3,711 research outputs found

    Commensuration and Interlayer Coherence in Twisted Bilayer Graphene

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    The low energy electronic spectra of rotationally faulted graphene bilayers are studied using a long wavelength theory applicable to general commensurate fault angles. Lattice commensuration requires low energy electronic coherence across a fault and preempts massless Dirac behavior near the neutrality point. Sublattice exchange symmetry distinguishes two families of commensurate faults that have distinct low energy spectra which can be interpreted as energy-renormalized forms of the spectra for the limiting Bernal and AA stacked structures. Sublattice-symmetric faults are generically fully gapped systems due to a pseudospin-orbit coupling appearing in their effective low energy Hamiltonians.Comment: 4 pages RevTeX, 3 jpg figure

    Electronic structure of turbostratic graphene

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    We explore the rotational degree of freedom between graphene layers via the simple prototype of the graphene twist bilayer, i.e., two layers rotated by some angle θ\theta. It is shown that, due to the weak interaction between graphene layers, many features of this system can be understood by interference conditions between the quantum states of the two layers, mathematically expressed as Diophantine problems. Based on this general analysis we demonstrate that while the Dirac cones from each layer are always effectively degenerate, the Fermi velocity vFv_F of the Dirac cones decreases as θ0\theta\to 0^\circ; the form we derive for vF(θ)v_F(\theta) agrees with that found via a continuum approximation in Phys. Rev. Lett., 99:256802, 2007. From tight binding calculations for structures with 1.47θ<301.47^\circ \le \theta < 30^\circ we find agreement with this formula for θ5\theta \gtrsim 5^\circ. In contrast, for θ5\theta \lesssim 5^\circ this formula breaks down and the Dirac bands become strongly warped as the limit θ0\theta \to 0 is approached. For an ideal system of twisted layers the limit as θ0\theta\to0^\circ is singular as for θ>0\theta > 0 the Dirac point is fourfold degenerate, while at θ=0\theta=0 one has the twofold degeneracy of the ABAB stacked bilayer. Interestingly, in this limit the electronic properties are in an essential way determined \emph{globally}, in contrast to the 'nearsightedness' [W. Kohn. Phys. Rev. Lett., 76:3168, 1996.] of electronic structure generally found in condensed matter.Comment: Article as to be published in Phys. Rev B. Main changes: K-point mapping tables fixed, several changes to presentation

    Liquid-crystal patterns of rectangular particles in a square nanocavity

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    Using density-functional theory in the restricted-orientation approximation, we analyse the liquid-crystal patterns and phase behaviour of a fluid of hard rectangular particles confined in a two-dimensional square nanocavity of side length HH composed of hard inner walls. Patterning in the cavity is governed by surface-induced order, capillary and frustration effects, and depends on the relative values of particle aspect ratio κL/σ\kappa\equiv L/\sigma, with LL the length and σ\sigma the width of the rectangles (LσL\ge\sigma), and cavity size HH. Ordering may be very different from bulk (HH\to\infty) behaviour when HH is a few times the particle length LL (nanocavity). Bulk and confinement properties are obtained for the cases κ=1\kappa=1, 3 and 6. In the confined fluid surface-induced frustration leads to four-fold symmetry breaking in all phases (which become two-fold symmetric). Since no director distorsion can arise in our model by construction, frustration in the director orientation is relaxed by the creation of domain walls (where the director changes by 9090^{\circ}); this configuration is necessary to stabilise periodic phases. For κ=1\kappa=1 the crystal becomes stable with commensuration transitions taking place as HH is varied. In the case κ=3\kappa=3 the commensuration transitions involve columnar phases with different number of columns. Finally, in the case κ=6\kappa=6, the high-density region of the phase diagram is dominated by commensuration transitions between smectic structures; at lower densities there is a symmetry-breaking isotropic \to nematic transition exhibiting non-monotonic behaviour with cavity size.Comment: 31 pages, 15 figure

    Quantum interference at the twist boundary in graphene

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    We explore the consequences of a rotation between graphene layers for the electronic spectrum. We derive the commensuration condition in real space and show that the interlayer electronic coupling is governed by an equivalent commensuration in reciprocal space. The larger the commensuration cell, the weaker the interlayer coupling, with exact decoupling for incommensurate rotations and in the θ → 0 limit. Furthermore, from first-principles calculations we determine that even for the smallest possible commensuration cell the decoupling is effectively perfect, and thus graphene layers will be seen to decouple for all rotation angles

    Magnetic hour-glass dispersion and its relation to high-temperature superconductivity in iron-tuned Fe1+y_{1+y}Te0.7_{0.7}Se0.3_{0.3}

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    High-temperature superconductivity remains arguably the largest outstanding enigma of condensed matter physics. The discovery of iron-based high-temperature superconductors has renewed the importance of understanding superconductivity in materials susceptible to magnetic order and fluctuations. Intriguingly they show magnetic fluctuations reminiscent of the superconducting (SC) cuprates, including a 'resonance' and an 'hour-glass' shaped dispersion, which provide an opportunity to new insight to the coupling between spin fluctuations and superconductivity. Here we report inelastic neutron scattering data on Fe1+y_{1+y}Te0.7_{0.7}Se0.3_{0.3} using excess iron concentration to tune between a SC (y=0.02y=0.02) and a non-SC (y=0.05y=0.05) ground states. We find incommensurate spectra in both samples but discover that in the one that becomes SC, a constriction towards a commensurate hourglass shape develop well above TcT_c. Conversely a spin-gap and concomitant spectral weight shift happen below TcT_c. Our results imply that the hourglass shaped dispersion is most likely a pre-requisite for superconductivity, whereas the spin-gap and shift of spectral weight are consequences of superconductivity. We explain this observation by pointing out that an inwards dispersion towards the commensurate wave-vector is needed for the opening of a spin gap to lower the magnetic exchange energy and hence provide the necessary condensation energy for the SC state to emerge