FORMATION OF THE (√3x√3)R30º SUPERSTRUCTURE.
Experimental details on the formation of the structure:
The experiments were performed in situ in two different ultra high vacuum (UHV)
systems from different institutions (Madrid and Eindhoven). The Madrid UHV system has
a base pressure of 1x10-10 mbar and it is equipped with Auger electron spectroscopy, lowenergy electron diffraction optics, STM at room temperature (300 K) and thermal
programmed desorption (TPD). The one in Eindhoven has a base pressure of 6x10-11
mbar, a LEED optics and a low temperature STM (4 K). The temperature was monitored by
an IR pyrometer with an emissivity of 0.25.
Standard cycles of sputtering and annealing (at 1200 K, 20 min.) were performed to
clean the platinum surface. The first annealing cycle was performed in an oxygen
atmosphere (P=1.10-6 mbar) and the next cycle in UHV with a maximum pressure of 7x1010
mbar. The STM image on the left corresponds to the clean Pt(111) surface.
The graphene samples were grown by slowly evaporating in situ molecular precursors
(C60H30 and C60) on a previously atomically cleaned Pt(111) surface held at 900K and
1000K, respectively (Pmax = 7x10-10 mbar during the whole process). The molecular
precursors were sublimated by thermal evaporation (660 K for C60H30 and 720K for
fullerenes). Similar samples were obtained by evaporating the precursors on the clean
surface at 300 K and by subsequent annealing, but in general, smaller domains of the
different phases are achieved with this method.
The STM images were recorded in topographic mode, using typical values for the tunnel
current of 0.1 – 4 nA and bias voltages ranging from -2000mV to -50mV and 50mV to
2000mV. Images were analyzed with the WsxM software [I. Horcas, R. Fernández, J. M.
Gómez-Rodríguez, J. Colchero, J. Gómez-Herrero, A. M. Baro, Rev. Sci. Instrum. 2007, 78,
013705 1-8.].
Graphene was also grown using ethylene gas by exposing the Pt surface at 1000K to 200L
of gas.
High resolution core level measurements at 400 eV of photon energy were recorded with a
PHOIBOS analyser eqeuiped with a home made delay line detector system. Measurements
were performed in normal emission conditions and with an overall energy resolution of
50 meV. Fitting of the data was performed with Doniach Sunjich functions convoluted with
gaussian broadening. Fitting parameters for the narrow C1s peaks for both preparation
conditions are the same, whereas the small components for the sample prepared out C60
are slightly broader.
Theoretical details for the calculations
a.- DFT.
Density functional theory has been used to compute equilibrium geometries and their
corresponding electronic structure [P. Hohenberg and W. Kohn, Phys. Rev. 136, B864
(1964)]. Wavefunctions are expanded in plane-waves as implemented in the CASTEP
program [S.J. Clark, M.D. Segall, C.J. Pickard et al., Z. Kristallogr. 220, 567 (2005);
http://www.accelrys.com] up to a cutoff of 350 eV and are sampled on a Monkhorst-Pack
6x6x1 mesh inside the Brillouin zone [H.J. Monkhorst and J.D. Pack, Phys. Rev. B 13, 5188
(1976)]. C and Pt atoms are described by ultra-soft pseudopotentials [D. Vanderbilt, Phys.
Rev. B 41, 7892 (1990)] and the local density approximation is used for the exchange and
correlation potential. [D.M. Ceperley and B.J. Alder, Phys. Rev. Lett. 45, 566-569 (1980)].
Bulk fcc Pt has been optimized separately on a 8x8x8 Monkhorst-Pack to give an
equilibrium lattice value of 3.917 Ang (exp. value is 3.92 Ang) for a residual stress less
than 0.001 GPa and negligible residual forces. The choice of a LDA exchange and
correlation functional has little influence, as shown by a Generalized Gradients
Approximation based in Perdew-Wang-91 that results in lattice parameter 1/100 larger
than the experimental one. Similarly, description of a single graphene layer with this
formalism is very good, resulting in an equilibrium 2D lattice parameter for the
rhombohedral unit cell of 2.439 Ang (2.438 Ang for PW91), to be compared with the value
for graphite (2.461 Ang). The Pt(111) surface has been modeled by a seven-layers slab
that converges to a 2D lattice parameter shorter than the projected bulk value by 0.5/100.
b.- STM
To simulate STM images we use the non-equilibrium Keldysh’s Green-functions
formalism [L.V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964)] as implemented by
Flores et al. [F. Flores et al., Progress in Surf. Sci. 48, 27 (1995)] . In this formalism,
the Hamiltonian of the problem is written as the superposition of two sub-systems
solved independently (Tip and Sample) and a term describing their interaction:
H  HT  HS  HI
The tunnelling current is computed using the density of states on both the Tip and
the Sample, and some effective hopping matrices that contain up to any order the
multiple scattering between the Tip and the Sample. This effect is important when
the Tip-Sample separation is small and it is responsible for the saturation of the
current when a contact is established. The expression can be written as [e.g. eq. 30
and 29 in [J.M. Blanco, F. Flores, R. Perez, Progress in Surf. Sci. 81, 403 (1996)]:
J
4e

EF  e V
 Tr T

~e f f ( E )T~e f f ( E  eV ) dE
T S
S S
S T
T T
EF
In our calculation, the effective hopping includes all the multiple scattering terms,
i.e., the probability for one electron to be propagated from the tip to the sample
including all the processes with different number of electronic reflexions in both
subsystems:

A
T~Te S f f I  TT Sg SA T
S S Tg T

1
T
A
TT S TT S TT Sg SA T
TT S . . .
S S Tg T T
STEP ROUNDING PROCESS.
Step 2 shows incomplete coverage for a better appreciation of the substrate steps. In order
to achieve a complete coverage of the sample with 1ML of graphene, more than 3ML were
deposited.
DENSITY OF STATES (DOS) OF THE MOIRE AND (√3X√3)R30º STRUCTURES
Comparison between DOS of the Moire structure and our proposed (√3x√3)R30º : a)Ptatoms contributions: the Pt-hollow (red circles) has bigger values (around the Fermi
energy) than the prototypical Pt-atom (black squares) below the Moire, which is similar to
the Pt-top (green triangles) on our model. This large DOS of Pt-hollow atom explains the
bright spot in the STM image and the less brilliant one for the second Pt. b) C-atoms
contributions: Moire’s (blue triangles) contributes less than the C-over the vacancy
(green diamonds). Its influence on the STM current is due to this incresead DOS. The
brown diamonds corresponds to C on top Pt (the other 6 C-atoms have similar DOS
contributions, and are small enough to not be observed in the STM image).
QUANTITATIVE AGREEMENT IN THE CALCULATED AND EXPERIMENTAL STM
IMAGES
The simulated and experimental STM images in Fig. 3 not only agree on all the significant
visual features over the 2D scan region, but a semi-quantitative agreement can be
sustained by analyzing a scan profile along a line going through the unit cell (blue line).
Leaving aside the small noise level and lateral drift (that can be estimated by comparing
equivalent peaks), three maxima (M1, M2 and M3) and three minima can be identified in
the experimental (black continuous line) and theoretical profiles (blue dashed line) that
admit a one to one correspondence not easy to find on theoretical simulations of
experiments on complex surfaces.