Final Report Summary - NANO-GRAPHENE (Understanding the Electronic Properties of Carbon Nanotubes and Graphene as Quantum Conductors)
The project focused on the study of low dimensional systems such as carbon nanotubes, semiconducting wires, quantum Hall effect edge states, graphene, as well as other two-dimensional lattices.The main goal of the project was to explore the formation of exotic phases in such systems, due to a combination of factors such as Coulomb and spin-orbit interactions, proximity with a superconductor, an applied magnetic field, finite-size effects, and disorder, as well as predict experimental signature for the detection of these phases. The main phenomena that we have focused on were charge fractionalization in carbon nanotubes, the spin-charge separation in out-of-equilibrium superconductors in the presence of a Zeeman field, the formation of Andreev bound states in one-dimensional systems, the effects of disorder in graphene and graphene-like nanoribbons, and the formation of Majorana fermions in both one-dimensional and two-dimensional systems. We have calculated the local density of states in these systems, which is measurable in scanning tunnelling experiments (STM). In particular, an important prediction that we made, was that the spin-polarized density of states is an important tool that can get access to important information about some exotic physics such as a nonconventional SC order parameter, or the formation of Majoranas, that could not be obtained by alternative measurements. Some of our calculations have been performed in conjunction with experiments, such as STM measurements of the density of states in disordered graphene, of Andreev bound states in nanotubes, as well measurements testing the spin-charge separation in superconductors. A second quantity that we have introduced and calculated is the Majorana polarization which provides a quantitative spatial description of the formation of Majorana fermions in a given system. The mathematical tools that we have used to calculate the local density of states and the Majorana polarization were analytical (T-matrix, bosonization, Dyson's equation), as well as numerical (tight-binding, exact diagonalization). The research activity during the project resulted in 27 publications (including a PRL and a Nature Physics), one accepted, and four submitted preprints.