  One-dimensional (1D) graphene superlattices have been predicted to exhibit
zero-energy modes a decade ago, but an experimental proof has remained missing.
Motivated by a recent experiment that could possibly shed light on this, 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 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 with strong modulation is proposed at the end of this work,
generating well aligned zero modes up to 6 within a reasonable gate strength.
