One-Dimensional Physics of Interacting Electrons and Phonons in Carbon Nanotubes

Abstract

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.