Magnetotransport in single-layer graphene in a large parallel magnetic field

Graphene on hexagonal boron nitride (h-BN) is an atomically flat conducting system that is ideally suited for probing the effect of Zeeman splitting on electron transport. We demonstrate by magnetotransport measurements that a parallel magnetic field up to 30 Tesla does not affect the transport properties of graphene on h-BN even at charge neutrality where such an effect is expected to be maximal. The only magnetoresistance detected at low carrier concentrations is shown to be associated with a small perpendicular component of the field which cannot be fully eliminated in the experiment. Despite the high mobility of charge carriers at low temperatures, we argue that the effects of Zeeman splitting are fully masked by electrostatic potential fluctuations at charge neutrality.

Figure 1

Panel (a): Resistivity ${\rho }_{xx}$ versus gate voltage $V_{\mathrm{G}}$ for $B=0$ (gray line) and $B=30\text{T}$ (black solid line). Inset: Resistivity ${\rho }_{xx}$ versus $V_{\mathrm{G}}$ in the vicinity of the CNP. Panel (b): Magnetoresistance as a function of $B$ in the best parallel-field configuration, $\theta =89.{91}^{\circ }\pm 0.{01}^{\circ }$. Different lines are for different concentrations of charge carriers: corresponding gate voltages are indicated with the dashed lines in panel (a). Inset: Configuration of magnetic field orientation with respect to the graphene plane (shown in gray) and definition of tilt angle $\theta$. $\theta ={90}^{\circ }$ corresponds to a purely in-plane field.

Figure 2

Panel (a): Magnetoresistance at the CNP as a function of $B_{\perp }$ at 1.4 K for three different angles $\theta$. The inset illustrates the symmetry of ${\rho }_{xx}$ measured at $\theta =89.{91}^{\circ }$ with the black curve the original data between $-10$ and 20 T and the orange line the symmetrized curve between $-10$ and 10 T. Panel (b): Hall resistivity of the sample at a large hole concentration ($n=1\times {10}^{12}{\text{cm}}^{-2}$) measured as a function of total magnetic field for the same angles. The solid lines represent the expected behavior ${\rho }_{xy}=-Bcos\theta /\left(ne\right)$ at the angles used.

Figure 3

Longitudinal conductivity ${\sigma }_{xx}=1/{\rho }_{xx}$ as a function of charge carrier density $n$ for $T=1.4\text{K}$ and $B=0$ for hole doping. The red dashed line is a fit to the expected linear behavior for $n\gg n_{\mathrm{Q}}^{*}$, i.e., $log{\sigma }_{xx}=logn+\text{const}.$ The intercept of the linear fit with the value of the residual conductivity (horizontal gray dashed line) indicates the residual quasiparticle density $n_{\mathrm{Q}}^{*}$ due to electrostatic potential fluctuations.