Magnetotransport in disordered graphene exposed to ozone: From weak to strong localization

We present a magnetotransport study of graphene samples into which a mild disorder was introduced by exposure to ozone. Unlike the conductivity of pristine graphene, the conductivity of graphene samples exposed to ozone becomes very sensitive to temperature: it decreases by more than three orders of magnitude between 100 and 1 K. By varying either an external gate voltage or temperature, we continuously tune the transport properties from the weak to the strong localization regime. We show that the transition occurs as the phase coherence length becomes comparable to the localization length. We also highlight the important role of disorder-enhanced electron-electron interaction on the resistivity.

Figure 1

(Color online) Atomic force microscopy image of the device contacted with four electrodes. The white contour highlights the sample shape.

Figure 2

(Color online) Raman spectrum of the device shown in Fig. 1 before (top) and after (bottom) exposure to ozone. G and 2D modes are shown; defects created by ozone reveal themselves as a strong D mode. Both panels have the same intensity axis.

Figure 3

(Color online) Four-point resistance of the sample as a function of backgate bias $V_g$ (a) before and (b) after ozone exposure. In (b), temperatures are $T=1.7$, 3, 5, 10, 20, 40, and 100 K. Inset to panel (b) displays the corresponding four-point conductivity as a function of backgate bias $V_g$.

Figure 4

(Color online) Resistivity as a function of magnetic field, for $T=1.7$, 5, 15, 50, and 100 K. Fits to Eq. (1) are shown by dashed lines away from the Dirac point and for conductivity values larger than $e^2/h$. Inset of Fig. 4e displays the resistivity at the Dirac point at 5, 15, 50, and 100 K (top to bottom).

Figure 5

(Color online) (a) Temperature dependence of the resistance at the Dirac point. (b) At low temperature, the sample resistance is fit to the two-dimensional variable-range hopping model for several gate biases in the vicinity of the Dirac point.

Figure 6

(Color online) (a) Characteristic lengths as a function of backgate bias $V_g$. $L_e$ is the elastic mean-free path. Coherence lengths $L_{\varphi }$ at $T=1.7$, 3, 5, 15, 25, 50, 70, and 100 K (top to bottom) are shown. ${\xi }_{VRH}$ is the localization length estimated from the variable-range hopping model [Eq. (2)] and ${\xi }_D$ is the localization length estimated from the scaling theory [Eq. (3)]. (b) Phase diagram (temperature $T$ and charge density $n$) showing the semimetallic regime where WL is observed and the insulator regime where SL prevails. The top axis shows the corresponding backgate biases $\Delta V_g$ measured from the Dirac point.

Figure 7

(Color online) Temperature dependence of the conductivity at $V_g=-40\text{V}$ and $B=4\text{T}$ (dots), and fit to Eq. (4) (solid line).