Few-layer graphene (FLG) has been predicted to exist in various crystallographic stacking sequences, which can strongly influence the electronic properties of FLG. We demonstrate an accurate and efficient method to characterize stacking order in FLG using the distinctive features of the Raman 2D-mode. Raman imaging allows us to visualize directly the spatial distribution of Bernal (ABA) and rhombohedral (ABC) stacking in tri- and tetra-layer graphene. We find that 15% of exfoliated graphene tri- and tetra-layers is comprised of micron-sized domains of rhombohedral stacking, rather than of usual Bernal stacking. These domains are stable and remain unchanged for temperatures exceeding $800^{\circ}$C.

Chun Hung Lui Zhiqiang Li Zheyuan Chen Paul V. Klimov Louis E. Brus Tony F. Heinz

In a Bernal graphene bilayer, carbon atoms belong to two inequivalent sublattices A and B, with atoms that are coupled to the other layer by $p_\sigma$ bonds belonging to sublattice A and the other atoms belonging to sublattice B. We analyze the density of states and the conductivity of Bernal graphene bilayers when atoms of sublattice A or B only are randomly functionalized. We find that for a selective functionalization on sublattice B only, a mobility gap of the order of 0.5 eV is formed close to the Dirac energy at concentration of adatoms c > 0.01. In addition, at some other energies conductivity presents anomalous behaviors. We show that these properties are related to the bipartite structure of the graphene layer.

Ahmed Missaoui Jouda Jemaa Khabthani Nejm-Eddine Jaidane Didier Mayou Guy Trambly de Laissardière

The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P(x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P(x+1), which leads to the log-concavity of P(x+c) for any $c\geq 1$ due to Llamas and Mart\'{\i}nez-Bernal. As a consequence, we obtain the ratio monotonicity of the Boros-Moll polynomials obtained by Chen and Xia without resorting to the recurrence relations of the coefficients.

William Y. C. Chen Arthur L. B. Yang Elaine L. F. Zhou

Analogues for Hilbert C*-modules of classical results of Fourier series theory in Hilbert spaces are considered. Relations between different properties of orthogonal and orthonormal systems for Hilbert C*-modules are studied with special attention paid on the differences with the well-known Hilbert space situation.

Giovanni Landi Alexander Pavlov

We study the effect of chiral-tunneling in Bernal and Rombhohedral stacked trilayer-graphene (3LG). Based on the chirality of the electronic bands, at the K-point, (Rombhohedral) Bernal-3LG exhibits 100% (50%) transparency across a heterojunction. Utilizing this property, we further investigate the effect of electron collimation in 3LG. Due to the difference in the Berry's phase, we show that, Rombhohedral-3LG is a better electron collimator, compared to monolayer and Bernal-bilayer graphene. Since, Bernal-3LG can be decomposed into two separate channels consisting of a monolayer and a modified Bernal-bilayer graphene; the Bernal-3LG is weaker electron collimator, compared to Rombhohedral-3LG.

S. Bala Kumar Jing Guoa

We reply to the objections raised in a recent Comment (arXiv:1706.03023) regarding our observation of slow magnetic fluctuations and critical slowing down of magnetic fluctuations in the pseudogap phase of YBa$_2$Cu$_3$O$_y$ by zero-field and longitudinal-field muon spin relaxation (arXiv:1703.06799).

Jian Zhang Z. F. Ding C. Tan K. Huang O. O. Bernal P. -C. Ho G. D. Morris A. D. Hillier P. K. Biswas S. P. Cottrell H. Xiang X. Yao D. E. MacLaughlin Lei Shu

Monitoring electronic properties of 2D materials is an essential step to open a way for applications such as electronic devices and sensors. From this perspective, Bernal bilayer graphene (BLG) is a fairly simple system that offers great possibilities for tuning electronic gap and charge carriers' mobility by selective functionalization (adsorptions of atoms or molecules). Here, we present a detailed numerical study of BLG electronic properties when two types of adsorption site are present simultaneously. We focus on realistic cases that could be realized experimentally with adsorbate concentration c varying from 0.25% to 5%. For a given value of c, when the electronic doping is lower than c we show that quantum effects, which are ignored in usual semi-classical calculations, strongly affect the electronic structure and the transport properties. A wide range of behaviors is indeed found, such as gap opening, metallic behavior or abnormal conductivity, which depend on the adsorbate positions, the c value, the doping, and eventually the coupling between midgap states which can create a midgap band. These behaviors are understood by simple arguments based on the fact that BLG lattice is bipartite. We also analyze the conductivity at low temperature, where multiple scattering effects cannot be ignored. Moreover, when the Fermi energy lies in the band of midgap states, the average velocity of charge carriers cancels but conduction is still possible thanks to quantum fluctuations of the velocity.

Jouda Jemaa Khabthani Ahmed Missaoui Didier Mayou Guy Trambly de Laissardière

We construct a family of 1-convex threefolds, with exceptional curve C of type (0,-2), which are not embeddable in C^m \times CP_n. In order to show that they are not Kaehler we exhibit a real 3-dimensional chain A whose boundary is the complex curve C.

Giovanni Bassanelli Marco Leoni

We show that in type A or C any degenerate flag variety is in fact isomorphic to a Schubert variety in an appropriate partial flag manifold.

Giovanni Cerulli Irelli Martina Lanini

Muon spin relaxation (muSR) experiments have been carried out at low temperatures in the non-Fermi-liquid heavy-fermion compound YbRh_2Si_2. The longitudinal-field muSR relaxation function is exponential, indicative that the dynamic spin fluctuations are homogeneous. The relaxation rate 1/T_1 varies with applied field as H^{-y}, y = 1.0 \pm 0.1, which implies a scaling law of the form \chi''(\omega) \propto \omega^{-y} f(\omega/T), \lim_{x\to0} f(x) = x for the dynamic spin susceptibility.

K. Ishida D. E. MacLaughlin O. O. Bernal R. H. Heffner G. J. Nieuwenhuys O. Trovarelli C. Geibel F. Steglich