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A class of graphene wound into three-dimensional periodic curved surfaces ("graphitic zeolites") is proposed and their electronic structures are obtained to explore how the massless Dirac fermions behave on periodic surfaces. We find in the…
Three-dimensional (3D) topological Dirac semimetal is a new kind of material that has a linear energy dispersion in 3D momentum space and can be viewed as an analog of graphene. Extensive efforts have been devoted to the understanding of…
Electrons moving in graphene behave as massless Dirac fermions, and they exhibit fascinating low-frequency electrical transport phenomena. Their dynamic response, however, is little known at frequencies above one terahertz (THz). Such…
Graphene, a two dimensional (2D) carbon sheet, acquires many of its amazing properties from the Dirac point nature of its electronic structures with negligible spin-orbit coupling. Extending to 3D space, graphene networks with negative…
This article reviews the basic theoretical aspects of graphene, a one atom thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric…
The Dirac equation in curved space is used to study the optical transmittance of deformed graphene along a given direction. Our theoretical analysis of the available experimental data for the light transmittance suggests that the periodic…
Realization of a three-dimensional (3D) analogue of graphene has been a central challenge in topological materials science. Graphene is stabilized by covalent bonding unlike conventional spin-orbit type 3D Dirac semimetals (DSMs). In this…
We review the transmission of Dirac electrons through a potential barrier in the presence of circularly polarized light. A different type of transmission is demonstrated and explained. Perfect transmission for nearly head-on collision in…
We investigate the electromechanical coupling in 2d materials. For non-Bravais lattices, we find important corrections to the standard macroscopic strain - microscopic atomic-displacement theory. We put forward a general and systematic…
Graphene is a truly two-dimensional atomic crystal with exceptional electronic and mechanical properties. Whereas conventional bulk and thin-film materials have been studied extensively, the key mechanical properties of graphene, such as…
We show that the low-energy electronic structure of graphene under a one-dimensional inhomogeneous magnetic field can be mapped into that of graphene under an electric field or vice versa. As a direct application of this transformation, we…
Local curvature, or bending, of a graphene sheet is known to increase the chemical reactivity presenting an opportunity for templated chemical functionalization. Using first principles calculations based on density functional theory (DFT)…
The recent experimental discovery of ${\rm Cd_3 As_2}$ and ${\rm Na_3 Bi}$ Dirac semimetals enables the study of the properties of chiral quasi-particles in three spatial dimensions. As demonstrated by photoemission, Dirac semimetals are…
We will present brief overview on the electronic and transport properties of graphene nanoribbons focusing on the effect of edge shapes and impurity scattering. The low-energy electronic states of graphene have two non-equivalent massless…
We discuss the novel electronic properties of graphene under an external periodic scalar or vector potential, and the analytical and numerical methods used to investigate them. When graphene is subjected to a one-dimensional periodic scalar…
It is highly desirable to integrate graphene into existing semiconductor technology, where the combined system is thermodynamically stable yet maintain a Dirac cone at the Fermi level. Firstprinciples calculations reveal that a certain…
Three-dimensional (3D) topological Dirac semimetals (TDSs) represent a novel state of quantum matter that can be viewed as '3D graphene'. In contrast to two-dimensional (2D) Dirac fermions in graphene or on the surface of 3D topological…
Peculiar electronic properties of graphene, including the universal dc conductivity and the pseudodiffusive shot noise, are usually attributed to a small vicinity of the charge-neutrality point, away from which electron's effective mass…
Theory of nuclear magnetic resonance (NMR) in graphene is presented. The canonical form of the electron-nucleus hyperfine interaction is strongly modified by the linear electronic dispersion. The NMR shift and spin-lattice relaxation time…
Formation of wrinkles is a common phenomenon in the large area growth of two dimensional layered materials on metallic substrates. Wrinkles can significantly affect the working of 2D materials based large scale electronic devices and…