Our samples were prepared by evaporating Co atoms onto a back-gated graphene/SiO2 device held inside the scanning tunnelling microscope at 4.2 K (see Methods). Figure 1 shows a representative 10×10 nm2 scanning tunnelling microscopy (STM) image of a graphene surface following Co adatom deposition. Co adatoms appear as 4-Å-high dome-like protrusions on the graphene surface (two cobalt adatoms can be seen in Fig. 1).

Figure 1
figure 1

10×10 nm2 STM topograph showing two cobalt adatoms resting atop a graphene sheet on a SiO2 substrate (tunnelling parameters: Vb=−0.25 V, I=10 pA, VG=0 V).

We made differential conductance, dI/dV, measurements with the STM tip held over individual Co adatoms to measure their energy-dependent local density of states (LDOS). Figure 2a shows typical dI/dV spectra obtained from a single Co adatom for different applied back-gate voltages, VG (changing VG changes the graphene charge-carrier density). Three different types of feature are observed in these spectra. The first is a dip observed at the Fermi level (EF) with a full-width at half-maximum of 10 meV (see the inset for a higher-resolution spectrum). The energy and width of this feature does not vary significantly with VG. The second feature is a series of resonant peaks in the dI/dV signal marked A, B, C and D in Fig. 2a. These peaks have a typical full-width at half-maximum of 25±5 meV. Their behaviour differs from the dip at EF in that their energy locations move in the same direction (and by similar amounts) as the Dirac point voltage (VD) as VD is varied by application of VG (VD marks the location of a dip seen in the graphene LDOS which is associated with the Dirac point energy6). The third feature corresponds to the peak in the dI/dV signal marked S in Fig. 2a. The energy of this feature changes as VG is varied, but it shifts energetically in the opposite direction compared with VD and disperses significantly faster. Figure 2a focuses only on spectra measured for −60 V<VG<−20 V because all dispersive features (A, B, C, D, S) shift out of the measurement window (−0.15 V<Vb<+0.15 V; Vb is the voltage of the sample with respect to the tip) for −20 V<VG<+60 V (see Supplementary Information for measurements of −20 V<VG<+60 V). Figure 2b summarizes how these spectral features shift in energy as a function of VG. Also plotted in Fig. 2b is the gate-dependent variation in Dirac point voltage (VD) measured on the graphene surface at least 10 nm away from any Co atom.

Figure 2: Gate-dependent dI/dV spectra of Co adatom on graphene.
figure 2

a, dI/dV spectra taken with the tip directly above a cobalt adatom on graphene for different back-gate voltages (VG) (initial tunnelling parameters: Vb=+0.15 V, I=22 pA; wiggle voltage Vrms=4 mV). Carrier-density-dependent spectral features are labelled A, B, C, D and S. Inset: High-resolution dI/dV spectrum of the dip-like feature at the Fermi level (initial tunnelling parameters: Vb=−0.08 V, I=8 pA, VG=−50 V; wiggle voltage Vrms=1 mV). b, Gate-voltage dependence of dI/dV spectral features observed in a. The error bars represent the uncertainty in the Lorentzian fitting of each spectral feature after a linear background subtraction. The open circles indicate the Dirac point voltage (VD) measured 10 nm from the cobalt atom.

To better understand how the presence of a Co adatom affects the behaviour of graphene, dI/dV measurements were also made on the bare graphene surface adjacent to a Co adatom. Figure 3a shows dI/dV (Vb) and I(Vb) curves measured on graphene 2.5 nm away (laterally) from the centre of a Co adatom. The dI/dV spectrum shows a 126-meV-wide gap-like feature at EF as expected for clean graphene (this is known to arise from inelastic tunnelling6), but an extra sharp dip is also observed 220 meV above EF. We measured how this new dI/dV feature varies spatially through the use of dI/dV mapping. Figure 3b–d shows dI/dV maps acquired near a single Co atom with different VG and Vb. The most striking aspect of these images is a narrow ring, arising from the spectral dip feature above EF, that appears centred around the Co adatom. The diameter of this ring is strongly dependent on Vb and VG. For example, Fig. 3c,d shows the ring diameter increasing as VG decreases, and Fig. 3b,d shows the diameter increasing as Vb increases.

Figure 3: dI/dV conductance measurements of the graphene surface near Co adatoms and surface defects.
figure 3

a, Off-atom dI/dV (Vb) and I(Vb) spectra of the graphene surface with the tip held a lateral distance 2.5 nm from the centre of a cobalt adatom (initial tunnelling parameters: Vb=+0.4 V, I=10 pA, VG=−40 V). bd, dI/dV maps of a single cobalt adatom and the surrounding graphene surface for varying Vb and VG values. The ‘X’ in b indicates the STM tip position for the spectrum shown in a. e, dI/dV map of a bare graphene surface (that is, without cobalt adatoms) that has been annealed at 500 °C in vacuum. Observed ring-like features are centred on defects in the graphene (tunnelling parameters: Vb=+0.7 V, I=8 pA, VG=−4 V). f, dI/dV spectrum taken with the tip held over the defect site found at the centre of a defect-induced ring such as those seen in e. Two prominent features are observed, labelled R and S (initial tunnelling parameters: Vb=−0.5 V, I=5 pA, VG=−2.5 V). Inset: STM topograph of the defect site found at the centre of a ring-like feature similar to those shown in e (tunnelling parameters: Vb=−0.3 V, I=10 pA, VG=−60 V).

dI/dV maps were also acquired over the bare graphene surface (that is, in the absence of cobalt adatoms) after annealing to higher temperatures (400–500 °C), as seen in Fig. 3e. Ring-like features similar to those found around Co adatoms are visible. The inset of Fig. 3f shows an STM topograph of the centre of one of these rings, revealing a defect in the graphene. A dI/dV spectrum taken at the site of such a defect (Fig. 3f) shows two clear spectroscopic features, R and S. R is observed to disperse in the same direction as VD when VG is varied, whereas S disperses in the opposite direction. The gate-voltage dependence of R is thus similar to that seen for the Co resonant states A, B, C and D, whereas the gate dependence of S is similar to the Co S feature. For fixed VG, however, the energies of R and S (seen for numerous defects) differ from the characteristic energies of the spectral features observed for Co adatoms.

The spectroscopic features we observed for cobalt adatoms and intrinsic graphene defects can be understood within a general impurity-physics framework, which we now describe. We start with the dip feature at EF observed for cobalt adatoms. This is not a conventional band-structure feature because it remains pinned to EF even as EF is swept through the graphene band-structure by back-gating. One possible origin of this feature is the Kondo effect, which can lead to a resonance at EF due to spin-screening of a local moment7. While cobalt is expected to be magnetic on graphene8,9,10, a Kondo resonance is generally expected to have a strongly gate-dependent width11, which is not observed here. This opens the possibility that the dip at EF arises from another origin, such as vibrational inelastic electron tunnelling12. Inelastic electron tunnelling causes an increase in dI/dV conductance at vibrational-energy thresholds for both positive and negative biases, and so can produce dip-like features in dI/dV spectra with a half-width equal to the vibrational mode energy12. To test this latter possibility, we carried out ab initio calculations of the vibrational energies of a Co adatom on graphene (see Methods). Our simulation indicates that this system has in-plane vibrational modes of 12 and 27 meV, as well as out-of-plane modes of 17, 40 and 53 meV. The lowest-energy mode calculated here is similar in magnitude to the 5 meV half-width of the dip we observe for cobalt adatoms, suggesting a possible inelastic electron tunnelling origin for this experimental feature.

We now turn to the cobalt-induced resonance features marked A, B, C and D in Fig. 2a,b. We identify these features with the impurity DOS of the combined cobalt/graphene electronic structure because they shift energetically in the same direction as the Dirac point voltage (VD) as EF is swept through the graphene band-structure. Figure 4a(i),b(i) shows sketches of how an impurity-induced DOS feature can be expected to shift as a result of applied gate bias. A likely explanation for these resonances (owing to their narrow energy width and spatial localization) is that they arise from a hybridization of cobalt atomic levels with graphene continuum states. Such resonances have been predicted for transition-metal atoms on graphene9,10,13, but our observed energy-level spacings and multiplicity do not precisely match these predictions. A possible explanation for the multiplicity of modes is hybrid electronic–vibrational (that is, vibronic)14 states, which are expected to have an energy spacing equal to the energy of a vibrational mode (our experimentally observed energy spacing is on the order of the energies we calculated for the out-of-plane Co/graphene vibrational modes). Finally, we point out that these states might be related to predicted fluctuations in LDOS due to screening of a ‘supercritical’ Coulomb impurity on graphene (that is, quasi-Rydberg states predicted in an ‘atomic-collapse’ scenario)15,16.

Figure 4: Schematic diagram of the tip and back-gate-induced ionization of an adatom on graphene.
figure 4

a(i), For Vb=0 and VG0 V the adatom impurity DOS feature (that is, resonance) is below EF and the adatom is neutral. a(ii), When a negative voltage is applied to the STM tip (Vb>0) the graphene bands shift upwards relative to EF (that is, there is a reduction in the local electron density of the graphene). A large enough shift pulls the impurity state above EF, thus changing the adatom charge state. b(i), For Vb=0 and VG<−35 V the Co impurity state is above EF and the Co adatom is charged (ionized). b(ii), When a positive bias is applied to the STM tip (Vb<0) the graphene bands shift downwards relative to EF. A large enough shift will push the impurity state below EF, thus returning the cobalt atom to a neutral state. c, Schematic diagram showing the positional dependence of the band-bending induced by an STM tip (considering Vb and work-function differences). In this figure the Co adatom is neutral, and the gating effect due to the tip at the position of the Co atom is less than in a and b, where the tip was considered to be directly above the adatom (see Supplementary Information).

Regardless of their origin, the Co-atom DOS features can be either emptied or filled with electrons as they are moved above or below EF through application of a gate voltage. The energy position of these resonances with respect to EF determines the ionization state of a Co atom, and the Co ionization state can thus be externally controlled using a gate voltage. This interpretation is supported by the existence of both the S state and the ring structure surrounding each atom. We first discuss the S state, which moves in the opposite direction in energy compared with both VD and the resonant peaks when a gate voltage is applied (Fig. 2a,b). This behaviour is the reverse of what is expected for a typical DOS feature, but makes sense in the context of Co-atom ionization17. Here the application of a tip bias (as well as any difference in tip–sample work functions) causes a local gating of the sample under the tip, which is added to the more global gating caused by the back-gate electrode, thus inducing the impurity DOS to rise (Vb>0) or fall (Vb<0) with respect to EF. The Co atom becomes ionized when the tip bias is great enough to cause impurity states to cross EF, thus creating a screening-induced response in the dI/dV signal (that is, the S peak). As shown in Fig. 4, this mechanism works equally well in the case when the impurity state is placed above EF by the back-gate (VG<−35 V) and when the impurity state is held below EF(VG>−35 V), except that the S peak is seen on opposite sides of EF for these two cases. Such behaviour is seen in the data of Fig. 2a,b, where the resonant peaks and S state lie on opposite sides of EF and (in the case of state A) even cross EF at the same VG. This ionization framework also explains the behaviour of the R and S resonances seen for graphene defects (the R and S defect features play the same role as the cobalt A and S features, respectively).

Such ionization behaviour can be quantitatively analysed for our data using a simple double-gate model (that is, graphene plus back-gate plus tip-gate). Here we fix the back-gate voltage (VG) and calculate the local band-bending arising from the electric potential difference (as well as the work-function difference) between the STM tip and the graphene substrate beneath it (that is, we calculate the change in the local graphene electronic density due to tip–sample capacitance)18,19. For the case of VG=−40 V we calculate that an applied potential difference of Vb=−105 mV will cause impurity ionization for states observed at Vb=+45 mV or less (see Methods and Supplementary Information). This correlates well with our spectroscopy of Co adatoms for VG=−40 V, where we observe an impurity state (A) at Vb=+44 mV and an ionization peak (S) at Vb=−100 mV.

The gate-dependent ionization of cobalt atoms also explains the ring structure seen surrounding each atom in dI/dV maps and topography (Fig. 3). As shown in Fig. 4c, when the tip is displaced laterally from an atom its electric field can still induce a local gating that shifts cobalt impurity states with respect to EF, causing ionization (such tip-induced gating has been previously observed in different physical systems17,20,21). This ionization leads to a change in graphene LDOS surrounding the atom arising from screening charge, and a resulting change in the measured dI/dV at the radius, r0, where the ionization takes place. The cobalt atom is ionized when the tip is held at a lateral distance r<r0 for such a bias and gate voltage (that is, tip inside the ring), whereas for r>r0 the atom is not ionized (that is, tip outside the ring). The size of r0 is dependent on Vb,VG, tip height and tip shape. For example, if VG is changed such that the impurity DOS features are further from EF, then the STM tip will need to be brought closer to the Co adatom to ionize it. This expected behaviour corresponds to the experimental behaviour shown in Fig. 3b–d. This type of behaviour also explains the appearance of ring structures around graphene defects, as seen in Fig. 3e,f, indicating that defects can induce localized states (as predicted theoretically22,23) that exhibit gate-induced charging/discharging. Tip-induced ionization rings have previously been seen in systems exhibiting an energy gap (unlike graphene) such as impurities on C60 films17 and dopants in semiconductor systems20,21.

The rings we observe in graphene around cobalt atoms are indicative of a screening cloud that surrounds each charged adatom. We have observed rings with diameters greater than 12 nm (for VG<−50 V), indicating that the screening clouds can be quite large and will probably affect macroscopic transport measurements (charged impurity scattering in general has already been proposed as a main limitation of graphene mobility1,24). The positioning of localized graphene impurity and defect states either above or below the Dirac point can thus explain asymmetries in graphene electron and hole conduction observed in recent transport measurements1,2. Although often viewed as a problem, such behaviour could potentially be used in a graphene chemical sensor. In this scenario, changes in the graphene conductivity at particular back-gate voltages could be correlated with the ionization thresholds of particular chemical species.


Our experiments were carried out using an Omicron LT-STM operating in ultrahigh vacuum (<10−11 torr) and at 4.2 K. Scanning tunnelling microscope tips were calibrated spectroscopically against the Au(111) Shockley surface state before all measurements. STM differential conductance (dI/dV) was measured by lock-in detection of the a.c. tunnel current modulated by a 1–5 mV (rms), 350–500 Hz signal added to the tunnelling bias Vb. The dI/dV (Vb) and I(Vb) measurements were made under open feedback conditions with the tip in a fixed position. Single graphene sheets were prepared using either mechanical exfoliation25 or by chemical vapour deposition26. In both cases the graphene sheets were placed on a 285-nm-thick SiO2 layer grown atop a heavily doped Si crystal, which was used as a back-gate electrode25. Electrical contact was made to the graphene by direct deposition of Ti (10-nm-thick)/Au (30-nm-thick) electrodes through a stencil mask. Samples were annealed at temperatures between 200 °C and 400 °C for several hours in ultrahigh vacuum to clean them before cooling. Co adatoms were deposited by e-beam evaporation onto pristine, cold (<10 K) graphene surfaces showing large areas (for example, 20×20 nm2) with no observable defects.

These measurements were reproduced on more than 50 Co adatoms measured with ten different PtIr tips on five different graphene devices (three exfoliated, two chemical vapour deposition grown). Although the majority of atoms measured in this work showed the behaviour described here, a fraction (30%) of atom-like protrusions observed in our measurements strayed from this behaviour in non-systematic ways. We attribute these either to Co dimers and trimers that formed as a result of diffusion during evaporation, or to Co adatoms that have attached to defects in the graphene surface. To test for atomic-hydrogen contamination in our system (which can lead to dip-like features at the Fermi energy27), we also evaporated Co atoms onto a Cu(111) surface. Subsequent dI/dV measurements of 50 Co/Cu(111) adatoms showed the typical 5-mV-wide Kondo feature expected for this system. None of the height abnormalities or spectroscopic artefacts related to hydrogen contamination27 were observed.

To understand the possible role of defects in our measurements, defects were introduced into some graphene surfaces through high-temperature annealing (400–500 °C) (a topographic image of a typical defect can be seen in Fig. 3f, inset). We observe that the presence of nearby defects did not change the behaviour of subsequently deposited Co adatoms. Furthermore, atomic manipulation was used to insure that Co adatoms studied were not bound to defect sites.

Our ab initio calculations of the vibrational modes of a Co adatom on graphene were carried out with the Quantum-Espresso code28 using density functional theory within the generalized gradient approximation29. Ultrasoft pseudopotentials and a plane-wave basis set were used. Kinetic-energy cutoffs of 45 Ry and 360 Ry were used for the wavefunctions and charge density, respectively. The system was modelled with a 4×4 graphene supercell containing 32 C atoms and one Co atom on a hollow site. Vibrational modes were calculated using density functional perturbation theory30.

In our calculation of the ionization threshold voltage of a Co adatom we roughly modelled the tip as a flat electrode with a work function tip=4.8 eV and held 6 Å above the graphene surface. The actual tip starts as an electrochemically etched PtIr wire, but undergoes some interaction with a gold surface, so the final shape and composition (and work function) are uncertain. Additionally, there is always uncertainty in the precise distance of an STM tip from a surface. While our model provides a good framework for understanding the data, the accuracy is limited at present because the expected band-bending is a nonlinear function of VG,Vb, work-function difference and tip height. Changing parameters such as tip or the tip height by 30% could easily change the calculated threshold of ionization by a factor of two (see Supplementary Information).