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Register a new userHigher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe$_2$ (X=Mo,W)
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In recent years, transition metal dichalcogenides (TMDs) have garnered great interest as topological materials -- monolayers of centrosymmetric $beta$-phase TMDs have been identified as 2D topological insulators (TIs), and bulk crystals of noncentrosymmetric $gamma$-phase MoTe$_2$ and WTe$_2$ have been identified as type-II Weyl semimetals. However, ARPES and STM probes of these TMDs have revealed huge, arc-like surface states that overwhelm, and are sometimes mistaken for, the much smaller topological surface Fermi arcs of bulk type-II Weyl points. In this letter, we use first-principles calculations and (nested) Wilson loops to analyze the bulk and surface electronic structure of both $beta$- and $gamma$-MoTe$_2$, finding that $beta$-MoTe$_2$ ($gamma$-MoTe$_2$ gapped with symmetry-preserving distortion) is an inversion-symmetry-indicated $mathbb{Z}_{4}$-nontrivial ($noncentrosymmetric, non$-$symmetry$-$indicated$) higher-order TI (HOTI) driven by double band inversion. Both structural phases of MoTe$_2$ exhibit the same surface features as WTe$_2$, revealing that the large Fermi arcs are in fact not topologically trivial, but are rather the characteristic split and gapped fourfold surface states of a HOTI. We also show that, when the effects of SOC are neglected, $beta$-MoTe$_2$ is a nodal-line semimetal with $mathbb{Z}_{2}$-nontrivial monopole nodal lines (MNLSM). This finding confirms that MNLSMs driven by double band inversion are the weak-SOC limit of HOTIs, implying that MNLSMs are higher-order topological $semimetals$ with flat-band-like hinge states, which we find to originate from the corner modes of 2D fragile TIs.
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We performed comparable polarized Raman scattering studies of MoTe2 and WTe2. By rotating crystals to tune the angle between the principal axis of the crystals and the polarization of the incident/scattered light, we obtained the angle dependence of the intensities for all the observed modes, which is perfectly consistent with careful symmetry analysis. Combining these results with first-principles calculations, we clearly identified the observed phonon modes in the different phases of both crystals. Fifteen Raman-active phonon modes (10Ag+5Bg) in the high-symmetry phase 1T-MoTe2 (300 K) were well assigned, and all the symmetry-allowed Raman modes (11A1+6A2) in the low-symmetry phase Td-MoTe2 (10 K) and 12 Raman phonons (8A1+4A2) in Td-WTe2 were observed and identified. The present work provides basic information about the lattice dynamics in transition-metal dichalcogenides and may shed some light on the understanding of the extremely large magnetoresistance (MR) in this class of materials.
Weyl semimetals have sparked intense research interest, but experimental work has been limited to the TaAs family of compounds. Recently, a number of theoretical works have predicted that compounds in the Mo$_x$W$_{1-x}$Te$_2$ series are Weyl semimetals. Such proposals are particularly exciting because Mo$_x$W$_{1-x}$Te$_2$ has a quasi two-dimensional crystal structure well-suited to many transport experiments, while WTe$_2$ and MoTe$_2$ have already been the subject of numerous proposals for device applications. However, with available ARPES techniques it is challenging to demonstrate a Weyl semimetal in Mo$_x$W$_{1-x}$Te$_2$. According to the predictions, the Weyl points are above the Fermi level, the system approaches two critical points as a function of doping, there are many irrelevant bulk bands, the Fermi arcs are nearly degenerate with bulk bands and the bulk band gap is small. Here, we study Mo$_x$W$_{1-x}$Te$_2$ for $x = 0.07$ and 0.45 using pump-probe ARPES. The system exhibits a dramatic response to the pump laser and we successfully access states $> 0.2$eV above the Fermi level. For the first time, we observe direct, experimental signatures of Fermi arcs in Mo$_x$W$_{1-x}$Te$_2$, which agree well with theoretical calculations of the surface states. However, we caution that the interpretation of these features depends sensitively on free parameters in the surface state calculation. We comment on the prospect of conclusively demonstrating a Weyl semimetal in Mo$_x$W$_{1-x}$Te$_2$.
The structural polymorphism in transition metal dichalcogenides (TMDs) provides exciting opportunities for developing advanced electronics. For example, MoTe$_2$ crystallizes in the 2H semiconducting phase at ambient temperature and pressure, but transitions into the 1T$^prime$ semimetallic phase at high temperatures. Alloying MoTe$_2$ with WTe$_2$ reduces the energy barrier between these two phases, while also allowing access to the T$_d$ Weyl semimetal phase. The MoWTe$_2$ alloy system is therefore promising for developing phase change memory technology. However, achieving this goal necessitates a detailed understanding of the phase composition in the MoTe$_2$-WTe$_2$ system. We combine polarization-resolved Raman spectroscopy with X-ray diffraction (XRD) and scanning transmission electron microscopy (STEM) to study MoWTe$_2$ alloys over the full compositional range x from 0 to 1. We identify Raman and XRD signatures characteristic of the 2H, 1T$^prime$, and T$_d$ structural phases that agree with density-functional theory (DFT) calculations, and use them to identify phase fields in the MoTe$_2$-WTe$_2$ system, including single-phase 2H, 1T$^prime$, and T$_d$ regions, as well as a two-phase 1T$^prime$ + T$_d$ region. Disorder arising from compositional fluctuations in MoWTe$_2$ alloys breaks inversion and translational symmetry, leading to the activation of an infrared 1T$^prime$-MoTe$_2$ mode and the enhancement of a double-resonance Raman process in 2H-MoWTe$_2$ alloys. Compositional fluctuations limit the phonon correlation length, which we estimate by fitting the observed asymmetric Raman lineshapes with a phonon confinement model. These observations reveal the important role of disorder in MoWTe$_2$ alloys, clarify the structural phase boundaries, and provide a foundation for future explorations of phase transitions and electronic phenomena in this system.
The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk-boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.
Recently, the celebrated Keldysh potential has been widely used to describe the Coulomb interaction of few-body complexes in monolayer transition-metal dichalcogenides. Using this potential to model charged excitons (trions), one finds a strong dependence of the binding energy on whether the monolayer is suspended in air, supported on SiO$_2$, or encapsulated in hexagonal boron-nitride. However, empirical values of the trion binding energies show weak dependence on the monolayer configuration. This deficiency indicates that the description of the Coulomb potential is still lacking in this important class of materials. We address this problem and derive a new potential form, which takes into account the three atomic sheets that compose a monolayer of transition-metal dichalcogenides. The new potential self-consistently supports (i) the non-hydrogenic Rydberg series of neutral excitons, and (ii) the weak dependence of the trion binding energy on the environment. Furthermore, we identify an important trion-lattice coupling due to the phonon cloud in the vicinity of charged complexes. Neutral excitons, on the other hand, have weaker coupling to the lattice due to the confluence of their charge neutrality and small Bohr radius.
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