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We analyze a manifestation of the partial ordering transition of adatoms on graphene in resistivity measurements. We find that Kekule mosaic ordering of adatoms increases sheet resistance of graphene, due to a gap opening in its spectrum, and that critical fluctuations of the order parameter lead to a non-monotonic temperature dependence of resistivity, with a cusp-like minimum at T=T_c.
Several recent works have proposed that electron-electron interactions in
bilayer graphene can be tuned with the help of external parameters, making it
possible to stabilize different fractional quantum Hall states. In these prior
works, phase diagrams have been calculated based on a single Landau level
approximation. We go beyond this approximation and investigate the influence of
polarization effects and virtual interband transitions on stability of
fractional quantum Hall states in bilayer graphene. We find that for realistic
values of the dielectric constant, the phase diagram is strongly modified by
these effects. We illustrate this by evaluating the region of stability of the
We give a microscopic derivation of the chiral Luttinger liquid theory for the Laughlin states. Starting from the wave function describing an arbitrary incompressibly deformed Laughlin state (IDLS) we quantize these deformations. In this way we obtain the low-energy projections of local microscopic operators and derive the quantum field theory of edge excitations directly from quantum mechanics of electrons. This shows that to describe experimental and numeric deviations from chiral Luttinger liquid theory one needs to go beyond Laughlin's approximation. We show that in the large N limit the IDLS is described by the dispersionless Toda hierarchy.