Cloning of Zero Modes in One-Dimensional Graphene Superlattices

TL;DR

This study uses quantum transport simulations to demonstrate the cloning of zero-energy modes in one-dimensional graphene superlattices, revealing controllable miniband transport and proposing a method to generate multiple zero modes experimentally.

Contribution

It provides the first detailed simulation-based evidence of zero mode cloning in 1D graphene superlattices and suggests a practical approach to realize multiple zero modes.

Findings

Zero modes can be cloned to higher energies accessible by tuning density.

Ballistic miniband transport can be modulated via magnetic focusing.

A symmetric periodic potential can generate up to 6 zero modes.

Abstract

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.