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Register a new userWigner crystal phases in bilayer graphene
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It is generally believed that a Wigner Crystal in single layer graphene can not form because the magnitudes of the Coulomb interaction and the kinetic energy scale similarly with decreasing electron density. However, this scaling argument does not hold for the low energy states in bilayer graphene. We consider the formation of a Wigner Crystal in weakly doped bilayer graphene with an energy gap opened by a perpendicular electric field. We argue that in this system the formation of the Wigner Crystal is not only possible, but different phases of the crystal with very peculiar properties may exist here depending on the system parameters.
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We present a detailed theoretical analysis of the Wigner crystal states in confined semiconducting carbon nanotubes. We show by robust scaling arguments as well as by detailed semi-microscopic calculations that the effective exchange interaction has an SU(4) symmetry, and can reach values even as large as $Jsim 100 {rm ,K}$ in weakly screened, small diameter nanotubes, close to the Wigner crystal - electron liquid crossover. Modeling the nanotube carefully and analyzing the magnetic structure of the inhomogeneous electron crystal, we recover the experimentally observed phase boundaries of Deshpande and Bockrath [V. V. Deshpande and M. Bockrath, Nature Physics $mathbf 4$, 314 (2008)]. Spin-orbit coupling only slightly modifies these phase boundaries, but breaks the spin symmetry down to SU(2)$times$SU(2), and in Wigner molecules it gives rise to interesting excitation spectra, reflecting the underlying SU(4) as well as the residual SU(2)$times$SU(2) symmetries.
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By combining angle-resolved photoemission spectroscopy and scanning tunneling microscopy we reveal the structural and electronic properties of multilayer graphene on Ru(0001). We prove that large ethylene exposure allows to synthesize two distinct phases of bilayer graphene with different properties. The first phase has Bernal AB stacking with respect to the first graphene layer, displays weak vertical interaction and electron doping. The long-range ordered moire pattern modulates the crystal potential and induces replicas of the Dirac cone and minigaps. The second phase has AA stacking sequence with respect to the first layer, displays weak structural and electronic modulation and p-doping. The linearly dispersing Dirac state reveals the nearly-freestanding character of this novel second layer phase.
We present the first measurements of cyclotron resonance of electrons and holes in bilayer graphene. In magnetic fields up to B = 18 T we observe four distinct intraband transitions in both the conduction and valence bands. The transition energies are roughly linear in B between the lowest Landau levels, whereas they follow sqrt{B} for the higher transitions. This highly unusual behavior represents a change from a parabolic to a linear energy dispersion. The density of states derived from our data generally agrees with the existing lowest order tight binding calculation for bilayer graphene. However in comparing data to theory, a single set of fitting parameters fails to describe the experimental results.
We report the first experimental study of the quantum interference correction to the conductivity of bilayer graphene. Low-field, positive magnetoconductivity due to the weak localisation effect is investigated at different carrier densities, including those around the electroneutrality region. Unlike conventional 2D systems, weak localisation in bilayer graphene is affected by elastic scattering processes such as intervalley scattering. Analysis of the dephasing determined from the magnetoconductivity is complemented by a study of the field- and density-dependent fluctuations of the conductance. Good agreement in the value of the coherence length is found between these two studies.
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