Flat edge modes of graphene and of Z2 topological insulator

A graphene nano-ribbon in the zigzag edge geometry exhibits a specific type of gapless edge modes with a partly flat band dispersion. We argue that the appearance of such edge modes are naturally understood by regarding graphene as the gapless limit of a Z2 topological insulator. To illustrate this idea, we consider both Kane-Mele (graphene-based) and Bernevig-Hughes-Zhang models: the latter is proposed for HgTe/CdTe 2D quantum well. Much focus is on the role of valley degrees of freedom, especially, on how they are projected onto and determine the 1D edge spectrum in different edge geometries

Weak localization of Dirac fermions in graphene beyond the diffusion regime

We develop a microscopic theory of the weak localization of two-dimensional massless Dirac fermions which is valid in the whole range of classically weak magnetic fields. The theory is applied to calculate magnetoresistance caused by the weak localization in graphene and conducting surfaces of bulk topological insulators.Comment: 5 pages, 2 figure

Charge Fractionalization in nonchiral Luttinger systems

One-dimensional metals, such as quantum wires or carbon nanotubes, can carry charge in arbitrary units, smaller or larger than a single electron charge. However, according to Luttinger theory, which describes the low-energy excitations of such systems, when a single electron is injected by tunneling into the middle of such a wire, it will tend to break up into separate charge pulses, moving in opposite directions, which carry definite fractions $f$ and $(1-f)$ of the electron charge, determined by a parameter $g$ that measures the strength of charge interactions in the wire. (The injected electron will also produce a spin excitation, which will travel at a different velocity than the charge excitations.) Observing charge fractionalization physics in an experiment is a challenge in those (nonchiral) low-dimensional systems which are adiabatically coupled to Fermi liquid leads. We theoretically discuss a first important step towards the observation of charge fractionalization in quantum wires based on momentum-resolved tunneling and multi-terminal geometries, and explain the recent experimental results of H. Steinberg {\it et al.}, Nature Physics {\bf 4}, 116 (2008).Comment: 31 pages, final version to appear in Annals of Physic