Theory of integer quantum Hall effect in graphene

The observed quantization of the Hall conductivity in graphene at high magnetic fields is explained as being due to the dynamically generated spatial modulation of either the electron spin or the density, as decided by the details of Coulomb interaction on the scale of lattice constant. It is predicted that at a large in-plane component of the magnetic field such ordering may be present only at the filling factor $f=\pm 1$ and absent otherwise. Other experimental consequences of the theory are outlined.

Figure 1

The proposed phase diagram of graphene in the magnetic field. $D_z=g_{z}B$ is the Zeeman energy, $r$ is the chemical potential, and $m_0=2g_x{B}_{\perp }∕\pi$ is the characteristic size of the “relativistic” many-body gap $m$. $g_x$ is the larger of the couplings in the CDW and AF channels (see the text).

Figure 2

The phase diagram at half-filling $(r=0)$. The translationally symmetric magnet exists for $g_c,g_a<\pi g_{z}B∕2B_{\perp }$.