environment. By combining X-ray electron spectroscopies and first-principles calculations, we report a complete determination of CrI₃ and VI₃ electronic ground states. We show that the transition metal-induced orbital filling drives the stabilization of distinct electronic phases: a wide bandgap in CrI₃ and a Mott insulating state in VI₃. Comparison of surface-sensitive (angular-resolved photoemission spectroscopy) and bulk-sensitive (X-ray absorption spectroscopy) measurements in VI₃ reveals a surface-only V²⁺ oxidation state, suggesting that ground state electronic properties are strongly influenced by dimensionality effects. Our results have direct implications in band engineering and layer-dependent properties of two-dimensional systems.

Coexistence of the hourglass and nodal-line dispersions in Nb3SiTe6 revealed by ARPES

The non-symmorphic crystal symmetry protection in the layered topological semimetal Nb₃SiTe₆ can generate exotic band crossings. Herein, high-quality Nb₃SiTe₆ single crystal was synthesized via chemical vapor transport. The lattice structure of Nb₃SiTe₆ was characterized by scanning transmission electron microscopy, X-ray diffraction, core-level photoemission, and Raman spectroscopies. Angle-resolved photoemission spectroscopy was used to reveal its topological properties by presenting band structures along different high-symmetry directions. Our data show that nontrivial band features coexist in Nb₃SiTe₆, including an hourglass-type dispersion formed by two bands along the S-R high-symmetry line, two node lines along the S-X path and the S-R-U path, respectively. These results provide a context for the understanding and exploration of the exotic topological properties of Nb₃SiTe₆.

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The hourglass-type dispersion is clearly visible from the results of the experiment

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Two bulk nodal-lines were found along the S-X and S-R-U high-symmetric directions

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The flat band shows the material hosts a quasi-one-dimensional characteristic

Observation of One-Dimensional Dirac Fermions in Silicon Nanoribbons

Dirac materials, which feature Dirac cones in the reciprocal space, have been one of the hottest topics in condensed matter physics in the past decade. To date, 2D and 3D Dirac Fermions have been extensively studied, while their 1D counterparts are rare. Recently, Si nanoribbons (SiNRs), which are composed of alternating pentagonal Si rings, have attracted intensive attention. However, the electronic structure and topological properties of SiNRs are still elusive. Here, by angle-resolved photoemission spectroscopy, scanning tunneling microscopy/spectroscopy measurements, first-principles calculations, and tight-binding model analysis, we demonstrate the existence of 1D Dirac Fermions in SiNRs. Our theoretical analysis shows that the Dirac cones derive from the armchairlike Si chain in the center of the nanoribbon and can be described by the Su-Schrieffer-Heeger model. These results establish SiNRs as a platform for studying the novel physical properties in 1D Dirac materials.

One-Dimensional Metal Embedded in Two-Dimensional Semiconductor in Nb2Six-1Te4

The ternary van der Waals material Nb₂Si_x-1Te₄ demonstrates many interesting properties as the content of Si is changed, ranging from metallic Nb₃SiTe₆ (x = 5/3) to narrow-gap semiconductor Nb₂SiTe₄ (x = 2) and with the emergence of one-dimensional Dirac fermion excitations in between. An in-depth understanding of their properties with different stoichiometry is important. Here we use scanning tunneling microscopy and spectroscopy to reveal that Nb₂Si_x-1Te₄ is a system with spontaneously developed and self-aligned one-dimensional metallic chains embedded in a two-dimensional semiconductor. Electron quasiparticles form one- and two-dimensional standing waves side by side. This special microscopic structure results in strong transport anisotropy. Along the chain direction the material behaves like a metal, while perpendicular to the chain direction, it behaves like a semiconductor. These findings provide an important basis for further investigation of this intriguing system.