Propriedades eletrônicas de uma bicamada de grafeno com ponte tipo buraco de minhoca de Ellis-Bronnikov generalizado - Souza, Thiago Felício de (2023)
In this work, we investigate the spinless stationary Schrodinger equation for the electron when it is permanently constrained to move in a generalized Ellis-Bronnikov wormhole surface is investigated means of a confined potential. It was verified that the curvature of the surface gives rise to a geometric potential that, consequently, affects the electronic dynamics. The analytical results are determined in the limiting cases R → 0 and u → ∞, and the qualitative ones after analyzing the graphs of the effective potential with the meridian-coordinate u. With this, it is seen that the case of the catenoid-type Lorentzian variety is a special case of the model we work with, since it only gives us a potential well, and that n controls the deformation of the wormhole, different from R, which tells us about its size. The catenoid-cylinder transition is present when we increase n, that is, the energy scale decreases as we grow n. For n > 2, potential wells appear symmetrically for u = 0 and become deeper when increasing n, confining the electron at the edges.