Thèse proposée par (PhD thesis proposed by) Cristina BENA

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.

To understand these effects the selected PhD candidate can choose to work on one of the following two projects. The first project is to study one-dimensional systems such as carbon nanotubes and topological insulating wires exhibiting end Majorana fermionic states, as well as two-dimensional topological insulators and the corresponding one-dimensional chiral edge states. For these systems one needs to focus on quantities measurable by electronic transport, such as the conductance and the noise, as well as on quantities measurable by scanning tunneling microscopy (STM) such as the local density of states (LDOS). The candidate should have, besides a thorough knowledge of solid state physics, a solid background in quantum field theory, and many-body physics.

The second project is to analyze the recently developed STM experiments on graphene, to calculate the LDOS in graphene in the presence of different types of disorder on different types of substrates, and to propose new STM measurements that will elucidate the physics of graphene in the fractional quantum Hall regime. This project can be approached via analytical tools which require many-body and quantum field theory knowledge, and/or via numerical tools, which will necessitate learning and using numerical techniques such as recursive Green's functions, or the density functional theory.

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