Graphene : from diffusive to ultraclean-interacting systems

In this thesis electron transport in disordered, substrate supported
graphene and suspended ultraclean graphene is studied.
We investigate graphene lying on top of silicon oxide and contacted with
superconducting aluminium electrodes.
The conductions fluctuations (CF) are studied in single layer graphene
devices. The CF are found to be enhanced by superconductivity by a factor
of 1.4 to 2. This (near) doubling of the CF indicates that the phase
coherence length is l >= L/2.
Compared to previous work, we find a relatively weak dependence of the CF
on the gate voltage, and hence on the carrier density. We also
demonstrate that whether the CF are larger or smaller at the charge
neutrality point can be strongly dependent on the series resistance Rc,
which needs to be subtracted.
Furthermore, ultraclean suspended graphene is investigated. We explain
the fabrication steps and show measurements at low temperatures of
suspended single layer graphene and bilayer graphene devices.
For suspended single layer graphene we find that very small perpendicular
magnetic fields (>100 mT) are sufficient to form Landau level
quantisation. At fields above 0.4 T, the graphene becomes insulating and
we observe that this transition is independent of temperature from 0.24 K
to 1.5 K.
Moreover, we study the electrical transport in clean current annealed
suspended bilayer graphene. Bilayer graphene bears an eight-fold
degeneracy due to spin, valley and layer symmetry, allowing for a wealth
of broken symmetry states induced by magnetic or electric fields, by
strain, or even spontaneously by interaction. We find two kinds of
devices. In bilayers of type B1 the eight-fold
zero-energy Landau level is partially lifted above a threshold field
revealing an insulating v=0 quantum Hall state at the charge neutrality
point (CNP).
In bilayers of type B2 the LL lifting is full and gap-like features
appear in IV spectroscopy even at zero magnetic field, suggesting an
insulating spontaneously broken symmetry state. Unlike B1, the minimum
conductance in B2 is not exponentially suppressed, but remains finite
with a value G < e2/h even in a large magnetic field. We suggest that
this phase of B2 is insulating in the bulk and bound by compressible edge
states.
In the last part, we probe the quantum Hall effect in suspended bilayer
graphene Hall crosses. Four contacts allow to determine the homogeneity
of the current annealing.
From the quantum Hall signal we extract a surprisingly low mobility of
10'000 - 40'000 m2/Vs, much lower than expected from previously reported
field effect mobilities. The observed features in IV spectroscopy are
found to show a strong growth in size with perpendicular magnetic field.