Valley conductance and reflection probabilities in substrate-induced graphene superlattice

Abstract

We study the transport properties of mass-less and spin-less Dirac fermions in a substrate-induced graphene super-lattice. The tight binding model for the super-lattice gives the energy band structure and we classify the topological regions (trivial and non-trivial) depending on the topological order parameter. The transfer matrix approach is used to compute the probabilities of the reflection and transmission in terms of structural parameters and we investigate the valley-switching phenomenon for all values of incident electron energies (E). We observe that the Dirac fermions with valley degree of freedom sometimes completely and other times partially reflect and transmit to the other valley under some specific values of structure parameters suggesting that we have a finite value of switching probability (≤100%) for all values of E. Moreover, the conductance exhibits striking behaviour, showing a peak at each Dirac point, which merges and subsequently vanishes depending on the structure parameters.