Bilayer graphene bears an eightfold 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 study the electrical transport in clean current annealed suspended bilayer graphene. We find two kinds of devices. In bilayers of type B1 the eightfold zero-energy Landau level is partially lifted above a threshold field revealing an insulating ν=0 quantum-Hall state at the charge neutrality point. In bilayers of type B2 the Landau level lifting is full and a gap appears in the differential conductance 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 is < or approximately equall to e(2)/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.

Graphene is a 2-dimensional (2D) carbon allotrope with the atoms arranged in a honeycomb lattice. The low-energy electronic excitations in this 2D crystal are described by massless Dirac fermions that have a linear dispersion relation similar to photons. Taking advantage of this optics-like electron dynamics, generic optical elements like lenses, beam splitters and wave guides have been proposed for electrons in engineered ballistic graphene. Tuning of these elements relies on the ability to adjust the carrier concentration in defined areas, including the possibility to create bipolar regions of opposite charge (p-n regions). However, the combination of ballistic transport and complex electrostatic gating remains challenging. Here, we report on the fabrication and characterization of fully suspended graphene p-n junctions. By local electro-static gating, resonant cavities can be defined, leading to complex Fabry-Perot interference patterns in the unipolar and the bipolar regime. The amplitude of the observed conductance oscillations accounts for quantum interference of electrons that propagate ballistically over long distances exceeding 1 micron. We also demonstrate that the visibility of the interference pattern is enhanced by Klein collimation at the p-n interface. This finding paves the way to more complex gate-controlled ballistic graphene devices and brings electron optics in graphene closer to reality.Comment: 15 pages, 5 figure

We observe very small gate-voltage shifts in the transfer characteristic of as-prepared graphene field-effect transistors (GFETs) when the pH of the buffer is changed. This observation is in strong contrast to Si-based ion-sensitive FETs. The low gate-shift of a GFET can be further reduced if the graphene surface is covered with a hydrophobic fluorobenzene layer. If a thin Al-oxide layer is applied instead, the opposite happens. This suggests that clean graphene does not sense the chemical potential of protons. A GFET can therefore be used as a reference electrode in an aqueous electrolyte. Our finding sheds light on the large variety of pH-induced gate shifts that have been published for GFETs in the recent literature.

We have measured the current(I)-voltage(V ) characteristics of a single-wall carbon nanotube quantum dot coupled to superconducting source and drain contacts in the intermediate coupling regime. Whereas the enhanced differential conductance dI/dV due to the Kondo resonance is observed in the normal state, this feature around zero bias voltage is absent in the superconducting state. Nonetheless, a pronounced even-odd effect appears at finite bias in the dI/dV sub-gap structure caused by Andreev reflection. The first-order Andreev peak appearing around V = ∆/e is markedly enhanced in gate-voltage regions, in which the charge state of the quantum dot is odd. This enhancement is explained by a 'hidden' Kondo resonance, pinned to one contact only. A comparison with a single-impurity Anderson model, which is solved numerically in a slave-boson meanfield ansatz, yields good agreement with the experiment. There is a growing interest in the exploration of correlated charge transport through nanoscaled lowdimensional systems involving both superconductors and normal metals [1,2,3,4,5,6]. The penetration of the pair amplitude ∆ from a superconductor (S) into a normal metal (N), the proximity effect, is a manifestation of correlated charge transport mediated by Andreev processes taking place at the S-N interface [7] and leading in S-N-S junctions to the Josephson effect [8] and sup-gap current peaks due to multiple Andreev reflection (MAR) [9]. The superconducting proximity effect has been studied in great detail in the mesoscopic size regime of diffusive, but phase coherent conductors [10]. Andreev transport has also been the key quantity in experiments elucidating charge transport in single atom contacts [5,11]. On the other hand, Andreev transport through a quantum dot coupled to superconductors, is just emerging now [12,13,14,15]. If the dot is weakly coupled to the leads, Andreev processes are suppressed by the charging energy U of the dot [3,16,17]. If the dot is sufficiently small, size quantization takes place, forming a quantum dot (QD) with discrete eigenstates ('levels') at energies E {i} . Transport then occurs through individual levels [3]. Since the level 'positions' E {i} , and sometimes also the coupling strengths of the levels to both source and drain contacts Γ 1,2 , can be tuned through gate voltages, a physically tunable model system of the Anderson 'impurity problem' is realized. With one electron on the QD (half-filling), a many-electron ground-state forms, involving both the dot-state and conduction electrons from the leads in an energy window given by the the Kondo temperature T K [18,19].

Snake states are trajectories of charge carriers curving back and forth along an interface. There are two types of snake states, formed by either inverting the magnetic field direction or the charge carrier type at an interface. The former has been demonstrated in GaAs–AlGaAs heterostructures, whereas the latter has become conceivable only with the advance of ballistic graphene where a gap-less p–n interface governed by Klein tunnelling can be formed. Such snake states were hidden in previous experiments due to limited sample quality. Here we report on magneto-conductance oscillations due to snake states in a ballistic suspended graphene p–n junction, which occur already at a very small magnetic field of 20 mT. The visibility of 30% is enabled by Klein collimation. Our finding is firmly supported by quantum transport simulations. We demonstrate the high tunability of the device and operate it in different magnetic field regimes.