Tunneling spectroscopy of carbon nanostructures: A romance in many dimensions

In this dissertation we present results from various methods of tunneling spectroscopy in carbon nanotubes, which shed light on electron -- electron interaction in carbon nanotubes and low dimensional systems in general. We also apply those methods to two dimensional graphene sheets. We first review the fabrication techniques used to make the devices studied here. Some of the techniques are standard in nanofabrication, and some were developed in-house to make the particular device geometries studied here possible. In particular, we developed recipes for the growth and contact of clean, ultra-long carbon nanotubes as well as for the fabrication of non-invasive top tunnel probes. We then present results on normal metal tunneling spectroscopy of carbon nanotube devices of varying length. We measure the exponent of the conductance power law in the density of states as a function of device length over two orders of magnitude and find unexpected evidence of finite size effects in long devices. Next, we present results from the first measurement of the non-equilibrium electron energy distribution function in carbon nanotubes measured via non-equilibrium superconducting tunneling spectroscopy and find little evidence of scattering at low temperatures, which is consistent with a clean, strongly interacting Luttinger liquid. In addition, we discuss two ways we are working to extend this powerful technique. We also present results of superconducting tunneling spectroscopy of a clean carbon nanotube quantum dot. We are able to characterize the energy spectrum of the quantum dot and distinguish between spin singlet and spin triplet shell filling. We observe elastic and inelastic co-tunneling features which are not visible when the probe is made normal by a magnetic field. These co-tunneling rates have important technological implications for carbon nanotubes as single electron transistors. We also observe an energetically forbidden conductance inside the superconducting gap that could be related to inelastic scattering in the carbon nanotube quantum dot. Finally, we present results from the first application of the superconducting tunneling spectroscopy technique to graphene, a two dimensional system. We observe conductance oscillations consistent with Fabry-Perot interference. We also observe a gate dependant pair of subgap peaks, symmetric about bias voltage. We hypothesize that these peaks are due to conductance through bound Andreev states confined to a graphene quantum dot below the superconducting tunnel probe.