Fine structure of the lowest Landau level in suspended trilayer graphene

Magnetotransport experiments on ABC-stacked suspended trilayer graphene reveal a complete splitting of the 12-fold degenerated lowest Landau level, and, in particular, the opening of an exchange-driven gap at the charge neutrality point. A quantitative analysis of distinctness of the quantum Hall plateaus as a function of field yields a hierarchy of the filling factors: $\nu =6$, 4, and 0 are the most pronounced, followed by $\nu =3$, and finally $\nu =1$, 2, and 5. Apart from the appearance of a $\nu =4$ state, which is probably caused by a layer asymmetry, this sequence is in agreement with Hund's rules for ABC-stacked trilayer graphene.

Figure 1

Conductance traces at $T=1.3$ K for magnetic fields between 0 and 30 T. The dashed line through the 0 T data is used to estimate the device mobility. The numbers indicate the quantization of $G$ in integer units of $e^2/h$.

Figure 2

(a) Derivative $D=V_G\times dR/d{V}_G$ for magnetic fields between 0 and 7 T. Curves are shifted upwards proportional to the magnetic field value. The dashed lines mark the position of the minima in $D$ with the corresponding filling factor. The arrow illustrates the definition of the oscillation amplitude $A_{\nu }$ at $\nu =2$. (b) Gate-voltage positions of the minima in $D$ as a function of field. The lines indicate the expected linear behavior for the given filling factors. (c) Oscillation amplitude $A_{\nu }$ as a function of $1/B$ for the different filling factors.

Figure 3

(a) $R_{\text{CNP}}$ in a magnetic field perpendicular to the two-dimensional electron system plotted as a function of $B/T$ for different temperatures. (b) $R_{\text{CNP}}$ at 1.3 K in tilted magnetic fields plotted as a function of the perpendicular field component $B_{\perp }$.

Figure 4

(a) Resistance at the CNP in a parallel magnetic field plotted as a function $B/T$. The solid lines show the expected resistance decrease, $R\propto \exp (-2{\mu }_{B}B/k_B{B}_{\parallel }T)$, scaling with the bare Zeeman energy. (b) Proposed scenario for the behavior in a parallel magnetic field: A gap ${\Delta }_0$ present at 0 T closes due to spin splitting in both energy levels. An exchange mechanism prevents a further decrease of the gap for parallel fields above 2 T, and a finite gap ${\Delta }_{\text{ex}}=0.25$ meV remains.