Scanning tunneling microscopic (STM) studies of strain-induced local density of states modulations in single-layer graphene on SiO$_{2}$

We report strain-induced spatial modulations in the electronic density of states (DOS) of single-layer graphene on SiO$_{2}$. Spatially resolved topographic and spectroscopic measurements were performed simultaneously at 77 K and at pressures $<$ 10$^{-7}$ torr. Fourier transformation of local topography shows a distorted hexagon with lattice vectors ranging from a$_{0}$=3.0 $\pm $0.2{\AA} to 2.1$\pm $0.2 {\AA} as the result of surface corrugation from the roughness of the underlying substrate. A spatially varying strain map derived from local distortions of the lattice constants correlates well with the surface topography. Strained graphene, due to three dimensional surface corrugations of $\pm $ 5 {\AA} over 10 nm lateral distance, show parabolic ``U-shaped'' conductance vs. biased voltage spectra rather than the Dirac-like ``V-shaped'' spectra. In contrast, for regions of relaxed graphene, Dirac-like spectra are recovered. The Dirac voltage, V$_{D}$, determined from the biased voltage of conductance minimum, appears to be position independent at V$_{D}$=36$\pm $5 meV, while the minimum conductance and the degree of derivation from the Dirac-like spectra at low energies appear to correlate directly with the topography. This work was supported by NSF/NRI under Caltech/CSEM.