Interplay of boundary states of graphene nanoribbons with a Kondo impurity

We investigate the interplay of two highly localized, nearly degenerate electronic states, namely, a zero-energy edge mode in a graphene nanoribbon on the one hand and an Abrikosov-Suhl resonance located at a Kondo impurity on the other. On-surface synthesis of the ribbon structures in combination with intercalation of single-atom Kondo impurities by atomic manipulation in a scanning tunneling microscope junction offer full control of the atomic geometry of the system. Density functional theory provides the microscopic description to scrutinize the electronic features observed in experiment. We find the interaction of the two localized states and the resulting signatures of Kondo physics to be very sensitive to the placing of the atom, suggesting its use as a laboratory to study the interplay of the Kondo effect with other zero-bias anomalies as well as to tailor these states by controlling the atomic-scale coupling.

Figure 1

Assembly of Co-GNR complexes. (a), (b) Manipulation of Co atoms across the surface and underneath the GNR. $V=100\mathrm{mV}, I=11\mathrm{pA}$. (c) High-resolution STM image of the Co-GNR complex. The model shows magnified sketch of the Co intercalation position. Gray spheres depict C atoms and blue Co, respectively. $V=2\mathrm{mV}, I=48\mathrm{pA}$.

Figure 2

Au vs Co at GNR corner. DFT calculated side views of (a) a Co(1)-GNR complex and (b) a Au(1)-GNR complex revealing larger GNR distortion.

Figure 3

Tight-binding setup. (a) Model used for the tight-binding calculations containing 140 carbon atoms. Left GNR zigzag edge consists of $A$ atoms only, right edge of $B$ atoms. (b) Energy of the states closest to $E_{\mathrm{F}}$ in units of the nearest-neighbor hopping integral $t$. (c) Real-space distribution of the wave functions of HOMO and LUMO of the GNR, where disk size indicates the modulus of the wave function and color encodes the sign.

Figure 4

Co at corner site. (a) STM image of a Co(1)-GNR complex ($V=5\mathrm{mV}, I=30\mathrm{pA}$, mild Gaussian smoothing applied) along with a sketch of the configuration. (b) $dI/dV$ spectra taken at positions indicated in the sketch in (a). Red curve indicates a fit of an asymmetric Frota line. (c) Constant height AFM image and (d) current map of the complex shown in (a). Red crosses in (c) and (d) mark the same positions.

Figure 5

Calculated magnetization density. Evolution of the magnetization density with the Co atom moving from end state into the GNR's bulk; positions from top to bottom (1,3,4). Red volumes denote spin-up and blue colors spin-down magnetization. (Parameters: isosurface value of $\pm 0.001{\mu }_B/{\AA }^3$; spin DFT with the PBE exchange-correlation functional [63].)

Figure 6

Calculated LDOS. Electronic structure of cobalt intercalated at sites 1, 3, and 4 from top to bottom. Local density of states with Gaussian smearing of 40 meV. Negative values represent minority-spin states, positive values majority-spin states. Labels correspond to the carbon-ring sites as defined above.

Figure 7

Co at site 4. (a) $dI/dV$ spectra of a Co(4)-GNR complex. The inset sketches the intercalation sites of Au and Co atom and indicates the positions the spectra were taken at. (b) STM image ($V=4\mathrm{mV}, I=50\mathrm{pA}$), (c) AFM image, and (d) current map of the complex. Red crosses in (c) and (d) mark the same positions.

Figure 8

Co at site 3. (a) Upper panel: STM image ($V=5\mathrm{mV}, I=30\mathrm{pA}$, mild Gaussian smoothing applied). Lower panel: sketch of Co intercalation position. (b) $dI/dV$ spectra taken at positions indicated in (a). (c) Constant height AFM image of the Co(3)-GNR complex shown in (a). The protrusions below the GNR are presumably artifacts from a H atom, trapped below the tip and dragged along while scanning. (d) Current map of the area shown in (c). The red crosses in (c) and (d) mark the same positions.

Figure 9

Au and Co at one GNR. STM image of a GNR with an intercalated Co (bottom left corner) and Au (top right corner) atom. 2 mV, $I$ = 48 pA.

Figure 10

Au at corner position. (a) STM image of a Au(1)-GNR complex (left) next to a pristine GNR end (right). $V=2\mathrm{mV}, I=48\mathrm{pA}$. (b) $dI/dV$ spectra taken at the positions indicated by colored circles in (a).