Impurity scattering and size quantization effects in a single graphene nanoflake

By using Fourier-transform scanning tunneling spectroscopy we measure the interference patterns produced by the impurity scattering of confined Dirac quasiparticles in epitaxial graphene nanoflakes. Upon comparison of the experimental results with tight-binding calculations of realistic model flakes, we show that the characteristic features observed in the Fourier-transformed local density of states are related to scattering between different transverse modes (subbands) of a graphene nanoflake and allow direct insight into the gapped electronic spectrum of graphene. We also observe a strong reduction of quasiparticle lifetime which is attributed to the interaction with the underlying substrate. In addition, we show that the distribution of the on-site energies at flower defects leads to an effectively broken pseudospin selection rule, where intravalley backscattering is allowed.

Figure 1

(a) STM image of a GNF on Ag(111) ($V=0.1$ V; $I=300$ pA). (b) $dI/dV$ map of the area marked in (a) recorded at $V=10$ mV. (c) Corresponding FFT of the conductance map displaying intravalley (i) and intervalley (ii)–(iv) scattering features as well as reciprocal lattice and Moiré spots. Inset: close up of the scattering feature (iii). (d) Atomically resolved image showing Moiré and atomic lattice ($V=0.1$ V; $I=1.5$ nA). (e) STM image of a flower defect ($V=-0.2$ V; $I=800$ pA). (f) Dispersion relation of the flake shown in (a) with respect to the $K$ point, as derived from $dI/dV$ maps. Inset: schematic of the intervalley scattering process.

Figure 2

(a) Real space geometry of a metallic AGNR of width W. (b) Schematic representation of the constant energy contours of an AGNR with possible scattering processes (intervalley) indicated by arrows. Due to the transverse confinement $k_x=n\pi /W-K_{dx}$ is quantized giving rise to a number of scattering vectors originating at ${\vec{k}}_G^{\prime }$ (blue arrows) as compared to an infinite graphene sheet, where only points with antiparallel vectors ${\vec{k}}_G$ and ${\vec{k}}_G^{\prime }$ can be connected (thick blue arrow). (c) Resulting FT-LDOS of a metallic AGNR corresponding to the transitions depicted in (b).

Figure 3

(a) STM image of a compact GNF ($V=0.03$ V; $I=300$ pA). (b) Atomic model of a quasi-free-standing flake as used in the tight-binding calculations. (c) FT-LDOS of the region of the model flake marked in (b) assuming infinite quasiparticle lifetime and no symmetry breaking at grain boundary sites. The feature within the intervalley ring interior is directed towards the center of the FFT. (d) FT-LDOS including limited quasiparticle lifetime, thus yielding intervalley features aligned with the flake's long axis inside the scattering contour. (e) FT-LDOS including limited quasiparticle lifetime as well as AB sublattice symmetry breaking due to the implementation of a mass term at the rotational grain boundary sites. (f) FFT of the experimental $dI/dV$ map of the flake region marked in (a) exhibiting intravalley scattering (i), intervalley scattering (ii)–(iv), and higher order features (v). (g) Magnification of the scattering features visible in the experimental and theoretical FT-LDOS.