Confocal Raman spectroscopy has emerged as a major, versatile workhorse for the non-invasive characterization of graphene. Although it is successfully used to determine the number of layers, the quality of edges, and the effects of strain, doping and disorder, the nature of the experimentally observed broadening of the most prominent Raman 2D line has remained unclear. Here we show that the observed 2D line width contains valuable information on strain variations in graphene on length scales far below the laser spot size, that is, on the nanometre-scale. This finding is highly relevant as it has been shown recently that such nanometre-scaled strain variations limit the carrier mobility in high-quality graphene devices. Consequently, the 2D line width is a good and easily accessible quantity for classifying the crystalline quality, nanometre-scale flatness as well as local electronic properties of graphene, all important for future scientific and industrial applications.

One of the fundamental properties of semiconductors is their ability to support highly tunable electric currents in the presence of electric fields or carrier concentration gradients. These properties are described by transport coefficients such as electron and hole mobilities. Over the last decades, our understanding of carrier mobilities has largely been shaped by experimental investigations and empirical models. Recently, advances in electronic structure methods for real materials have made it possible to study these properties with predictive accuracy and without resorting to empirical parameters. These new developments are unlocking exciting new opportunities, from exploring carrier transport in quantum matter to in silico designing new semiconductors with tailored transport properties. In this article, we review the most recent developments in the area of ab initio calculations of carrier mobilities of semiconductors. Our aim is threefold: to make this rapidly-growing research area accessible to a broad community of condensed-matter theorists and materials scientists; to identify key challenges that need to be addressed in order to increase the predictive power of these methods; and to identify new opportunities for increasing the impact of these computational methods on the science and technology of advanced materials. The review is organized in three parts. In the first part, we offer a brief historical overview of approaches to the calculation of carrier mobilities, and we establish the conceptual framework underlying modern ab initio approaches. We summarize the Boltzmann theory of carrier transport and we discuss its scope of applicability, merits, and limitations in the broader context of many-body Green's function approaches. We discuss recent implementations of the Boltzmann formalism within the context of density functional theory and many-body perturbation theory calculations, placing an emphasis on the key computational challenges and suggested solutions. In the second part of the article, we review applications of these methods to materials of current interest, from three-dimensional semiconductors to layered and two-dimensional materials.In particular, we discuss in detail recent investigations of classic materials such as silicon, diamond, gallium arsenide, gallium nitride, gallium oxide, and lead halide perovskites as well as lowdimensional semiconductors such as graphene, silicene, phosphorene, molybdenum disulfide, and indium selenide. We also review recent efforts toward highthroughput calculations of carrier transport. In the last part, we identify important classes of materials for which an ab initio study of carrier mobilities arXiv:1908.01733v1 [cond-mat.mtrl-sci] 5 Aug 2019First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional mate is warranted. We discuss the extension of the methodology to study topological quantum matter and materials for spintronics and we comment on the possibility of incorporating Berry-phase effects ...

Many-body effects resulting from strong electron-electron and electron-phonon interactions play a significant role in graphene physics. We report on their manifestation in low B field magneto-phonon resonances in high-quality exfoliated single-layer and bilayer graphene encapsulated in hexagonal boron nitride. These resonances allow us to extract characteristic effective Fermi velocities, as high as 1.20 × 10(6) m/s, for the observed "dressed" Landau level transitions, as well as the broadening of the resonances, which increases with the Landau level index.

There are a number of theoretical proposals based on strain engineering of graphene and other two-dimensional materials, however purely mechanical control of strain fields in these systems has remained a major challenge. The two approaches mostly used so far either couple the electrical and mechanical properties of the system simultaneously or introduce some unwanted disturbances due to the substrate. Here, we report on silicon micromachined comb-drive actuators to controllably and reproducibly induce strain in a suspended graphene sheet in an entirely mechanical way. We use spatially resolved confocal Raman spectroscopy to quantify the induced strain, and we show that different strain fields can be obtained by engineering the clamping geometry, including tunable strain gradients of up to 1.4%/μm. Our approach also allows for multiple axis straining and is equally applicable to other two-dimensional materials, opening the door to investigating their mechanical and electromechanical properties. Our measurements also clearly identify defects at the edges of a graphene sheet as being weak spots responsible for its mechanical failure.