Coherent phases and collective electron phenomena in graphene

Unique band structure peculiarities of graphene imply that near Fermi level electrons are effectively described by two-dimensional Dirac equation for massless particles. We investigate how these peculiarities manifest in electron-hole pairing and properties of indirect magnetoexcitons in two spatially separated, independently gated graphene layers. We study electron-hole pairing in weak-coupling regime, find the gap in energy spectrum and discuss system behavior at various controlling parameters. In case of extremely strong coupling, we show that localized electron-hole pairs are absent in graphene, and thus a behavior of graphene bilayer versus coupling strength is cardinally different from crossover to local pairs in usual Fermi systems. We discuss spectroscopy of indirect magnetoexcitons in graphene and possibility of their superfluidity. The systems under consideration can reveal coherent properties, dissipationless currents and Josephson-like phenomena at room temperature.