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We develop a method to predict the existence of edge states in graphene ribbons for a large class of boundaries. This approach is based on the bulk-edge correspondence between the quantized value of the Zak phase Z(k), which is a Berry…
We consider plane junctions with graphene electrodes, which are formed by a single-level system ("molecule") placed between the edges of two single-layer graphene half planes. We calculate the edge Green functions of the electrodes and the…
Using first-principles plane wave calculations we predict that electronic and magnetic properties of graphene nanoribbons can be affected by defect-induced itinerant states. The band gaps of armchair nanoribbons can be modified by hydrogen…
We investigate the electronic band structure of an undoped graphene armchair nanoribbon. We demonstrate that such nanoribbon always has a gap in its electronic spectrum. Indeed, even in the situations where simple single-electron…
Armchair graphene nanoribbons are a highly promising class of semiconductors for all-carbon nanocircuitry. Here, we present a new perspective on their electronic structure from simple model Hamiltonians and $\textit{ab initio}$…
Strain has been extensively employed to tailor graphene's properties and has emerged as a powerful tool for engineering gauge fields and exploring fundamental phenomena in artificial platforms like photonic graphene. Here we discover that,…
Edge states are ubiquitous for many condensed matter systems with multicomponent wave functions. For example, edge states play a crucial role in transport in zigzag graphene nanoribbons. Here, we report microscopic calculations of quantum…
Bilayer graphene nanoribbon with zigzag edge is investigated with the tight binding model. Two stacking structures, alpha and beta, are considered. The band splitting is seen in the alpha structure, while the splitting in the wave number…
Novel physical properties have been reported recently by stacking graphene-like systems in different configurations. Here, we explore the nature of emergent localized states at the edges of twisted bilayer graphene nanoribbons. Based on an…
In this comprehensive study, we conduct a theoretical investigation into the Stark shift of topological states (TSs) in finite armchair graphene nanoribbons (AGNRs) and heterostructures under transverse electric fields. Our focus centers on…
Electron transport in small graphene nanoribbons is studied by microwave emulation experiments and tight-binding calculations. In particular, it is investigated under which conditions a transport gap can be observed. Our experiments provide…
The existence of bound states in the continuum was predicted at the dawn of quantum mechanics by von Neumann and Wigner. In this work we discuss the mechanism of formation of these exotic states and the feasibility to observe them…
Knowledge of the topology of the electronic ground state of materials has led to deep insights to novel phenomena such as the integer quantum Hall effect and fermion-number fractionalization, as well as other properties of matter. Joining…
Density functional theory calculations are used to investigate the electronic structures of localized states at reconstructed armchair graphene edges. We consider graphene nanoribbons with two different edge types and obtain the energy band…
Disorder effects on the density of states in carbon nanotubes are analyzed by a tight binding model with Gaussian bond or site disorder. Metallic armchair and semiconducting zigzag nanotubes are investigated. In the strong disorder limit,…
We study transport length scales in carbon nanotubes and graphene ribbons under the influence of Anderson disorder. We present generalized analytical expressions for the density of states, the elastic mean free path and the localization…
Analytical solutions of the edge states were obtained for the (N, 0) type carbon nanotubes with distorted ending bonds. It was found that the edge states are mixed via the distortion. The total energies for N=5 and N>=7 are lower in the…
In this paper we study the effect of absorption peak correlation in finite length carbon nanotubes and graphene nanoribbons. It is shown, in the orthogonal {\pi}-orbital tight-binding model with the nearest neighbor approximation, that if…
A theory of electron states for graphene nanoribbons with a smoothly varying width is developed. It is demonstrated that the standard adiabatic approximation allowing to neglect the mixing of different standing waves is more restrictive for…
We study edge states in AB-stacked bilayer graphene (BLG) ribbon where the Chern number of the corresponding two-dimensional (2D) bulk Hamiltonian is zero. The existence and topological features of edge states when two layers ended with the…