Estudo teórico do férmions de Dirac sem massa em um fita de grafeno com geometria helicoidal

Abstract

In the present work, the relativistic quantum motion of massless fermions in a helicoidal strip 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 state (LDOS) are obtained numerically by means of Numerov method. The combined effects of width of the strip (D), length of ribbon (L), twist parameter (ω) and B on the equations of motion and local density of states (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. Furthermore, the information on the twist angle is obtained from the study of elastic energy, where a methodology capable of linking the Theory of Elasticity with General Relativity is used, in which an expression for the elastic energy in the parameterization of the helicoid. It is observed that the elastic energy is continuous with respect to the twist angle and that, for more details on phase transitions and critical angle, an approach via DFT (Density Functional Theory) calculation would be necessary.