1. 4H-SiC substrate preparation - graphitization
annealing
Polished SiC substrate
SiC steps
Graphitized substrate

2. Patterning

3. e-beam lithography
Hall bar
FET
Quantum Interference loop

4. Epitaxial graphene grown on SiC
Highly ordered and well defined material
Transport layer is protected
Graphene properties : Dirac - chiral electrons
Anomalous Berry’s phase
Weak anti-localization
Landau level spectrum
Long electronic phase coherence length
Ballistic properties, high mobility
Anomalous transport : no quantum Hall effect
periodic and fractal-like spectrum for high mobility samples
AFM

5. Magneto-transport of a wide Hall bar (EG on Si-face)
Shubnikov - de Haas magnetoresistance maxima
Rxx (Ω/sq)
Rxy (Ω)
0.3-4K
Field(T)
400µm

6. Magneto-transport and Landau levels
Dirac particles:
linear E(k)
Magnetic field
Energy 3 EF 2 3 4 1 -1 -2 -3
1/Bn (T-1)
Landau index (n)
Energy
Magnetic field
Normal electrons:
quadratic E(k) EF
Landau plot :
Slope gives carrier density
ns= cm-2
Intercept at n=0 indicates
anomalous Berry’s phase
see K. Novoselov et al. Nature 438, 197 (2005);
Y. Zhang et al. Nature 438, 201 (2005)
W.de Heer et al., cond-mat /

7. Temperature dependence of the SdH peaks
Landau levels thermally populated
Lifshitz-Kosevich equation : A(T)/Ao= u/sinh(u) where u=2π2kBT/∆E(B)
Energy
Magnetic field
DE/kB(K) 1
∆E(B)=
vF= m/s T e m p e r a t u r e
V. Gusynin, Phys. Rev. B 71, (2005)

8. Transport is graphene-like surprising 3 layers
Low mobility µ=1100 cm2/Vs
Disordered as seen in STM (graphene on Si-face)
Phase coherence length lf(T=4K)~100nm
In agreement with STM-STS
Scattering by defects for graphene on the Si-face
G. Rutter, J. Stroscio et al., Science to be published
P. Mallet, J.-Y.Veuillen et al. cond-mat/

9. Interface charging Interface layer dominates transport
Neutral layers seen in Landau level IR spectroscopy
Sadowski PRL97, (2006)
5 nm
TEM -cross section
Daniel Ugarte, LNLS, Brasil
n~1012/cm2
n~1010/cm2 E
Graphene layers
SiC
Workfunction graphite-Workfunction SiC V ~0.3 eV
Built-in electric field E= V/L
L is of order of screening length.
Hence interface layer is charged ns~ E/0 ~1012/cm2
(Note: n~1010/cm2 for neutral graphite)
See also photoemission ARPES - A. Botswick et al. Nature Physics 3, 36 (2007)
E. Rolling et al. cond-mat/ (2005) - J. Phys Chem Solid 67, 2172 (2006)
T. Seyller et al. , Surface Science 600, 3906 (2006).