Excitonic Instability and Gap Generation in Monolayer Graphene

We analyze the excitonic instability in graphene by solving the Bethe–Salpeter equation for the electron-hole bound state. In the supercritical regime, we show that this equation has a tachyon in its spectrum. We argue that the excitonic instability is resolved through the formation of an electron-hole condensate leading to the gap (mass) generation in the quasiparticle spectrum. Such a gap could be observed in a free standing clean graphene.За допомогою рiвняння Бете–Солпiтера для електрон-дiркового зв’язаного стану дослiджено проблему екситонної нестабiльностi в графенi. Показано, що для надкритичної константи зв’язку спектр має тахiоннi розв’язки. Екситонна нестабiльнiсть приводить до формування електрон-дiркового конденсату та щiлини у спектрi квазiчастинок. Ця щiлина може бути спостережена у графенi без домiшок

Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities

We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear combination of atomic orbitals (LCAO) approach. For opposite charges of the Coulomb centers, an electric dipole potential results at large distances. We provide a nonperturbative analysis of the corresponding low-energy scattering problem