Quantized edge modes in atomic-scale point contacts in graphene.

The zigzag edges of single- or few-layer graphene are perfect one-dimensional conductors owing to a set of gapless states that are topologically protected against backscattering. Direct experimental evidence of these states has been limited so far to their local thermodynamic and magnetic properties, determined by the competing effects of edge topology and electron-electron interaction. However, experimental signatures of edge-bound electrical conduction have remained elusive, primarily due to the lack of graphitic nanostructures with low structural and/or chemical edge disorder. Here, we report the experimental detection of edge-mode electrical transport in suspended atomic-scale constrictions of single and multilayer graphene created during nanomechanical exfoliation of highly oriented pyrolytic graphite. The edge-mode transport leads to the observed quantization of conductance close to multiples of G0 = 2e2/h. At the same time, conductance plateaux at G0/2 and a split zero-bias anomaly in non-equilibrium transport suggest conduction via spin-polarized states in the presence of an electron-electron interaction.

Complex Quasi-Two-Dimensional Crystalline Order Embedded in VO_{2} and Other Crystals.

Metal oxides such as VO_{2} undergo structural transitions to low-symmetry phases characterized by intricate crystalline order, accompanied by rich electronic behavior. We derive a minimal ionic Hamiltonian based on symmetry and local energetics which describes structural transitions involving all four observed phases, in the correct order. An exact analysis shows that complexity results from the symmetry-induced constraints of the parent phase, which forces ionic displacements to form multiple interpenetrating groups using low-dimensional pathways and distant neighbors. Displacements within each group exhibit independent, quasi-two-dimensional order, which is frustrated and fragile. This selective ordering mechanism is not restricted to VO_{2}: it applies to other oxides that show similar complex order.

The negative-U Hubbard model with long-range Coulomb interaction: metal-insulator transition far from half-filling.

It is shown that a metal-insulator transition can occur far from half-filling in the negative-U Hubbard model in the presence of long-range repulsive interactions. Specifically, we consider the bcc lattice at an electron concentration of 2/3 and show that a CDW insulating state exists which is energetically favoured over the relevant metallic states. The repulsive interaction plays the same role as it does in stabilizing a Wigner crystal. Despite the absence of Fermi surface nesting, the CDW insulator appears at rather small values of the interaction, preceded by a CDW semimetal at even smaller values. This places severe restrictions on the region of the parameter space where superconductivity may exist. We believe that the model will show similar behaviour for other electron densities and other lattices.