Related papers: Interplay between boundary conditions and Wilson's…
We address the electronic structure and magnetic properties of vacancies and voids both in graphene and graphene ribbons. Using a mean field Hubbard model, we study the appearance of magnetic textures associated to removing a single atom…
We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Friedmann-Lemaitre universe. We explain and employ some basic concepts such as Dirac observables, Dirac brackets, gauge-fixing…
The stationary Dirac equation $(p\cdot\sigma)\psi=E\psi$, confined to a two-dimensional (2D) region, supports states propagating along the boundary and decaying exponentially away from the boundary. These edge states appear on the 2D…
The close approach of the Fermi energy EF of a Dirac semimetal to the Dirac point ED uncovers new physics such as velocity renormalization,1,2,3 and the Dirac plasma 4,5 at |EF -ED| < kBT, where kBT is the thermal energy. In graphene,…
Structure and coordinate dependence of the reflected wave, as well as boundary conditions for quasi-particles of graphene and the two dimensional electron gas in sheets with abrupt lattice edges are obtained and analyzed by the Green's…
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 $\textit{ab initio}$…
The zero gap surface states of a 3D-topological insulator host Dirac fermions with spin locked to the momentum. The gap-less Dirac fermions exhibit electronic behaviour different from those predicted in conventional materials. While…
This review aims at a theoretical discussion of Dirac points in two-dimensional systems. Whereas Dirac points and Dirac fermions are prominent low-energy electrons in graphene (two-dimensional graphite), research on Dirac fermions in…
We show that in bilayer graphene it is possible to achieve a very restrictive confinement of the massless Dirac fermions zero-modes by using inhomogeneous magnetic fields. Specifically, we show that, using a suitable nonuniform magnetic…
Experiments on hexagonal graphene-like structures using microwave measuring techniques are presented. The lowest transverse-electric resonance of coupled dielectric disks sandwiched between two metallic plates establishes a tight-binding…
A wide range of materials like graphene, topological insulators and transition metal dichalcogenides (TMDs) share an interesting property: the low energy excitations behave as Dirac particles. This emergent behavior of Dirac quasiparticles…
The virial and the Hellmann--Feynman theorems for massless Dirac electrons in a solid are derived and analyzed using generalized continuity equations and scaling transformations. Boundary conditions imposed on the wave function in a finite…
A graphene nanoribbon is a good candidate for a $(1+1)$ Chern-Simons topological insulator since it obeys particle-hole symmetry. We show that in a finite semiconducting armchair ribbon, which has two zigzag edges and two armchair edges, a…
The modified Dirac-Pauli equations, which are introduced by means of ${\gamma_5}$-mass factorization of the ordinary Klein-Gordon operator, are considered. We also take into account the interaction of fermions with the intensive homogenous…
We evaluate the dispersion relation for massless fermions, described by the Dirac equation, and for zero-spin bosons, described by the Klein-Gordon equation, moving in two dimensions and in the presence of a one-dimensional periodic…
Tailor-made graphene nanostructures can exhibit symmetry-protected topological boundary states that host localized spin-$1/2$ moments. However, one frequently observes charge transfer on coinage metal substrates, which results in spinless…
Electronic structures of the zigzag bilayer graphite nanoribbons(Z-BGNR) with various ribbon width $N$ are studied within the tight binding approximation. Neglecting the inter-layer hopping amplitude $\gamma_4$, which is an order of…
Graphene nanoribbons with armchair edges are studied for externally enhanced, but realistic parameter values: enhanced Rashba spin-orbit coupling due to proximity to a transition metal dichalcogenide like WS$_{2}$, and enhanced Zeeman field…
We construct the new one-dimensional Dirac Hamiltonians that are spectrally isomorphic (not isospectral) with the known exactly solvable models. Explicit formulas for their spectra and eigenstates are provided. The operators are utilized…
A method is derived to solve the massless Dirac-Weyl equation describing electron transport in a mono-layer of graphene with a scalar potential barrier U(x,t), homogeneous in the y-direction, of arbitrary x- and time dependence. Resonant…