Lorentz shear modulus of fractional quantum Hall states

We show that the Lorentz shear modulus of macroscopically homogeneous electronic states in the lowest Landau level is proportional to the bulk modulus of an equivalent system of interacting classical particles in the thermodynamic limit. Making use of this correspondence we calculate the Lorentz shear modulus of Laughlin's fractional quantum Hall states at filling factor $\nu=1/m$ ($m$ an odd integer) and find that it is equal to $\pm \hbar mn/4$, where $n$ is the density of particles and the sign depends on the direction of magnetic field. This is in agreement with the recent result obtained by Read in arXiv:0805.2507 and corrects our previous result published in Phys. Rev. B {\bf 76}, 161305 (R) (2007).Comment: 8 pages, 3 figure

Real-Time Observation of Interlayer Vibrations in Bilayer and Few-Layer Graphene

International audienceWe report real-time observation of the interlayer shearing mode, corresponding; to the lateral oscillation of graphene planes, for bi- and few-layer graphene. Using a femtosecond pump-probe technique, we have followed coherent oscillations of this vibrational mode directly in the time domain. The shearing-mode frequency, as expected for an interlayer mode, exhibits a strong and systematic dependence on the number of layers, varying from 1.32 THz for the bulk limit to 0.85 THz for bilayer graphene. We explored the role of interactions with the external environment on this vibrational mode by comparing the response observed for graphene layers supported by different substrates and suspended in free space. No significant frequency shifts were observed

Asymmetric tubular oxygen-permeable ceramic membrane reactor for partial oxidation of methane

10.1021/jp0682917Journal of Physical Chemistry C111269194-920