Electron optics in suspended graphene
Graphene is an intriguing material: electrons are chiral Dirac particles yielding a plethora of new phenomena such as Klein tunneling, fractional quantum Hall plateaus and unconventional Andreev reflection. All these effects require graphene of high quality and low carrier density. In the language of graphene, one needs to approach the so-called charge neutrality point, also known as the Dirac point, as close as possible. However, in real devices there is typically a considerable random potential present due to charge impurities in the substrate or adsorbates on graphene itself. Mobilities in most practical devices are modest. Though values two orders of magnitude larger than in silicon devices can easily be obtained, typical graphene devices are way off state-of-the-art high mobility III-V heterojunction layers, where mobilities in 103 m2/Vs are possible.
To overcome this problem, we have developed a versatile technology that allows to suspend graphene and complement it with arbitrary bottom and top-gate structures. Using current annealing we demonstrate exceptional high mobilities in monolayer graphene approaching 102 m2/Vs. These suspended devices are ballistic over micrometer length scales and display intriguing interference patterns in the electrical conductance when different gate potentials are applied. Specifically I will discuss different types of Fabry-Perot resonances that appear in different gate voltage regimes of ballistic pn devices . I will also present recent electric transport measurements in magnetic field, where intriguing features appear in the intermediate field range in between the low-field Klein-tunneling regime and the quantum Hall regime. We observe a large number of non-dispersing states which might be due to so-called snake states confined to the pn interface. Furthermore, I will use the opportunity to discuss first results on electron guiding in ultraclean monolayer graphene. Similar to light guiding, electrons can be confined by total internal reflection due to different effective refractive indices. In graphene, the latter can be obtained simply by changing the carrier density through gating. Unlike a conventional unipolar material, one can in addition guide electron waves through the formation of bipolar boundaries. This should yield a high guiding efficiency. Finally, I will briefly mention our efforts in realizing lensing using negative refractive electron optics in graphene.
 P. Rickhaus et al., Nature Communications 4, 2342 (2013)