In the presence of spin-orbit coupling (SOC), achieving both spin and valley polarized Dirac state is significant to promote the fantastic integration of Dirac physics, spintronics and valleytronics. Based on ab initio calculations, here we demonstrate that a class of spin-valley-coupled Dirac semimetals (svc-DSMs) in the functionalized SbAs monolayers (MLs) can host such desired state. Distinguished from the graphene-like 2D Dirac materials, the Dirac cones in svc-DSMs hold giant spin-splitting induced by strong SOC under inversion symmetry breaking. In the 2.3% strained SbAsH 2 ML, the Dirac fermions in inequivalent valleys have opposite Berry curvature and spin moment, giving rise to Dirac spin-valley Hall effect with constant spin Hall conductivity as well as massless and dissipationless transport. Topological analysis reveals that the svc-DSM emerges at the boundary between trivial and 2D topological insulators, which provides a promising platform for realizing the flexible and controllable tuning among different quantum states.The rise of graphene 1-3 has inspired significant efforts in searching for other 2D Dirac materials (DMs) 4-10 with linear energy dispersion. As the host of massless Dirac fermions, 2D DMs have become the playground for investigating many quantum relativistic phenomena [11][12][13] in the emerging field of Dirac physics. Like graphene, without considering spin-orbit coupling (SOC), the Dirac points in these 2D DMs are protected by symmetry. However, the presence of SOC will open a global bulk gap at the Dirac points and introduce the topologically protected gapless edge states. [13][14][15] Therefore, 2D DMs are formally a quantum spin Hall insulator 13 under time-reversal symmetry [ Fig. 1(a)] or quantum anomalous Hall insulator 12 with time-reversal breaking [ Fig. 1(b)]. In a pioneering theoretical study, Yong and Kane 16 employed symmetry analysis and a two-site tight-binding model to examine the possibility that the Dirac points can not be gapped by SOC [ Fig. 1(c)]. They concluded that nonsymmorphic space group symmetry plays an essential role in protecting the 2D Dirac points against SOC, named as spin-orbit Dirac points (SDPs). Although the first realistic 2D material hosting SDPs was predicted recently 17 , its SDPs are not located at the Fermi level and its Dirac dispersion is contaminated by some extraneous non-Dirac bands. Hence, how to achieve a 2D Dirac semimetal hosting SDPs with clean Dirac bands at the Fermi level remains a great challenge.On the other hand, the discovery of valley-dependent effects in MoS 2 monolayer 18,19 without inversion symmetry aroused an upsurge in the field of 2D valleytronics. 20 For hexagonal 2D materials such as graphene and monolayer group-VI transition metal dichalcogenides, the conically shaped valleys at +K and -K 4 FIG. 1. Schematic electronic band structures without SOC (left) and with SOC (right) for different 2D Dirac materials: (a) quantum spin Hall insulator, (b) quantum anomalous Hall insulator, (c) symmetry-protected Dirac semim...

Owing to the natural compatibility with current semiconductor industry, silicon allotropes with diverse structural and electronic properties provide promising platforms for the next-generation Si-based devices. After screening 230 all-silicon crystals in the zeolite frameworks by first-principles calculations, we disclose two structurally stable Si allotropes (AHT-Si 24 and VFI-Si 36 ) containing open channels as topological node-line semimetals with Dirac nodal points forming a nodal loop in the k z =0 plane of Brillouin zone. Interestingly, their nodal loops protected by inversion and time-reversal symmetries are robust against SU(2) symmetry breaking due to very weak spin-orbit coupling of Si. When the nodal lines are projected onto the (001) surface, flat surface bands can be observed because of the nontrivial topology of the bulk band structures. Our discoveries extend the topological physics to the three-dimensional Si materials, highlighting the possibility to realize low-cost, nontoxic and semiconductor-compatible Si-based electronics with topological quantum states.

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