Effect of zitterbewegung on the propagation of wave packets in ABC-stacked multilayer graphene: an analytical and computational approach.

The time evolution of a low-energy two-dimensional Gaussian wave packet in ABC-stacked n-layer graphene (ABC-NLG) is investigated. Expectation values of the position (x, y) of center-of-mass and the total probability densities of the wave packet are calculated analytically using the Green's function method. These results are confirmed using an alternative numerical method based on the split-operator technique within the Dirac approach for ABC-NLG, which additionally allows to include external fields and potentials. The main features of the zitterbewegung (trembling motion) of wave packets in graphene are demonstrated and are found to depend not only on the wave packet width and initial pseudospin polarization, but also on the number of layers. Moreover, the analytical and numerical methods proposed here allow to investigate wave packet dynamics in graphene systems with an arbitrary number of layers and arbitrary potential landscapes.

Confined states in graphene quantum blisters.

Bilayer graphene samples may exhibit regions where the two layers are locally delaminated forming a so-called quantum blister in the graphene sheet. Electron and hole states can be confined in this graphene quantum blisters (GQB) by applying a global electrostatic bias. We scrutinize the electronic properties of these confined states under the variation of interlayer bias, coupling, and blister's size. The spectra display strong anti-crossings due to the coupling of the confined states on upper and lower layers inside the blister. These spectra are layer localized where the respective confined states reside on either layer or equally distributed. For finite angular momentum, this layer localization can be at the edge of the blister and corresponds to degenerate modes of opposite momenta. Furthermore, the energy levels in GQB exhibit electron-hole symmetry that is sensitive to the electrostatic bias. Finally, we demonstrate that confinement in GQB persists even in the presence of a variation in the inter-layer coupling.

Quantum transport across van der Waals domain walls in bilayer graphene.

Bilayer graphene can exhibit deformations such that the two graphene sheets are locally detached from each other resulting in a structure consisting of domains with different van der Waals inter-layer coupling. Here we investigate how the presence of these domains affects the transport properties of bilayer graphene. We derive analytical expressions for the transmission probability, and the corresponding conductance, across walls separating different inter-layer coupling domains. We find that the transmission can exhibit a valley-dependent layer asymmetry and that the domain walls have a considerable effect on the chiral tunnelling properties of the charge carriers. We show that transport measurements allow one to obtain the strength with which the two layers are coupled. We perform numerical calculations for systems with two domain walls and find that the availability of multiple transport channels in bilayer graphene significantly modifies the conductance dependence on inter-layer potential asymmetry.