Leaves and Stems, Rotons and Solitons, Magnets and Arrays, One Ground State Lost, Many Found, and Two Fields
Open Access
- Author:
- Nisoli, Cristiano
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- March 02, 2007
- Committee Members:
- Vincent Henry Crespi, Committee Chair/Co-Chair
Peter C Eklund, Committee Member
Henry C Foley, Committee Member
Gerald Dennis Mahan, Committee Member - Keywords:
- phyllotaxis
spin ice
graphene
nanotubes
elasticity
solitons
rotons
phonons - Abstract:
- A complete physical system typically requires three elements: particle, interaction, and manifold. Condensed matter physics provides a rich framework for generating new effective particles and new interactions such as quasiparticles, Cooper pairs or composite fermions. Rather than generate new effective particles or interactions within familiar flat space, one can also ask how novel geometrical constraints on the underlying manifold can generate new physics, even for old familiar interactions~cite{Thomson,Nelson}. Perhaps the simplest effective interaction is a featureless long-ranged repulsion, which leads to simple structures in flat space: in two dimensions, a triangular lattice. In contrast, interacting repulsive particles on a cylinder generate a rich degenerate family of helical structures that follow Fibonacci rules first seen in phyllotaxis, the study of plant morphology~cite{phyllo, phyllo2,phyllo3,Church,his,Levitov}. After demonstrating phyllotactic patterns in an experimental 'magnetic cactus`` we show that linear dynamics of phyllotaxis generates rotons and the nonlinear regime supports a large family of dynamically stable topological solitons that can fragment, merge, or interconvert upon collision, with propagation speeds governed by energy conservation and phase matching. These new phenomena should be observable in a wide range of systems, from quantum to classical and from nanometer-scale to macroscopic. In an attempt to mimic the zero point entropy of water and spin ice~cite{Giaque, Shulson, Pauling}, we have engineered arrays of nanoislands, called 'artificial spin ice`` such that their simple magnetic interaction can be frustrated by their mutual disposition. While the magnetic cactus was degenerate - although not extensively so - yet could be annealed into its ground state, the artificial spin ice is theoretically non degenerate, yet attempts to anneal it yield a disordered state, described by an athermal manifold of extensive degeneracy. We show how to predict its non trivial thermodynamics with good agreement with experimental data and no fitted parameters, using a principle of maximum likelihood reminiscent of entropy. When a flat graphene sheet is rolled in the cylindrical geometry of a carbon nanotube, a mesoscopic system is born, with macroscopic length, yet atomic scale radius~cite{ji, imperial, Dresselhaus}. We will show here how to adapt to it the standard elastic formalism for macroscopic objects so that its atomic complexities can be taken into account, and yet still solved analytically. Disparate experimental and numerical results find explanation in this unifying framework. {f Disclaimer}: this is a steroid-free thesis: it was not 'bulked up`` with anabolic injections of previously know methods or of accepted theories, which could be found in countless variations of flavors in reviews, textbooks, and other thesis. To the best of our knowledge, it reports only novel results, how interesting or relevant being left to the reader to decide. Attempt was made to write it in a self consistent way, to a level accessible to a graduate student in physics. We have added only a small introduction to elasticity of continua in Chapter 2, since it seems more common of curricula in engineering rather than in physics, in USA.