Understanding the Electronic Properties of Carbon .. (Nano-Graphene)
Understanding the Electronic Properties of Carbon Nanotubes and Graphene as Quantum Conductors
Start date: May 1, 2011,
End date: Apr 30, 2016
In low-dimensional systems the strength of electronic interactions is enhanced, which can give rise to fascinating phenomena such as charge fractionalization, spin-charge separation and fractional or non-Abelian statistics. Furthermore, the effects of disorder and external factors (such as the substrate, the leads, magnetic fields, or the coupling with a gate or an STM tip), are much stronger in low-dimensional systems than in three-dimensional systems, and can greatly alter their properties. The first goal of this project is to find experimental signatures of the exotic phenomena caused by interactions, both in carbon nanotubes, and in regular and graphene fractional quantum Hall systems. The second goal is to understand how the interplay between disorder, interactions and external factors impacts the physics and the possible technological use of nanotubes and graphene in electronic nanodevices. To achieve these goals I intend to calculate theoretically quantities measurable by electronic transport, such as the conductance and the noise, in particular the noise at high-frequencies, as well as quantities measurable by scanning tunneling microscopy (STM), such as the local density of states (LDOS). Furthermore I intend to analyze and explain the recently developed STM experiments on graphene, and to propose new STM measurements that will elucidate the physics of graphene in the fractional quantum Hall regime. Some of the theoretical techniques that I plan to use are the perturbative non-equilibrium Keldysh formalism, conformal field theory and the Bethe ansatz, the T-matrix approximation, the Born approximation and numerical methods such as ab-initio and recursive Green's functions.
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