Gap opening in the zeroth Landau level of graphene

We have measured a strong increase of the low-temperature resistivity ${\rho }_{xx}$ and a zero-value plateau in the Hall conductivity ${\sigma }_{xy}$ at the charge neutrality point in graphene subjected to high magnetic fields up to 30 T. We explain our results by a simple model involving a field dependent splitting of the lowest Landau level of the order of a few Kelvin, as extracted from activated transport measurements. The model reproduces both the increase in ${\rho }_{xx}$ and the anomalous $\nu =0$ plateau in ${\sigma }_{xy}$ in terms of coexisting electrons and holes in the same split zero-energy Landau level.

Figure 1

(Color online) (a) ${\rho }_{xy}$ as a function of back-gate voltage $V_G$ (top $x$-axis) and charge carrier concentration $n$ (bottom $x$ axis) measured between contacts 3 and 5 as shown in the scanning electron micrograph in the top left inset at a fixed magnetic field $B=30\text{T}$. (b) ${\rho }_{xx}$ at $B=30\text{T}$ measured at the same temperatures as in (a). Note the $x$-axis break and the 20 times magnification for high electron/hole concentrations. The left inset in (b) shows the temperature dependence of ${\rho }_{xx}$ at the charge CNP for different $B$. The right inset displays the magnetic field dependence of ${\rho }_{xx}$ at the CNP for different $T$.

Figure 2

(Color online) (a) Concentration dependence of ${\sigma }_{xy}$ (top panel) and ${\sigma }_{xx}$ (bottom panel) at $B=30\text{T}$. The inset sketches the principle of activated transport between two broadened Landau levels. (b) Arrhenius plots of the temperature dependence of ${\sigma }_{xx}$ at the CNP in the thermally activated transport regime. (c) Energy gaps $\Delta$ as extracted from the slopes of the Arrhenius plots. For comparison, the dotted black line represents the expected gap for a bare Zeeman spin-splitting ${\Delta }_Z=g{\mu }_{B}B$ with a free-electron $g$-factor $g=2$.

Figure 3

(Color online) (a) Schematic illustration of the density of states for electrons (red/gray) and holes (blue/dark gray) in graphene in a magnetic field without splitting (top) and including splitting (bottom). The width of the higher Landau levels is in reality much larger than illustrated (see text). (b) ${\sigma }_{xy}$ and ${\sigma }_{xx}$ as a function of charge carrier concentration for unsplit (dotted lines) and split (solid line) Landau levels calculated for $B=30\text{T}$ and $T=1\text{K}$ and using $g=2$.