Strong Suppression of Weak Localization in Graphene

Low-field magnetoresistance is ubiquitous in low-dimensional metallic systems with high resistivity and well understood as arising due to quantum interference on self-intersecting diffusive trajectories. We have found that in graphene this weak-localization magnetoresistance is strongly suppressed and, in some cases, completely absent. The unexpected observation is attributed to mesoscopic corrugations of graphene sheets which can cause a dephasing effect similar to that of a random magnetic field.

Figure 1

Right inset: High-resolution AFM image of a graphene flake before microfabrication. The top (darker) part of the image, where no ripples are visible, is an oxidized Si wafer (the step height is $\approx 6\AA$). The smaller inset shows a 3 times magnified AFM image with contrast enhanced in order to see the ripples more clearly. Left inset: Scanning electron micrograph of one of our devices. Some larger ripples can also be seen on electron microscopy images. Main panel: Changes in resistivity of graphene with changing gate voltage. The arrows indicate gate voltages that correspond to magnetoresistance traces in Fig. 2a.

Figure 2

(a) Many graphene devices exhibited no sign of weak localization or antilocalization. Solid curves correspond to gate voltages shown by arrows in Fig. 1 ($\approx 10$, 20, and 50 V from top to bottom curve, respectively). The curves are shifted for clarity ($\rho \approx 1.5$, 0.8, and $0.4\mathrm{k}\Omega$ from top to bottom). The lowest curve corresponds to $k_{F}l\approx 50$. Notice magnification factors for the $\delta \rho$ scale against each of the curves. These factors were chosen so that the expected WL peak for all the curves would be of approximately the same size as the peak shown by the dashed curve calculated using the standard WL theory [11, 12]. (b) Magnetoresistance behavior at zero $V_g$ where $\rho$ reaches its maximum $\approx 6\mathrm{k}\Omega$. For such high resistivity (i.e., $\approx h/e^2$ per each type of carriers), a metal-insulator transition is generally expected but it does not occur in the case of graphene [2]. Both absolute value of $\rho$ and its magnetoresistance $\delta \rho (B)$ are practically temperature independent below 100 K. (c) Multilayer films [10] exhibited the standard weak-localization behavior. Shown is a device with $\rho \approx 1.2\mathrm{k}\Omega$ and mobility $\approx 10\hspace{0.17em}000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ (no gate voltage applied). A clear WL peak is seen at zero $B$. In higher fields, multilayer devices exhibit a large linear ($\propto B$) magnetoresistance. All curves shown in Fig. 2 were measured at 4 K.

Figure 3

A graphene device exhibiting some remnants of weak localization. The main panel shows its low-field magnetoresistance (solid curve; $n\approx 3\times {10}^{12}{\mathrm{cm}}^{-2}$; $l\approx 80\mathrm{nm}$; $T=4\mathrm{K}$). The dashed curve is the standard theory [11, 12] but scaled along the $y$ axis by a factor of 0.11 in order to fit the experimental curve. Because $L_{\varphi }$ can also be found from the correlation field of UCF, the absolute amplitude of the WL peak is the only fitting parameter. Left inset: Height $\Delta \rho$ of the MR peak as a function of $T$. Symbols are experimental data (normalized to $\Delta \rho$ at 4 K); $\ln T$ dependence is shown by the dashed line. Right inset: Phase-breaking length $L_{\varphi }$ (symbols) is well described by $1/\sqrt{T}$ dependence (dashed curve).