Chirality dependent frequency shift of radial breathing mode in metallic carbon nanotubes

A phonon frequency shift of the radial breathing mode for metallic single wall carbon nanotubes is predicted as a function of Fermi energy. Armchair nanotubes do not show any frequency shift while zigzag nanotubes exhibit phonon softening, but this softening is not associated with the broadening. This chirality dependence originates from a curvature-induced energy gap and a special electron-phonon coupling mechanism for radial breathing modes. Because of the particle-hole symmetry, only the off-site deformation potential contributes to the frequency shift. On the other hand, the on-site potential contributes to the Raman intensity, and the radial breathing mode intensity is stronger than that of the $G$ band. The relationship between the chirality dependence of the frequency shift of the radial breathing mode and the $\Gamma$ point optical phonon frequency shift is discussed.Comment: 12 pages, 7 figure

Selection Rules for One- and Two-Photon Absorption by Excitons in Carbon Nanotubes

Recent optical absorption/emission experiments showed that the lower energy optical transitions in carbon nanotubes are excitonic in nature, as predicted by theory. These experiments were based on the symmetry aspects of free electron-hole states and bound excitonic states. The present work shows, however, that group theory does not predict the selection rules needed to explain the two photon experiments. We obtain the symmetries and selection rules for the optical transitions of excitons in single-wall carbon nanotubes within the approach of the group of the wavevector, thus providing important information for the interpretation of theoretical and experimental optical spectra of these materials.Comment: 4 pages, 1 figure, 1 tabl

Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications

The carbon nanotubes field has evolved substantially since the publication of the bestseller "Carbon Nanotubes: Synthesis, Structure, Properties and Applications". The present volume builds on the generic aspects of the aforementioned book, which emphasizes the fundamentals, with the new volume emphasizing areas that have grown rapidly since the first volume, guiding future directions where research is needed and highlighting applications. The volume also includes an emphasis on areas like graphene, other carbon-like and other tube-like materials because these fields are likely to affect and influence developments in nanotubes in the next 5 years

Solid state properties: from bulk to nano

This book fills a gap between many of the basic solid state physics and materials science books that are currently available. It is written for a mixed audience of electrical engineering and applied physics students who have some knowledge of elementary undergraduate quantum mechanics and statistical mechanics. This book, based on a successful course taught at MIT, is divided pedagogically into three parts: (I) Electronic Structure, (II) Transport Properties, and (III) Optical Properties. Each topic is explained in the context of bulk materials and then extended to low-dimensional materials where applicable. Problem sets review the content of each chapter to help students to understand the material described in each of the chapters more deeply and to prepare them to master the next chapters