Helicoidal graphene nanoribbons: Chiraltronics

Abstract

We present a calculation of the effective geometry-induced quantum potential for the carriers in graphene shaped as a helicoidal nanoribbon. In this geometry the twist of the nanoribbon plays the role of an effective transverse electric field in graphene and this is reminiscent of the Hall effect. However, this effective electric field has a different sign for the two iso-spin states and translates into a mechanism to separate the two chiral species on the opposing rims of the nanoribbon. Iso-spin transitions are expected with the emission or absorption of microwave radiation which could be adjusted to be in the THz region.

Optical conductivity of curved graphene

“…for η = Aω ≪ 1, the second order differential equation (47) reduces to the Mathieu equation [42] Note that with such definitions q can take, in principle, any value. Using a different approach, the limit of the small curvature for a corrugated graphene sheet was also considered in [37], where the authors reduced the problem to the solution of a Mathieu equation [43]. The small deformation limit was studied using a geometrical language in [31], where the authors built the corresponding Dirac equation but did not consider its general solution, as provided in our work.…”

“…e is the electron electric charge, g s = 4 is the spin and pseudospin degenerescence, S is the area of the graphene sheet, Ω is the light frequency, Ω mn = E m − E n is the transition energy, f (ε) = (1+e β ε ) −1 is the Fermi-Dirac distribution function, β = 1/k B T and v i mn = m|v i |n are the matrix elements of the velocity operator in the Hamiltonian eigenvector basis (37).…”

DFT study on electronic properties of single‐ and double‐shell icosahedral fullerenes

“…The regression coefficients associated to the above curves are equal to 0.998 and 0.968, respectively; nevertheless an exponential curve gives better regression coefficient. Atanasov and Ellenbogen [13] recently calculated the H-L gaps of single-shell spherical-like icosahedral fullerenes. The gaps were 1.14 eV and 0.63 eV for fullerenes with 180 and 720 carbons, respectively, and sizes almost equal to iC 180 and iC 720 (Table 1).…”

“…Moreover, accurate electrostatics-based formulas were used for calculating ionization potential and electron affinity of single-shell fullerenes in ref. [13], which can be used for obtaining the electronegativity. Again, the electronegativity values found in ref.…”

“…Polyhedral carbon nanoparticles exhibit large graphene facets connected with curved or sharp zones, clearly visible by high-resolution TEM images and Raman spectroscopy as reported also by Pujals et al [7] Several theoretical works analyzed structures and electronic properties of spherical and polyhedral multi-layer fullerenes. [8][9][10][11][12][13][14][15][16][17] However, comparative studies on their electronic features as a function of nanoparticle size and number of concentric shells are scarce. In this article, fully optimized structures of single-and double-shell icosahedral fullerenes were used to get important electronic properties such as HOMO-LUMO gap (H-L gap), electronegativity, hardness, softness, and density of states (DOS) in the frame of density functional theory (DFT).…”