Local density of states and scanning tunneling currents in graphene

Abstract

We present exact analytical calculations of scanning tunneling currents in locally disordered graphene using a multimode description of the microscope tip. Analytical expressions for the local density of states (LDOS) are given for energies beyond the Dirac cone approximation. We show that the LDOS at the $A$ and $B$ sublattices of graphene are out of phase by $\pi$ implying that the averaged LDOS, as one moves away from the impurity, shows no trace of the $2q_F$ (with $q_F$ the Fermi momentum) Friedel modulation. This means that a STM experiment lacking atomic resolution at the sublattice level will not be able of detecting the presence of the Friedel oscillations [this seems to be the case in the experiments reported in Phys. Rev. Lett. {\bf 101}, 206802 (2008)]. The momentum maps of the LDOS for different types of impurities are given. In the case of the vacancy, $2q_F$ features are seen in these maps. In all momentum space maps, $K$ and $K+K^{\prime }$ features are seen. The $K+K^{\prime }$ features are different from what is seen around zero momentum. An interpretation for these features is given. The calculations reported here are valid for chemical substitution impurities, such as boron and nitrogen atoms, as well as for vacancies. It is shown that the density of states close to the impurity is very sensitive to type of disorder: diagonal, non-diagonal, or vacancies. In the case of weakly coupled (to the carbon atoms) impurities, the local density of states presents strong resonances at finite energies, which leads to steps in the scanning tunneling currents and to suppression of the Fano factor.

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Cited by in corpus (12)

• Colloquium: The transport properties of graphene: An introduction
• Dirac materials
• Grain Boundary Loops in Graphene
• Unified description of the dc conductivity of monolayer and bilayer graphene at finite densities based on resonant scatterers
• Role of pseudospin in quasiparticle interferences in epitaxial graphene probed by high-resolution scanning tunneling microscopy
• Local density of states and Friedel oscillation in graphene
• Spectroscopy of Twisted Bilayer Graphene Correlated Insulators
• Electric-field-tunable electronic nematic order in twisted double-bilayer graphene
• Impurity-induced magnetic moments on the graphene-lattice Hubbard model: an inhomogeneous cluster DMFT study
• Dual-probe spectroscopic fingerprints of defects in graphene
• Transport anomaly at the ordering transition for adatoms on graphene
• Markov Inequality as a Tool for Linear-Scaling Estimation of Local Observables