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Flat-band in twisted graphene bilayer has garnered widespread attention, and whether flat-bands can be realized in carbon monolayer is an interesting topic worth exploring in condensed matter physics. In this work, we demonstrate that, based on the theory of compact localized states, a series of two-dimensional carbon allotropes with flat-bands can be achieved. Two of them named as 191-8-66-C-r567x-1 and 191-10-90-C-r567x-1 are confirmed to be dynamically stable carbon phases with isolated or weakly overlapped flat-bands at the Fermi-level. The maximum Fermi velocities of the flat-band electrons are evaluated to be 1x10^4 m/s and 0.786x10^4 m/s, both of which are lower than the Fermi velocity of the flat-band electrons in magic-angle graphene (4x10^4 m/s). Furthermore, 191-8-66-C-r567x-1 has been confirmed to be a flat-band related magnetic half-metal with a magnetic moment of 1.854 miuB per cell, while 191-10-90-C-r567x-1 is a flat-band related magnetic normal metal with a magnetic moment of 1.663 miuB per cell. These results not only show that flat-bands can be constructed in carbon monolayer, but also indicate the potential for achieving metal-free magnetic materials with light elements based on flat-band theory., Comment: 10 pages, 3 figures

Topological semimetals (TSMs) have attracted numerous attention due to their exotic physical properties and great application potentials. Silicon-based TMSs are of particularly importance because of their high abundance, nontoxicity and natural compatibility with current semiconductor industry. In this work, an ideal low-energy topological nodal-line semimetal (TNLSM) silicon (I4/mcm-Si$_{48}$) with a clean band crossing at Fermi level is screened from thousands of silicon allotropes by the transferable tight-binding and DFT-HSE calculations. The results of formation energy, phonon dispersion, ab initio molecular dynamics and elastic constants show that I4/mcm-Si48 possesses good stability and is more stable than several synthetized silicon structures. By analyzing the symmetry, it reveals that the topological nodal-line of I4/mcm-Si48 is protected by mirror symmetry and inversion, time-reversal and SU(2) spin-rotation symmetries, and the nearly flat drumhead-like surface spectrum is observed. Furthermore, I4/mcm-Si48 exhibits exotic photoelectric properties and the Dirac fermions with high Fermi velocity (3.4$\sim$4.36$\times$10$^5$ m/s) can be excited by low energy photons. Our study provides a promising topological nodal-line semimetal for fundamental research and potential practical applications in semiconductor-compatible high-speed photoelectric devices., Comment: 10 pages, 5 figures

Based on first-principles method we predict a new low-energy Stone-Wales graphene SW40, which has an orthorhombic lattice with Pbam symmetry and 40 carbon atoms in its crystalline cell forming well-arranged Stone-Wales patterns. The calculated total energy of SW40 is just about 133 meV higher than that of graphene, indicating its excellent stability exceeds all the previously proposed graphene allotropes. We find that SW40 processes intrinsic Type-III Dirac-cone (Phys. Rev. Lett., 120, 237403, 2018) formed by band-crossing of a local linear-band and a local flat-band, which can result in highly anisotropic Fermions in the system. Interestingly, such intrinsic type-III Dirac-cone can be effectively tuned by inner-layer strains and it will be transferred into Type-II and Type-I Dirac-cones under tensile and compressed strains, respectively. Finally, a general tight-binding model was constructed to understand the electronic properties nearby the Fermi-level in SW40. The results show that type-III Dirac-cone feature can be well understood by the $\pi$-electron interactions between adjacent Stone-Wales defects., Comment: 7 pages, 4 figures