Title:
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The electron-phonon interaction in graphitic materials and superconductors
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In this thesis we study the effects of the interaction between electrons and phonon modes
in condensed matter systems. We explore two theoretical outcomes of theelectron-phonon
interaction: Charge wave order and superconductivity. The main aims of this thesis are to
establish ways of making graphitic materials useful for digital computing, and to investigate
unconventional forms of superconductivity.
Low order perturbation theory is combined with a Green's function analysis to calculate
electron band gaps in a bilayer graphitic material that. forms electron-phonon interactions via
an adjacent polarisable substrate. Self-consistent equations are derived and computationally
solved to examine band gap enhancement in bilayer graphene and bilayer boron nitride. We also compare results for several different systems to identify the most promising ones for future
developments. Our results show a promising new method of gap creation, for gaps of up
to leV, in a simple bilayer graphene system where the electron-phonon interaction causes
enhanced charge density wave order.
The possibility of three-dimensional high temperature bipolaronic superconductivity is examined numerically through continuous-time quantum Monte Carlo simulations backed
up by an exact analytical approximation for large phonon-frequency. Bose-Einstein condensation
of bipolarons in a cubic system is estimated to occur at temperatures as high as
90-120K at low carrier concentrations, where bipolarons are small and mobile.
We also develop formalism for calculating the superconducting band gap of BCS like superconductivity
in intercalated graphitic materials (IGMs). Green's function analysis combined
with low order perturbation theory is used to derive a set of generalised self-consistent
equations designed to accommodate the tight binding parameters of all IGMs.
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