Direct evidence of the contribution of surface states to the Kondo resonance

Using low-temperature scanning tunneling microscopy/spectroscopy, the Kondo resonance was observed on an isolated 5, 10, 15, 20-tetrakis-(4-bromophenyl)-porphyrin-Co (TBrPP-Co) molecule adsorbed on the $\text{Si}\left(111\right)\text{−}\sqrt{3}\times \sqrt{3}\text{Ag}$ substrate. As the substrate has a two-dimensional surface state and does not have bulk states around the Fermi level $\left(E_{\text{F}}\right)$, the Fano-shaped peak near $E_{\text{F}}$ observed above the molecule caging a spin-active cobalt atom is a direct evidence of the contribution of the surface-state electrons to the Kondo resonance. The long decay length $\left(\sim 1.6\text{nm}\right)$ of the resonance also supports for the surface-state contribution.

Figure 1

(Color online) STM images of a $\text{Si}\left(111\right)\text{−}\sqrt{3}\times \sqrt{3}\text{Ag}$ substrate with 0.002 ML TBrPP-Co molecules adsorbed in it. (a) large-scale STM image on which both the isolated TBrPP-Co molecules (larger dots) and Ag adsorbates (smaller dots) are found (size: $80\text{nm}\times 80\text{nm}$, sample bias voltage $V_{\text{s}}:2.0\text{V}$, tunneling current $I_{\text{t}}:20\text{pA}$). Inset of (a) atomically resolved image of an uncovered region by the molecules. (b) Highly resolved image of the isolated TBrPP-Co molecules and Ag adsorbates. The background triangular lattice arises from the $\sqrt{3}\times \sqrt{3}$ structure of the substrate (size: $30\text{nm}\times 30\text{nm}$, $V_{\text{s}}:2.0\text{V}$, $I_{\text{t}}:20\text{pA}$). Inset of (b) shows a planar-shape model of the TBrPP-Co molecule. (c) Typical tunneling conductance spectrum taken on the clean $\text{Si}\left(111\right)\text{−}\sqrt{3}\times \sqrt{3}\text{Ag}$ region. The distinct peak at $\sim -1\text{V}$ corresponds to the $S_2/S_3$ surface states of the substrate.

Figure 2

(Color online) standing wave patterns observed on the same surface as that of Fig. 1. (a) and (b) $dI/dV$ images taken in the same step-crossing area at different $V_{\text{s}}$ [$+393\text{mV}$ for (a) and $+293\text{mV}$ for (b), $I_{\text{t}}:140\text{pA}$, size: $30\text{nm}\times 30\text{nm}$ for (a) and $25\text{nm}\times 25\text{nm}$ for (b)]. The modulation amplitude and frequency are 3 mV and 713 Hz, respectively, for the $dI/dV$ images. Inset of (b): Fourier-transformed pattern of (b). The central ring arises from the standing wave and the six surrounding dots are attributed to the $\sqrt{3}\times \sqrt{3}$ reconstruction of the substrate. (c) STM image taken with a small $V_{\text{s}}$ (10.5 mV) to show DOS distribution at $E_{\text{F}}$. The image was taken on a flat terrace to avoid possible tip damage (size: $25\text{nm}\times 25\text{nm}$, $I_{\text{t}}:100\text{pA}$).

Figure 3

(Color online) (a) three-dimensional image of an isolated TBrPP-Co molecule with the $\sqrt{3}\times \sqrt{3}$ triangular lattice. The arrow indicates the direction of the tip displacement for the measurement of the lateral-distance-dependent $dI/dV$ spectra. (b) $dI/dV$ spectrum taken above the center of the isolated molecule using a lock-in method with the modulation amplitude and frequency of 5 mV and 713 Hz, respectively. The dotted line shows a Fano-shaped fitting curve using Eq. (1) at $r=0$.

Figure 4

(Color online) (a) series of $dI/dV$ spectra with various tip displacements taken in a lock-in method with the modulation amplitude and frequency of 5 mV and 713 Hz, respectively. The stabilizing $V_{\text{s}}$ and $I_{\text{t}}$ were 130 mV and 100 pA, respectively, for $r=0–1.0\text{nm}$ and 1.8–2.5 nm, and 260 mV and 100 pA for $r=1.2$ and 1.4 nm. The vertical solid line indicates the Kondo resonance peaks located at 3 mV below the $E_{\text{F}}$. The dashed lines indicate the peaks located at around 30 and $-25\text{mV}$ with respect to the $E_{\text{F}}$. (b) normalized amplitude $A\left(r\right)/A\left(0\right)$ as a function of the lateral displacement $r$ calculated from the $dI/dV$ curves shown in (a). Since the molecule becomes unstable and easily rotatable at low bias voltages in the displacement of $r=1.2$ and 1.4 nm, the two spectra were taken at larger tip-sample gap distance by adjusting the stabilizing tunneling condition. The arrows in (b) imply that the amplitude at $r=1.2$ and 1.4 nm should be larger if the stabilization condition had been same as that of the other tip displacements.