This thesis summarizes our work in the past few years in the field of transport studies of carbon nanotubes and graphene. The first half of the thesis focuses on carbon nanotube (CNT) Josephson junctions (JJ) formed by coupling CNTs to superconducting electrodes. They exhibited Fabry Perot resonance patterns, enhanced differential conductance peaks, multiple Andreev reflection peaks, gate-tunable supercurrent transistor behaviors, hysteretic current-voltage line shape and "superconductor-insulator" transition. The junction behavior can be understood based on the dissipation dynamics and phase diffusion on the model of resistively and capacitively shunted junctions (RCSJ). In addition, we investigated Fano resonance on a particular device. The transport spectroscopy exhibited "inverse" Coulomb blockade structures superimposed on Fabry-Perot resonance patterns, indicating quantum interference between a channel that is well-coupled to the electrodes and another channel that is poorly-coupled channel. Our transport data was reproduced reasonably by the simulation.
The second half of the thesis discusses our results on graphene. Firstly, by developing a technique to fabricate suspended top gates, we were able to fabricate exceedingly clean, high quality graphene pnp junctions. In the high magnetic fields, we observed quantum hall plateaus at fractional values, which arise from edge state propagation and equilibration in regions with different filling factors, in agreement with the theoretical predictions. In zero magnetic fields, we observed Fabry-Perot conductance oscillations in the bipolar regime, demonstrating the high quality of our devices. Secondly, we explored specular Andreev reflection and have observed conductance peaks at the superconducting energy gap in normal metal - graphene - superconductor (NS) junctions. However, the intended goal of the project, observation of specular Andreev reflection, was not achieved. As significant progress has been made towards fabrication of high quality suspended devices, we expect that specular Andreev reflection could be observed in the near future.