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      Spectral butterfly and mixed Dirac-Schr\"odinger fermion behavior on armchair uniaxial strained graphene

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          Abstract

          An exact mapping of the tight-binding Hamiltonian for a graphene's nanoribbon under any armchair uniaxial strain into an effective one-dimensional system is presented. As an application, for a periodic modulation we have found a gap opening at the Fermi level and a complex fractal spectrum, akin to the Hofstadter butterfly resulting from the Harper model. The latter can be explained by the commensurability or incommensurability nature of the resulting effective potential. When compared with the zig-zag uniaxial periodic strain, the spectrum shows much bigger gaps, although in general the states have a more extended nature. For a special critical value of the strain amplitude and wavelength, a gap is open. At this point, the electrons behave as Dirac femions in one direction, while in the other, a Schr\"odinger behavior is observed.

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          The structure of suspended graphene sheets

          The recent discovery of graphene has sparked significant interest, which has so far been focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particle. However, the structure of graphene - a single layer of carbon atoms densely packed in a honeycomb crystal lattice - is also puzzling. On the one hand, graphene appears to be a strictly two-dimensional (2D) material and exhibits such a high crystal quality that electrons can travel submicron distances without scattering. On the other hand, perfect 2D crystals cannot exist in the free state, according to both theory and experiment. This is often reconciled by the fact that all graphene structures studied so far were an integral part of larger 3D structures, either supported by a bulk substrate or embedded in a 3D matrix. Here we report individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or air. These membranes are only one atom thick and still display a long-range crystalline order. However, our studies by transmission electron microscopy (TEM) have revealed that suspended graphene sheets are not perfectly flat but exhibit intrinsic microscopic roughening such that the surface normal varies by several degrees and out-of-plane deformations reach 1 nm. The atomically-thin single-crystal membranes offer an ample scope for fundamental research and new technologies whereas the observed corrugations in the third dimension may shed light on subtle reasons behind the stability of 2D crystals.
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            Gauge fields, ripples and wrinkles in graphene layers

            We analyze elastic deformations of graphene sheets which lead to effective gauge fields acting on the charge carriers. Corrugations in the substrate induce stresses, which, in turn, can give rise to mechanical instabilities and the formation of wrinkles. Similar effects may take place in suspended graphene samples under tension.
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              Author and article information

              Journal
              1409.1964

              Nanophysics
              Nanophysics

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