Interactions and Phase Transitions on Graphene’s Honeycomb Lattice

The low-energy theory of interacting electrons on graphene’s two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-$N$ limit is shown to have a semimetal–antiferromagnetic insulator quantum critical point in the universality class of the Gross-Neveu model. The same equivalence is conjectured to hold in the physical case $N=2$, and its consequences for various physical quantities are examined. The effects of the long-range Coulomb interaction and the magnetic field are discussed.

Figure 1

The large-$N$ flow diagram in the attractive plane $e=g_d=g_f={\tilde{g}}_x=0$. A, B, C, and G are the AF, bicritical, CDW, and the Gaussian fixed points, respectively. A and C are in the Gross-Neveu universality class. The extended Hubbard model in Eq. (2) defines the (dashed) line of initial conditions $g_c=(U-V)/4U_c$ and $g_a=-U/4U_c$, with $V$ as a fixed nearest-neighbor repulsion. Inset: the resulting phase diagram.