Efeito zitterbewegung na bicamada de grafeno com trigonal warping

Abstract

Analyzing the low-energy band structure in Bernal-stacked graphene bilayers (AB), three Dirac mini-cones are observed around the K and K′ valleys, whose physical rationale is associated with the well-known trigonal warping effect. This effect induces the asymmetry in the band structure. In this context, we theoretically investigate the time evolution of a Gaussian wave packet propagating through a graphene bilayer sample to examine the role of trigonal warping in the dynamics. Numerically solving the time-dependent Schrödinger equation is necessary to calculate the expected values of the position (x, y) of the center of mass and the total probability densities of the wave packet. This calculation is performed using a numerical formalism based on the split-operator technique. The method is applied within the framework of continuous Dirac Hamiltonians, both for the 2-band and 2-band models, taking into account the aforementioned effects arising from non-perpendicular interlayer hoppings in the case of graphene bilayers. In addition to a numerical approach, an analytical approach is pursued from the standpoint of quantum mechanics propagators using Green’s functions G(r, r′, t). Transient spatial oscillations due to the effect known as zitterbewegung are discussed for different initial pseudospin polarizations, widths, energies, and momenta of the initial wave packets.