Nonsymmorphic-symmetry-protected hourglass Dirac loop, nodal line, and Dirac point in bulk and monolayer 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>SiTe</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math>
 (
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 = Ta, Nb)

Li, Si; Liu, Ying; Wang, Shan-Shan; Yu, Zhi‐Ming; Guan, Shaokang; Sheng, Xian‐Lei; Yao, Yugui; Yang, Shengyuan A.

doi:10.1103/physrevb.97.045131

Cited by 137 publications

(67 citation statements)

References 97 publications

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“…On the other hand, similar to the parent compound NbSe2 [25], TaSi1/3Te2 [26] and other vdW TMDs [27], electrons are expected to be coherently hopping between NbSixTe2 layers, and forms 3D FSs and band structure dispersing along the kz direction [23]. Therefore, the electronic state without kz dispersing, as observed in our ARPES experiments here, is corresponding to the surface state.…”

Section: Pagesupporting

confidence: 64%

“…The interlayer Te-Te distance is in the range of typical van der Waals type and atomically thin NbSi1/3Te2 flakes were successfully fabricated by micro-exfoliation [22], that demonstrates the capability as a monomer for nanoelectronics based on van der Waals heterostructure. Topological semimetal phases are proposed in both bulk and single-layered NbSi1/3Te2 by first principle calculations study [23]. As the Si intercalation level increasing, more Nb atoms are paired and form the a(b) type chains.…”

Section: Pagementioning

confidence: 99%

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

et al. 2019

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Exotic properties in single or few layers of van der Waals materials carry great promise for applications in nanoscaled electronics, optoelectronics and flexible devices. The established, distinct examples include extremely high mobility and superior thermal conductivity in graphene, a large direct band gap in monolayer MoS2 and quantum spin Hall effect in WTe2 monolayer, etc. All these exotic properties arise from the electron quantum confinement effect in the twodimensional limit. Here we report a novel phenomenon due to one-dimensional (1D) confinement of carriers in a layered van der Waals material NbSi0.45Te2 revealed by angle-resolved photoemission spectroscopy, i.e. directional massless Dirac fermions. The 1D behavior of the carriers is directly related to a stripe-like structural modulation with the long-range translational symmetry only along the stripe direction, as perceived by scanning tunneling microscopy experiment. The four-fold degenerated node of 1D Dirac dispersion is essential and independent on band inversion, because of the protection by nonsymmorphic symmetry of the stripe structure. Our study not only provides a playground for investigating the striking properties of the essential directional massless Dirac fermions, but also introduces a unique monomer with 1D long-range order for engineering nano-electronic devices based on heterostructures of layered van der Waals materials.

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Section: Pagesupporting

confidence: 64%

Section: Pagementioning

confidence: 99%

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

et al. 2019

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“…The formation mechanism of Dirac bands discussed in this work is intrinsically different from the band crossing induced by nonsymmorphic crystalline symmetry reported in previous works [26][27][28][29][30]. There two bands exchange the eigenvalues of a single nonsymmorphic operator, a glided plane or a screw axis, as they disperse from one high symmetry momentum to another high symmetry momentum.…”

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confidence: 65%

Realization of Symmetry-Enforced Two-Dimensional Dirac Fermions in Nonsymmorphic α-Bismuthene

et al. 2020

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Two-dimensional (2D) Dirac-like electron gases have attracted tremendous research interest ever since the discovery of free-standing graphene [1-3]. The linear energy dispersion and non-trivial Berry phase play the pivotal role in the remarkable electronic, optical, mechanical and chemical properties of 2D Dirac materials [4]. The known 2D Dirac materials are gapless only within certain approximations, for example, in the absence of SOC. Here we report a route to establishing robust Dirac cones in 2D materials with nonsymmorphic crystal lattice. The nonsymmorphic symmetry enforces Dirac-like band dispersions around certain high-symmetry momenta in the presence of SOC [5, 6]. Through µ-ARPES measurements we observe Dirac-like band dispersions in α-bismuthene. The nonsymmorphic lattice symmetry is confirmed by µ-LEED and STM. Our firstprinciples simulations and theoretical topological analysis demonstrate the correspondence between nonsymmorphic symmetry and Dirac states. This mechanism can be straightforwardly generalized to other nonsymmorphic materials. The results open the door for the search of symmetry enforced Dirac fermions in the vast uncharted world of nonsymmorphic 2D materials.

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“…The symmetry conditions for stabilizing hourglass Dirac loops in 3D systems can be found in Ref. [18,45]. Third, the topological band features studied here are for the bulk states of a 2D system.…”

Section: Symmetry Analysis For Hourglass Weyl Loops In 2dmentioning

confidence: 91%

Hourglass Weyl loops in two dimensions: Theory and material realization in monolayer GaTeI family

Jiao

et al. 2019

Phys. Rev. Materials

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Nodal loops in two-dimensional (2D) systems are typically vulnerable against spin-orbit coupling (SOC). Here, we explore 2D systems with a type of doubly degenerate nodal loops that are robust under SOC and feature an hourglass type dispersion. We present symmetry conditions for realizing such hourglass Weyl loops, which involve nonsymmorphic lattice symmetries. Depending on the symmetry, the loops may exhibit different patterns in the Brillouin zone. Based on first-principles calculations, we identify the monolayer GaTeI-family materials as a realistic material platform to realize such loops. These materials host a single hourglass Weyl loop circling around a high-symmetry point. Interestingly, there is also a spin-orbit Dirac point enabled by an additional screw axis. We show that the hourglass Weyl loop and the Dirac point are robust under a variety of applied strains. By breaking the screw axis, the Dirac point can be transformed into a second Weyl loop. Furthermore, by breaking the glide mirror, the hourglass Weyl loop and the spin-orbit Dirac point can both be transformed into a pair of spin-orbit Weyl points. Our work offers guidance and realistic material candidates for exploring fascinating physics of several novel 2D emergent fermions. arXiv:1902.09283v2 [cond-mat.mtrl-sci]

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Nonsymmorphic-symmetry-protected hourglass Dirac loop, nodal line, and Dirac point in bulk and monolayer X3SiTe6 ( X = Ta, Nb)

Cited by 137 publications

References 97 publications

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

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

Realization of Symmetry-Enforced Two-Dimensional Dirac Fermions in Nonsymmorphic α-Bismuthene

Hourglass Weyl loops in two dimensions: Theory and material realization in monolayer GaTeI family

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