Since its discovery in 2004, graphene, a two-dimensional hexagonal carbon
allotrope, has generated great interest and spurred research activity from
materials science to particle physics and vice versa. In particular, graphene
has been found to exhibit outstanding electronic and mechanical properties, as
well as an unusual low-energy spectrum of Dirac quasiparticles giving rise to a
fractional quantum Hall effect when freely suspended and immersed in a magnetic
field. One of the most intriguing puzzles of graphene involves the
low-temperature conductivity at zero density, a central issue in the design of
graphene-based nanoelectronic components. While suspended graphene experiments
have shown a trend reminiscent of semiconductors, with rising resistivity at
low temperatures, most theories predict a constant or even decreasing
resistivity. However, lattice field theory calculations have revealed that
suspended graphene is at or near the critical coupling for excitonic gap
formation due to strong Coulomb interactions, which suggests a simple and
straightforward explanation for the experimental data. In this contribution we
review the current status of the field with emphasis on the issue of gap
formation, and outline recent progress and future points of contact between
condensed matter physics and Lattice QCD.Comment: 14 pages, 6 figures. Plenary talk given at the XXVIII International
Symposium on Lattice Field Theory (Lattice 2010), June 14-19, 2010,
Villasimius, Sardinia, Ital
