Transport fingerprints at graphene superlattice Dirac points induced by a boron nitride substrate

Rafael Martinez-Gordillo,Frank Ortmann,Miguel Pruneda,Stephan Roche

doi:10.1103/physrevb.89.161401

Abstract

We report peculiar transport fingerprints at the secondary Dirac points created by the interaction between graphene and boron nitride layers. By performing ab initio calculations, the electronic characteristics of the moir\'e patterns produced by the interaction between layers are first shown to be in good agreement with experimental data, and further used to calibrate the tight-binding model implemented for the transport study. By means of a real-space order-N quantum transport (Kubo) methodology, low-energy (Dirac point) transport properties are contrasted with those of high-energy (secondary) Dirac points, including both Anderson disorder and Gaussian impurities to respectively mimic short-range and long-range scattering potentials. Mean free paths at the secondary Dirac points are found to range from 10 nm to a few hundreds of nm depending on the static disorder, while the observation of satellite resistivity peaks depends on the strength of quantum interferences and localization effects.

Highlights

We report peculiar transport fingerprints at the secondary Dirac points created by the interaction between graphene and boron nitride layers
Mean free paths at the secondary Dirac points are found to range from 10 nm to a few hundreds of nm depending on the static disorder, while the observation of satellite resistivity peaks depends on the strength of quantum interferences and localization effects
The presence of these patterns suggests that hexagonal boron nitride (h-BN) generates a superimposed periodic potential on graphene, significantly modifying its electronic spectrum, as evidenced by the formation of two electron-hole symmetric high-energy secondary Dirac points [12], revealed in both atomic-scale scanning tunneling spectroscopic measurements [11], as well as in various mesoscopic transport measurements focusing on the formation of a fractal energy spectrum (Hofstadter’s butterfly) in the presence of strong external magnetic fields [13,14,15,16]

Summary

Introduction

We report peculiar transport fingerprints at the secondary Dirac points created by the interaction between graphene and boron nitride layers. By means of a real-space order-N quantum transport (Kubo) methodology, low-energy (Dirac point) transport properties are contrasted with those of high-energy (secondary) Dirac points, including both Anderson disorder and Gaussian impurities to respectively mimic short-range and long-range scattering potentials.

Results

Conclusion