| The one-dimensional (1D) world is quite different from its higher dimensional counterparts. For example, the electronic ground state in 1D is not a Fermi liquid as in most solids, due to the role of electron-electron interactions. Most commonly, electrons in 1D are described as a Luttinger liquid , where the low-energy excitations are decoupled bosonic charge and spin waves. Carbon nanotubes are clean 1D systems which have been shown to behave like a Luttinger liquid at high electron density. However, at low electron density and in the absence of disorder, the ground state is predicted to be a 1D Wigner crystal---an electron solid dominated by long-range Coulomb interaction. Moreover, short-range interaction mediated by the atomic lattice (umklapp scattering) is predicted to transform a nominal 1D metal into a Mott insulator.;In this thesis, we develop techniques to make extremely clean nanotube single-electron transistors. We study them in the few-electron/hole regime using Coulomb blockade spectroscopy in a magnetic field. In semiconducting nanotubes, we map out the antiferromagnetic exchange coupling as a function of carrier number and find excellent agreement to a Wigner crystal model. In nominally metallic nanotubes, we observe a universal energy gap in addition to the single-particle bandgap, implying that nanotubes are never metallic. The magnitude, radius dependence and low-energy neutral excitations of this additional gap indicate a Mott insulating origin.;Further, we use simultaneous electrical and Raman spectroscopy measurements to study the phonons scattered by an electric current. At high bias, suspended nanotubes show striking negative differential conductance, attributed to non-equilibrium phonons. We directly observe such "hot" phonon populations in the Raman response and also report preferential electron coupling to one of two optical phonon modes. In addition, using spatially-resolved Raman spectroscopy, we obtain a wealth of local information including the 1D temperature profile, a spatial map of the thermal conductivity and thermal contact resistances, which reveal the mechanism of thermal transport in nanotubes.;Finally, with multi-wall nanotubes (MWNTs), we use electrical breakdown as thermometry to provide evidence for ballistic phonon propagation and obtain an estimate for the quantum of thermal conductance. We also develop linear-bearing nanoswitches using the low-friction properties of MWNTs. |
