Figure 1

Constant energy lines for the one-particle spectrum in the BLG. LiTr as a function of density occurs when the Fermi-level intersects the separatrix (bold line) for (a) unbroken ${\mathcal{C}}_{6v}$ symmetry of the graphene lattice; (b) symmetry breaking ${\mathcal{C}}_{6v}\to {\mathcal{C}}_{2v}$. Circles mark Dirac points and $\pm$ indicates Berry phases, $\varphi =\pm \pi$. Insets show the tight-binding cartoons for the band structure (i) and the schematic evolutions of the Landau levels in the magnetic field and (ii) the number indicates the degeneracy per one spin and valley, $d_0$.Reuse & Permissions

Figure 2

Derivation of the RG equations. (a) Definitions of the elements; (b) polarization operator; (c) screening of the Coulomb interaction; [(d) and (e)] renormalization of one-particle spectrum; (f) gauge invariance of the scalar vertex; and (g) renormalization of the short-range interaction.Reuse & Permissions

Figure 3

[(a) and (b)] The curvature of the mean-field energy along the steepest decent direction. The square-root singularity is caused by the collision of the Dirac points shown on the inset. At ${\rm Y}<{{\rm Y}}_1<{{\rm Y}}_c$ extra local minimum and maximum are formed (a), such as $\left|u_1^{\text{max}}\right|>{\mathcal{E}}_{\text{LiTr}}$ (b), i.e., only two Dirac points remain. The total dashed area equals to zero. [(c) and (d)] The schematic phase diagrams for the finite temperature (c) and for quantum (d) (controlled by the gate voltage $V_g$) PTs. The insets show predicted hysteretic (or slow noise) behavior (dashed areas) of the conductivity for the corresponding paths on the phase diagram.Reuse & Permissions