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A system in a quantum superposition of distinct states usually exhibits many peculiar behaviors. Here we show that putting quasiparticles of graphene into superpositions of states in the two valleys can complete change the properties of the massless Dirac fermions. Due to the coexistence of both the quantum and relativistic characteristics, the superposition states exhibit many oddball behaviors in their chiral tunneling process. We further demonstrate that a recently observed line defect in graphene could be used to generate such superposition states. A possible experimental device to detect the novel behaviors of the relativistic superposition states in graphene is proposed., Comment: 4 Figures

Very recently, it was demonstrated explicitly that a zigzag graphene nanoribbon (GNR) exhibits a crossover of conductance from G0 to G0/2 with increasing the length (G0 = 2e2/h is the quantum of conductance) even at room-temperature [Baringhaus, et al. Nature 506, 349 (2014)]. Such a result is puzzling as none of previous theories seem to match the experimental observations. Here, we propose a model to explain the crossover from double-channel to single-channel ballistic transport in zigzag GNR. The sp3 distortion of carbon atoms at the GNR edges induces a large spin-orbit coupling on the edges atoms, which enhances spin-flip scattering of edge states of the zigzag GNR. With sufficient spin-flip scattering, the wave-function of edge states becomes a superposition of the spin-up and spin-down components. Then the coupling of the two edges becomes important. This removes the edge degree of freedom in the zigzag GNR and results in the evolution of the conductance from G0 to G0/2 with increasing the length., Comment: 4 Figures

The creation of van der Waals heterostructures based on a graphene monolayer and other two-dimensional crystals has attracted great interest because atomic registry of the two-dimensional crystals can modify the electronic spectra and properties of graphene. Twisted graphene bilayer can be viewed as a special van der Waals structure composed of two mutual misoriented graphene layers, where the sublayer graphene not only plays the role of a substrate, but also acts as an equivalent role as the top graphene layer in the structure. Here we report the electronic spectra of slightly twisted graphene bilayers studied by scanning tunneling microscopy and spectroscopy. Our experiment demonstrates that twist-induced van Hove singularities are ubiquitously present for rotation angles theta less than about 3.5o, corresponding to moir\'e-pattern periods D longer than 4 nm. However, they totally vanish for theta > 5.5o (D < 2.5 nm). Such a behavior indicates that the continuum models, which capture moir\'e-pattern periodicity more accurately at small rotation angles, are no longer applicable at large rotation angles., Comment: 5 figures

Despite the structures and properties of tilt grain boundaries of graphite surface and graphene have been extensively studied, their effect on the structures and electronic spectra of graphene layers has not been fully addressed. Here we study effects of one-dimensional tilt grain boundaries on structures and electronic spectra of graphene multilayers by scanning tunneling microscopy and spectroscopy. A tilt grain boundary of a top graphene sheet in graphene multilayers leads to a twist between consecutive layers and generates superstructures (Moir\'e patterns) on one side of the boundary. Our results demonstrate that the twisting changes the electronic spectra of Bernal graphene bilayer and graphene trilayers dramatically. We also study quantum-confined twisted graphene bilayer generated between two adjacent tilt grain boundaries and find that the band structure of such a system is still valid even when the number of superstructures is reduced to two in one direction. It implies that the electronic structure of this system is driven by the physics of a single Moir\'e spot., Comment: 4 figures in main text and 8 figures in SI

Strained graphene with lattice deformations has been demonstrated to give rise to large pseudomagnetic fields and host many exotic properties. Here, we propose a non-magnetic approach to realize a momentum-dependent out-of-plane spin splitting in strained graphene nanoribbons with a moderate spin-orbit coupling. This unique spin splitting distincts from the well-known Zeeman-type spin splitting and the Rashba-type spin splitting. Our analysis indicates that the competition between quantum spin Hall edge states and valley edge states in the nanoribbon leads to the unique spin splitting. The quantum spin Hall states at one edge of the nanoribbon are suppressed by the counterpropagating edge modes induced by the pseudomagnetic field. At the opposite edge, the quantum spin Hall states are not affected at all. Therefore, the degenerate quantum spin Hall states of opposite spin orientation, which propagate at the two opposite edges of the nanoribbon, are lifted. This result reveals a new method to manipulate the spin degrees of freedom of electrons., Comment: 5 Figures

The domestication and development of cattle has considerably impacted human societies, but the histories of cattle breeds have been poorly understood especially for African, Asian, and American breeds. Using genotypes from 43,043 autosomal single nucleotide polymorphism markers scored in 1,543 animals, we evaluate the population structure of 134 domesticated bovid breeds. Regardless of the analytical method or sample subset, the three major groups of Asian indicine, Eurasian taurine, and African taurine were consistently observed. Patterns of geographic dispersal resulting from co-migration with humans and exportation are recognizable in phylogenetic networks. All analytical methods reveal patterns of hybridization which occurred after divergence. Using 19 breeds, we map the cline of indicine introgression into Africa. We infer that African taurine possess a large portion of wild African auroch ancestry, causing their divergence from Eurasian taurine. We detect exportation patterns in Asia and identify a cline of Eurasian taurine/indicine hybridization in Asia. We also identify the influence of species other than Bos taurus in the formation of Asian breeds. We detect the pronounced influence of Shorthorn cattle in the formation of European breeds. Iberian and Italian cattle possess introgression from African taurine. American Criollo cattle are shown to be of Iberian, and not African, decent. Indicine introgression into American cattle occurred in the Americas, and not Europe. We argue that cattle migration, movement and trading followed by admixture have been important forces in shaping modern bovine genomic variation., Comment: 38 pages, 15 figures. Various changes made to respond to peer reviews. Mostly, arguments were clarified and additional f-statistics were added

Very recently, a new two-dimensional graphene-like topological insulator, Bi14Rh3I9, has been synthesized. The Bi-Rh sheets with a strong spin-orbit interaction are graphene analogues with a honeycomb net composed of RhBi8 cubes. Here we derive the low-energy effective Hamiltonian involving spin-orbit coupling for Bi14Rh3I9. In the absence of spin-orbit coupling, the Bi-Rh sheets show two inequivalent Dirac cones at the corners of the hexagonal Brillouin zone. The spin-orbit interaction opens a 2400 K bandgap at the Dirac points and establishes the quantum spin Hall effect in the Bi-Rh sheets. Our result indicates that the Bi14Rh3I9 may combine many unique electronic properties of graphene and topological insulators, and it should host a combination of quantum valley and spin Hall effects., Comment: This paper has been withdrawn by the author due to a crucial sign error in equation

The perfect transmission in graphene monolayer and the perfect reflection in Bernal graphene bilayer for electrons incident in the normal direction of a potential barrier are viewed as two incarnations of the Klein paradox. Here we show a new and unique incarnation of the Klein paradox. Owing to the different chiralities of the quasiparticles involved, the chiral fermions in twisted graphene bilayer shows adjustable probability of chiral tunnelling for normal incidence: they can be changed from perfect tunnelling to partial/perfect reflection, or vice versa, by controlling either the height of the barrier or the incident energy. As well as addressing basic physics about how the chiral fermions with different chiralities tunnel through a barrier, our results provide a facile route to tune the electronic properties of the twisted graphene bilayer., Comment: 4 figures

Theoretical research has predicted that ripples of graphene generates effective gauge field on its low energy electronic structure and could lead to zero-energy flat bands, which are the analog of Landau levels in real magnetic fields. Here we demonstrate, using a combination of scanning tunneling microscopy and tight-binding approximation, that the zero-energy Landau levels with vanishing Fermi velocities will form when the effective pseudomagnetic flux per ripple is larger than the flux quantum. Our analysis indicates that the effective gauge field of the ripples results in zero-energy flat bands in one direction but not in another. The Fermi velocities in the perpendicular direction of the ripples are not renormalized at all. The condition to generate the ripples is also discussed according to classical thin-film elasticity theory., Comment: 4 figures, Phys. Rev. B

We consider the electronic structure of a slightly twisted graphene bilayer and show the coexistence of van Hove singularities (VHSs) and superlattice Dirac points in a continuum approximation. The graphene-on-graphene moir\'e pattern gives rise to a periodic electronic potential, which leads to the emergence of the superlattice Dirac points due to the chiral nature of the charge carriers. Owning to the distinguishing real and reciprocal structures, the sublattice exchange even and odd structures of the twisted graphene bilayer (the two types of commensurate structures) result in two different structures of the superlattice Dirac points. We further calculate the effect of a strain on the low-energy electronic structure of the twisted graphene bilayer and demonstrate that the strain affects the position of the VHSs dramatically., Comment: 5 figures, to appear in Phys. Rev. B

Recent studies show that periodic potentials can generate superlattice Dirac points at energies in graphene (is the Fermi velocity of graphene and G is the reciprocal superlattice vector). Here, we perform scanning tunneling microscopy and spectroscopy studies of a corrugated graphene monolayer on Rh foil. We show that the quasi-periodic ripples of nanometer wavelength in the corrugated graphene give rise to weak one-dimensional (1D) electronic potentials and thereby lead to the emergence of the superlattice Dirac points. The position of the superlattice Dirac point is space-dependent and shows a wide distribution of values. We demonstrated that the space-dependent superlattice Dirac points is closely related to the space-dependent Fermi velocity, which may arise from the effect of the local strain and the strong electron-electron interaction in the corrugated graphene., Comment: 4figures

The interlayer coupling of twisted bilayer graphene could markedly affect its electronic band structure. A current challenge required to overcome in experiment is how to precisely control the coupling and therefore tune the electronic properties of the bilayer graphene. Here, we describe a facile method to modulate the local interlayer coupling by adsorption of single molecule magnets onto the twisted bilayer graphene and report the characterization of its electronic band structure using scanning tunneling microscopy and spectroscopy. The low-energy Van Hove singularities (VHSs) and superlattice Dirac cones, induced by the interlayer coupling and graphene-on-graphene moir\'e respectively, are observed in the tunneling spectra. Our experiment demonstrates that the energy difference of the two VHSs, which reflects the magnitude of interlayer coupling, can be tuned by the local coverage density of adsorption., Comment: 4 pages, 4 figures

Recent studies show that two low-energy Van Hove singularities (VHSs) seen as two pronounced peaks in the density of states (DOS) could be induced in twisted graphene bilayer. Here, we report angle dependent VHSs of slightly twisted graphene bilayer studied by scanning tunneling microscopy and spectroscopy. We show that energy difference of the two VHSs follows \DeltaEvhs ~ \hbar{\nu}F\DeltaK between 1.0^{\circ} and 3.0^{\circ} (here {\nu}F ~ 1.1\times106 m/s is the Fermi velocity of monolayer graphene, \DeltaK = 2Ksin(\theta/2) is the shift between the corresponding Dirac points of the twisted graphene bilayer). This result indicates that the rotation angle between graphene sheets not results in significant reduction of the Fermi velocity, which quite differs from that predicted by band structure calculations. However, around a twisted angle \theta ~ 1.3^{\circ}, the observed \DeltaEvhs ~ 0.11 eV is much less than the expected value \hbar{\nu}F\DeltaK ~ 0.28 eV at 1.3^{\circ}. The origin of the reduction of \DeltaEvhs at 1.3^{\circ} is discussed., Comment: To appear in Phys. Rev. Lett. (2012)