Chiral symmetry breaking and the quantum Hall effect in monolayer graphene

Monolayer graphene in a strong magnetic field exhibits quantum Hall states at filling fractions $\nu =0$ and $\nu =\pm 1$ that are not explained within a picture of noninteracting electrons. We propose that these states arise from interaction-induced chiral symmetry-breaking orders. We argue that when the chemical potential is at the Dirac point, weak on-site repulsion supports an easy-plane antiferromagnet state, which simultaneously gives rise to ferromagnetism oriented parallel to the magnetic field direction, whereas for $\left|\nu \right|=1$ easy-axis antiferromagnet and charge-density-wave orders coexist. We perform self-consistent calculations of the magnetic field dependence of the activation gap for the $\nu =0$ and $\left|\nu \right|=1$ states and obtain excellent agreement with recent experimental results. Implications of our study for fractional Hall states in monolayer graphene are highlighted.

Figure 1

Scaling of pure AFM order (black) at zero magnetic field criticality (${\delta }_a=0$). Red, blue, and green points show the observed gaps in Refs. [13, 14, 15], respectively, and the lines show fits to the ${\Delta }_0$ data. The magnetic field ($B$) is measured in units of $B_0\sim {\Lambda }^2\sim {10}^4$ T, the field associated with the lattice spacing. ${\Delta }_0$ is measured in units of $E_c=v_F\Lambda$. Inset: Dependence of ${\Delta }_0$ on ${\delta }_a$ at several different values of $B$ and for ${\delta }_f(=\pi /g_f)=0.05$.

Figure 2

Scaling of (a) FM order ($m$) and (b) total gap (${\Delta }_0$) at $\nu =0$ as a function of $B_{\parallel }$, for $B_{\perp }=0.0002$, $0.0004$, $0.0008$, $0.0016$, and $0.0032$ from bottom to top, with ${\delta }_a=0.225$ and ${\delta }_f=0.05$. $B_{\perp },B_{\parallel }$ are measured in units of $B_0$, and $m,{\Delta }_0$ in units of $E_c$ (see the caption of Fig. 1).

Figure 3

Scaling of ${\Delta }_1=C$ (in units of $E_c$) with perpendicular magnetic field $B$ (in units of $B_0$), for ${\delta }_c=0$, 0.03, 0.06, 0.08, 0.15, and 0.25 from top to bottom. Red and green dots are the gaps at $\nu =1$ reported in Refs. [13, 14], respectively. Inset: Scaling of $C$ after incorporating the logarithmic correction to scaling.