Massive Dirac fermions in single-layer graphene.

Motivated by the results of recent photoemission and tunneling studies, we discuss potential many-body sources of a finite gap in the Dirac fermion spectrum of graphene. Specifically, we focus on the putative Peierls- and Cooper-like pairing instabilities, which can be driven by sufficiently strong Coulomb and electron-phonon interactions, respectively. Our results compare favorably with the available experimental and Monte Carlo data.

Effect of fermi surface curvature on low-energy properties of fermions with singular interactions.

We discuss the effect of Fermi surface curvature on long-distance or time asymptotic behaviors of two-dimensional fermions interacting via a gapless mode described by an effective gauge-field-like propagator. By comparing the predictions based on the idea of multidimensional bosonization with those of the strong-coupling Eliashberg approach, we demonstrate that an agreement between the two requires a further extension of the former technique.

Electron localization properties in graphene.

We study localization properties of the Dirac-like electronic states in monolayers of graphite. In the framework of a general disorder model, we discuss the conditions under which such standard localization effects as the logarithmic temperature-dependent conductivity correction appear to be strongly suppressed, as compared to the case of a two-dimensional electron gas with parabolic dispersion, in agreement with recent experimental observations.

Dissipative dynamics of planar d-wave Josephson junctions.

We study quantum dynamics of and phase transitions in a Josephson junction between two planar d-wave superconductors where the processes of both quasiparticle and Cooper pair tunneling give rise to nonlocal dissipative terms in the effective action. By combining a perturbative weak coupling analysis in the charge representation with a variational approach in the phase representation at strong coupling, we ascertain a layout of the junction's phase diagram and discuss the corresponding behaviors.

Single-step implementation of universal quantum gates.

We construct optimized implementations of the controlled-NOT and other universal two-qubit gates that, unlike many of the previously proposed protocols, are carried out in a single step. The new protocols require tunable interqubit couplings but, in return, show a significant improvement in the quality of gate operations. We make specific predictions for coupled Josephson junction qubits and compare them with the results of recent experiments.