Topologically protected wave packets and quantum rings in silicene

We study chiral wave packets moving along the zero line of a symmetry-breaking potential of vertical electric field in buckled silicene using an atomistic tight-binding approach with initial conditions set by an analytical solution of the Dirac equation. We demonstrate that the wave packet moves with a constant untrembling velocity and with a preserved shape along the zero line. Backscattering by the edge of the crystal is observed that appears with the transition of the packet from K to K′ valley or vice versa. We propose a potential profile that splits the wave packet and next produces interference of the split parts that acts as a quantum ring. The transition time exhibits Aharonov-Bohm oscillations in the external magnetic field that are translated to conductance oscillations when the intervalley scattering is present within the ring. We study wave packet dynamics as function of the width of the packet up to the limit of plane waves. In the stationary transport limit the conductance oscillation period is doubled and the scattering density oscillates between the left and right arms of the ring as function of the magnetic field. We demonstrate that this effect is also found in a quantum ring defined by the zero lines of the symmetry-breaking potential in bilayer graphene.