1,761 research outputs found

    Optical-phonon resonances with saddle-point excitons in twisted-bilayer graphene

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    Twisted-bilayer graphene (tBLG) exhibits van Hove singularities in the density of states that can be tuned by changing the twisting angle θ\theta. A θ\theta-defined tBLG has been produced and characterized with optical reflectivity and resonance Raman scattering. The θ\theta-engineered optical response is shown to be consistent with persistent saddle-point excitons. Separate resonances with Stokes and anti-Stokes Raman scattering components can be achieved due to the sharpness of the two-dimensional saddle-point excitons, similar to what has been previously observed for one-dimensional carbon nanotubes. The excitation power dependence for the Stokes and anti-Stokes emissions indicate that the two processes are correlated and that they share the same phonon.Comment: 5 pages, 6 figure

    Bounds on Integrals of the Wigner Function

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    The integral of the Wigner function over a subregion of the phase-space of a quantum system may be less than zero or greater than one. It is shown that for systems with one degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over all possible states, reduces to the problem of finding the greatest and least eigenvalues of an hermitian operator corresponding to the subregion. The problem is solved exactly in the case of an arbitrary elliptical region. These bounds provide checks on experimentally measured quasiprobability distributions.Comment: 10 pages, 1 PostScript figure, Latex file; revised following referees' comments; to appear in Physical Review Letter
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