Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)

Abstract

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.

arXiv commentFinal version, 5 pg main text + 18 pg supplement, 4 + 6 figures, abstract abridged for arXiv posting - see paper for full abstract

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