Valley-driven Zitterbewegung in Kekulé-distorted graphene

Abstract

Graphene deposited on top of a copper(111) substrate may develop a Y-shaped Kekul\'e bond texture (Kekul\'e-Y), locking the momentum with the valley degree of freedom of its Dirac fermions. Consequently, the valley degeneracy of its band structure is broken, generating an energy dispersion with two nested Dirac cones with different Fermi velocities. This work investigates the dynamics of electronic wave packets in the Kekul\'e-Y superlattice with strength ${\mathrm{\ensuremath{\Delta}}}_{0}$. We show that, as a result of the valley-momentum coupling, a valley-driven oscillatory motion of the wave packets (Zitterbewegung) could appear, but with a drastically reduced attenuation rate and lower frequency (proportional to ${\mathrm{\ensuremath{\Delta}}}_{0}$) when compared to the Zitterbewegung effect associated with pristine graphene. Furthermore, we justify the presence of these Zitterbewegung frequencies in terms of the Berry connection matrix and a discrete symmetry present in the system. These results make Kekul\'e-Y graphene a compelling candidate for experimental observation of the Zitterbewegung phenomenon in a two-dimensional system.