Cloning of zero modes in one-dimensional graphene superlattices

One-dimensional (1D) graphene superlattices have been predicted to exhibit extra zero-energy modes about a decade ago, but an experimental proof has remained missing. Motivated by recent experimental progresses, here we perform quantum transport simulations for 1D graphene superlattices, considering electrostatically simulated potential profiles as realistic as possible. Combined with the analysis on the corresponding miniband structures, we find that the zero modes generated by the 1D superlattice potential can be further cloned to higher energies, which are also accessible by tuning the average carrier density. Our multiterminal transverse magnetic focusing simulations further reveal the modulation-controllable ballistic miniband transport for 1D graphene superlattices. A simple idea for creating a perfectly symmetric periodic potential is proposed at the end of this work for generating perfectly aligned zero modes. Our work provides a reliable guide to how the extra zero modes and their copies at higher energies feature in transport.