Field-induced quantum Hall ferromagnetism in suspended bilayer graphene

We have measured the magnetoresistance of freely suspended high-mobility bilayer graphene. For magnetic fields $B>1$ T we observe the opening of a field-induced gap at the charge neutrality point characterized by a diverging resistance. For higher fields the eightfold degenerated lowest Landau level lifts completely. Both the sequence of this symmetry breaking and the strong transition of the gap-size point to a ferromagnetic nature of the insulating phase developing at the charge neutrality point.

Figure 1

Resistance as a function of the concentration by sweeping the backgate from $-$60 to 60 V for 0 T (black squares) and 1 T (red circles). A constant contact resistance has been removed. (Top-left inset) Temperature dependence of the resistance at the CNP for 0 T and 1 T; top-right inset, SEM picture of our suspended device.

Figure 2

(a) Resistive behavior of the sample near the CNP at $T$ $=$ 1.3 K. The dots mark the positions $n=3\times {10}^{14},0\text{and}-3\times {10}^{14}$ m${}^{-2}$ where the gap opening has been analyzed (see text for more details). (b) Resistance $R_{\mathrm{CNP}}$ as a function of $B/T$ at $T$ $=$ 4.2 K and 1.3 K; (inset) qualitative picture of the DOS near the CNP. The conduction at energy $E$ is directly related to the thermal excitation of electrons to the conduction edges $E_{c1}$ and $E_{c2}$. (c) Calculated gap $\Delta$ as function field $B$ for $T=1.3$ K; the dashed line represents the theoretical single electron Zeeman-energy $g{\mu }_{B}B$.

Figure 3

(a) Gatesweeps $R\left(V_G\right)$ at constant magnetic fields $B$ $=$ 1 T, 5 T, 12 T, 17.5 T, and 30 T for $T$ $=$ 4.2 K; the curves are shifted up for clarity. (b) Derivative $dR/d{V}_G$ for the curves in (a). (c) Position of the minima for $\nu$ $=$ $\pm$12, $\pm$8, $\pm$4, $\pm$3, $\pm$2 and $\pm$1 as function of the magnetic field.

Figure 4

(a) $R_{xx}$ oscillations after removing linear background from $n\frac{dR}{dn}$ for $B$ $=$ 3 T, 5 T, 12 T, and 20 T at 4.2 K. (b) Dingle plot of $\nu$ $=$ 8 and $\nu$ $=$ 4: amplitude $A$ of the oscillations as a function of the inverse field $1/B$. (c) Dingle plot for $\nu$ $=$ 3, 2, and 1. (d) Schematic plot of the appearance filling factors with increasing magnetic field. The dashed lines show the center of the Landau level, while the gray shaded area is the Landau level broadening determined by the Dingle temperature $T_D$.

Figure 5

Relation between the induced charge carrier concentration per applied magnetic field $\alpha \left(B\right)=n/B$ and the applied magnetic field $B$ for $B$ $=$ 0 (solid circles) and $B\ne$ 0 (open circles). The plotted line shows the interpolated $\alpha \left(B\right)$ from which we determined a reliable value of the concentration $n$.