On the foundations of inversion geometry

Hoffman, Alan J.

doi:10.1090/s0002-9947-1951-0044137-1

Cited by 20 publications

(1 citation statement)

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“…The helicoidal surface is one of the simplest periodic curved surfaces in one direction [ 16 ] and that has vanished mean curvature (minimal surfaces). Helicoidal microstructures occur often in biology, for example, in macro‐molecules as DNA [ 17–19 ] and in the animal and plant kingdoms.…”

Section: Introductionmentioning

confidence: 99%

Effects of a Uniform Magnetic Field on Twisted Graphene Nanoribbons

et al. 2023

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In the present work, the relativistic quantum motion of massless fermions in a helicoidal graphene nanoribbon under the influence of a uniform magnetic field is investigated. Considering a uniform magnetic field (B) aligned along the axis of helicoid, this problem is explored in the context of Dirac equation in a curved space-time. As this system does not support exact solutions due to considered background, the bound-state solutions and local density of states (LDOS) are obtained numerically by means of the Numerov method. The combined effects of width of the nanoribbon (D), length of ribbon (L), twist parameter (𝝎), and B on the equations of motion and LDOS are analyzed and discussed. It is verified that the presence of B produces a constant minimum value of local density of state on the axis of helicoid, which is possible only for values large enough of 𝝎, in contrast to the case for B = 0 already studied in the literature.

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Section: Introductionmentioning

confidence: 99%