Recent studies show that two low-energy van Hove singularities (VHSs) seen as two pronounced peaks in the density of states could be induced in a twisted graphene bilayer. Here, we report angle-dependent VHSs of a slightly twisted graphene bilayer studied by scanning tunneling microscopy and spectroscopy. We show that energy difference of the two VHSs follows ΔE(vhs)∼ℏν(F)ΔK between 1.0° and 3.0° [here ν(F)∼1.1 × 10(6) m/s is the Fermi velocity of monolayer graphene, and ΔK = 2Ksin(θ/2) is the shift between the corresponding Dirac points of the twisted graphene bilayer]. This result indicates that the rotation angle between graphene sheets does not result in a significant reduction of the Fermi velocity, which quite differs from that predicted by band structure calculations. However, around a twisted angle θ∼1.3°, the observed ΔE(vhs)∼0.11 eV is much smaller than the expected value ℏν(F)ΔK∼0.28 eV at 1.3°. The origin of the reduction of ΔE(vhs) at 1.3° is discussed.

By combining scanning tunneling microscopy and spectroscopy, angle-resolved photoemission spectroscopy, and density functional theory band calculations, we directly observe and resolve the one-dimensional edge states of single bilayer (BL) Bi(111) islands on clean Bi(2)Te(3) and Bi(111)-covered Bi(2)Te(3) substrates. The edge states are localized in the vicinity of step edges having an ∼2  nm wide spatial distribution in real space and reside in the energy gap of the Bi(111) BL. Our results demonstrate the existence of nontrivial topological edge states of single Bi(111) bilayer as a two-dimensional topological insulator.

Based on first-principles and tight-binding calculations, we report that the topological edge states of zigzag Bi(111) nanoribbon can be significantly tuned by H edge adsorption. The Fermi velocity is increased by 1 order of magnitude, as the Dirac point is moved from the Brillouin zone boundary to the Brillouin zone center, and the real-space distribution of Dirac states are made twice more delocalized. These intriguing changes are explained by an orbital filtering effect of edge H atoms, which pushes certain components of the p orbital of edge Bi atoms out of the band gap regime that reshapes the topological edge states. In addition, the spin texture of the Dirac states is also modified, which is described by introducing an effective Hamiltonian. Our findings not only are of fundamental interest but also have practical implications in potential applications of topological insulators.

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Topological insulators and graphene present two unique classes of materials, which are characterized by spin-polarized (helical) and nonpolarized Dirac cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in topological insulators. Here, we report the experimental observation of the renormalized quasiparticle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi 2 Te 3 substrate from angle-resolved photoemission spectroscopy. First-principles band calculations indicate that the quasiparticle spectra are likely associated with the hybridization between the extrinsic substrate-induced Dirac states of Bi bilayer and the intrinsic surface Dirac states of Bi 2 Te 3 film at close energy proximity. Without such hybridization, only single-particle Dirac spectra are observed in a single Bi bilayer grown on Bi 2 Se 3 , where the extrinsic Dirac states Bi bilayer and the intrinsic Dirac states of Bi 2 Se 3 are well separated in energy. The possible origins of many-body interactions are discussed. Our findings provide a means to manipulate topological surface states.Dirac fermion | electronic structures | thin films M uch recent attention has been devoted to graphene (1-6) and topological insulators (TIs) (7-18), two unique material systems that exhibit conical linear electron bands of Dirac spectra. quasiparticles of Dirac fermions are distinct from those of ordinary Fermi liquids (19)(20)(21). Although rather difficult and rare, recent angle-resolved photoemission spectroscopy (ARPES) experiments (1, 2, 5, 6) have directly shown the existence of many-body quasiparticle spectra near Dirac point in graphene, manifesting electronelectron, electron-phonon, and electron-plasmon interactions. Similar to graphene, TIs also possess Dirac cone, albeit it is spinpolarized or helical Dirac cone. So far, however, no renormalized quasiparticle spectra near the helical Dirac point similar to graphene have been reported in any known TIs, and most studies of TIs are based on the single-particle picture (9,11,12,14,18). Here, we report direct experimental observation of a skewed helical Dirac point, a signature quasiparticle spectrum indicative of many-body interactions, by ARPES in a TI system of Bi(111) bilayer grown on Bi 2 Te 3 substrate, where a 2D TI is interfaced with a 3D TI (22).ARPES can probe the quasiparticle's scattering rate at different energy scales, and therefore can access the many-body interactions directly (23). Our experimental observation of the quasiparticle spectra manifesting many-body effects is characterized with a "vertically nondispersive" feature near Dirac point. Based on model density functional theory (DFT) calculations of electron bands as a function of the artificially changed interfacial distance between the Bi bilayer and substrate, we found that the renormalized quasi...

So far, most theoretically predicted and experimentally confirmed quantum anomalous Hall effect (QAHE) are limited in two-dimensional (2D) materials with out-of-plane magnetization. In this Letter, starting from 2D nodal-line semimetal, a general rule for searching QAHE with in-plane magnetization is mapped out. Due to the spin-orbital-coupling, we found that the magnetization will prefer an in-plane orientation if the orbital of degenerate nodal-line states at Fermi-level have the same absolute value of magnetic quantum number. Moreover, depending on the broken or conserved mirror symmetry, either QAHE or 2D semimetal can be realized. Based on first principles calculations, we further predict a real material of monolayer LaCl to be an intrinsic QAHE with in-plane magnetization. By tuning the directions of in-plane magnetization, the QAHE in LaCl demonstrates a threefold rotational symmetry with Chern number of either +1 or −1, and the transition point is characterized by a 2D semimetal phase. All these features are quantitatively reproduced by tight-binding model calculations, revealing the underlying physics clearly. Our results greatly extend the scope for material classes of QAHE, and hence stimulate immediate experimental interests.

We predict a family of 2D carbon (C) allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac fermions, using first-principle calculations within density functional theory. They have a square unit-cell containing two sizes of square C rings. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 × 10(5) to 7.2 × 10(5) m/s along different k directions. Near the Fermi level, the Dirac crescent can be nicely expressed by an extended 2D Dirac model Hamiltonian. Furthermore, tight-binding band fitting reveals that the Dirac crescent originates from the next-nearest-neighbor interactions between C atoms. S-graphynes may be used to build new 2D electronic devices taking advantages of their highly directional charge transport.

The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Here we show that a minimal basis of three orbitals (s, px, py) is required to produce a QSH phase via nearest-neighbour hopping in a two-dimensional trigonal lattice. Tight-binding model analyses and calculations show that the QSH phase arises from a spin–orbit coupling (SOC)-induced s–p band inversion or p–p bandgap opening at Brillouin zone centre (Γ point), whose topological phase diagram is mapped out in the parameter space of orbital energy and SOC. Remarkably, based on first-principles calculations, this exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ∼73 meV, facilitating the possible room-temperature measurement. Our results will extend the search for substrate supported QSH materials to new lattice and orbital types.