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The thickness $\theta(G)$ of a graph $G$ is the minimum number of planar spanning subgraphs into which the graph $G$ can be decomposed. As a topological invariant of a graph, it is a measurement of the closeness to planarity of a graph, and…

Combinatorics · Mathematics 2012-02-01 Yan Yang , Xiangheng Kong

In this work we investigated correlations between the internal microstructure and sample size (lateral as well as thickness) of mesoscopic, tens of nanometer thick graphite (multigraphene) samples and the temperature $(T)$ and field $(B)$…

Materials Science · Physics 2015-05-13 J. Barzola-Quiquia , J. -L. Yao , P. Rödiger , K. Schindler , P. Esquinazi

Diffusion and drift of a graphene flake on a graphite surface are analyzed. A potential energy relief of the graphene flake is computed using ab initio and empirical calculations. Based on the analysis of this relief, different mechanisms…

Mesoscale and Nanoscale Physics · Physics 2015-05-27 Irina V. Lebedeva , Andrey A. Knizhnik , Andrey M. Popov , Olga V. Ershova , Yurii E. Lozovik , Boris V. Potapkin

Over the past twenty years, the field of plasmonics has been revolutionized with the isolation and utilization of two--dimensional materials, particularly graphene. Consequently there is significant interest in rapid, robust, and highly…

Numerical Analysis · Mathematics 2024-10-10 David Nicholls , Tianyu Zhu

We have implemented a generic method, based on the 2n+1 theorem within density functional perturbation theory, to calculate the anharmonic scattering coefficients among three phonons with arbitrary wavevectors. The method is used to study…

Materials Science · Physics 2014-06-24 Lorenzo Paulatto , Francesco Mauri , Michele Lazzeri

The orbital magnetism is studied in graphene monolayer within the effective mass approximation. In models of short-range and long-range disorder, the magnetization is calculated with self-consistent Born approximation. In the zero-field…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 Mikito Koshino , Tsuneya Ando

Graphene is a one-atom-thick sheet of carbon atoms arranged in a honeycomb lattice. It was first obtained by exfoliation of graphite in 2004 and has since evolved into a thriving research topic because of its attractive mechanical, thermal,…

Optics · Physics 2014-06-04 Philippe Tassin , Thomas Koschny , Costas M. Soukoulis

We obtain analytic expressions for the conductivity of pristine (pure) graphene in the framework of the Dirac model using the polarization tensor in (2+1)-dimensions defined along the real frequency axis. It is found that at both zero and…

Materials Science · Physics 2016-07-13 G. L. Klimchitskaya , V. M. Mostepanenko

The effect of increased electron-density (from adsorbed Li atoms) in polyacenes and in nano-ribbons with zig-zag edge is discussed in terms of resonance theoretical considerations and in terms edge-localized frontier molecular orbitals. The…

Chemical Physics · Physics 2025-11-10 Yenni P. Ortiz , Douglas J. Klein , Thomas H. Seligman

In this work, we present numerical results for the second and third order conductivities of the plain graphene and gapped graphene monolayers associated with the second and third harmonic generation, the optical rectification and the…

Mesoscale and Nanoscale Physics · Physics 2020-02-05 G. B. Ventura , D. J. Passos , J. M. Viana Parente Lopes , J. M. B. Lopes dos Santos

Ab-initio calculations based on density functional theory (DFT) have been performed to study the optical properties of pure graphene and have been compared to that of individual boron (B), nitrogen (N) and BN co-doped graphene sheet. The…

Mesoscale and Nanoscale Physics · Physics 2020-05-22 Pooja Rani , Girija S Dubey , V. K. Jindal

The electronic structure of the zero-gap two-dimensional graphene has a charge neutrality point exactly at the Fermi level that limits the practical application of this material. There are several ways to modify the Fermi-level-region of…

Materials Science · Physics 2017-09-13 Elena Voloshina , Denis Usvyat , Martin Schuetz , Yuriy Dedkov , Beate Paulus

Nano-rippled graphene, a structurally modified graphene, presents a novel material with a large range of possible applications including sensors, electrodes, coatings, optoelectronics, spintronics and straintronics. In this work we have…

Mesoscale and Nanoscale Physics · Physics 2015-11-20 Iva Šrut Rakić , Davor Čapeta , Milivoj Plodinec , Marko Kralj

Fast modulation and switching of light at visible and near-infrared (vis-NIR) frequencies is of utmost importance for optical signal processing and sensing technologies. No fundamental limit appears to prevent us from designing…

Mesoscale and Nanoscale Physics · Physics 2015-06-25 Renwen Yu , Valerio Pruneri , F. Javier Garcia de Abajo

We study theoretically the single-electron triangular zigzag graphene quantum dot in three typical in-plane electric fields. The far-infrared absorption spectra of the dot are calculated by the tight-binding method and then the optical…

Mesoscale and Nanoscale Physics · Physics 2017-08-16 Qing-Rui Dong , Chun-Xiang Liu

Graphene superlattices formed by periodic strain are considered theoretically. It is shown that electron energy spectrum consists of minibands obtained by folding of the cone at the boundaries of the superlattice Brillouin zone with very…

Mesoscale and Nanoscale Physics · Physics 2015-06-03 Yu. Yu. Kiselev , L. E. Golub

We observe optical third harmonic generation from graphene and few-layer graphite flakes produced by exfoliation. The emission scales with the cube of the intensity of the incident near-infrared femtosecond pulses and has a wavelength that…

Mesoscale and Nanoscale Physics · Physics 2013-03-20 Nardeep Kumar , Jatinder Kumar , Chris Gerstenkorn , Rui Wang , Hsin-Ying Chiu , Arthur L. Smirl , Hui Zhao

Micrometer width and nanometer thick wires with different shapes were produced $\approx 3~\upmu$m below the surface of a diamond crystal using a microbeam of He$^+$ ions with 1.8~MeV energy. Initial samples are amorphous and after annealing…

Mesoscale and Nanoscale Physics · Physics 2017-04-05 J. Barzola-Quiquia , T. Lühmann , R. Wunderlich , M. Stiller , M. Zoraghi , J. Meijer , P. Esquinazi , J. Böttner , I. Estrela-Lopis

The microscopic quantum theory of nonlinear stimulated scattering of chiral particles in doped $AB$ stacked bilayer graphene on Coulomb field of charged impurities in the presence of strong coherent electromagnetic radiation is presented.…

Mesoscale and Nanoscale Physics · Physics 2019-07-26 A. G. Ghazaryan , Kh. V. Sedrakian

Local electrical imaging using microwave impedance microscope is performed on graphene in different modalities, yielding a rich hierarchy of the local conductivity. The low-conductivity graphite oxide and its derivatives show significant…

Mesoscale and Nanoscale Physics · Physics 2016-09-21 Worasom Kundhikanjana , Keji Lai , Hailiang Wang , Hongjie Dai , Michael A. Kelly , Zhi-xun Shen