Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer

We have studied temperature dependences of electron transport in graphene and its bilayer and found extremely low electron-phonon scattering rates that set the fundamental limit on possible charge carrier mobilities at room temperature. Our measurements show that mobilities higher than $200000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ are achievable, if extrinsic disorder is eliminated. A sharp (thresholdlike) increase in resistivity observed above $\sim 200\mathrm{K}$ is unexpected but can qualitatively be understood within a model of a rippled graphene sheet in which scattering occurs on intraripple flexural phonons.

Figure 1

Resistivity $\rho$ (blue curve) and conductivity $\sigma =1/\rho$ (green curve) of SLG as a function of gate voltage. If we subtract a constant of $\approx 100\Omega$ (used here as a fitting parameter), the remaining part ${\rho }_L(V_g)$ of resistivity becomes inversely proportional to $V_g$ (red curve). The thin black line (on top of the red curve for $V_g>0$) is to emphasize the linearity (the red curve is equally straight for negative $V_g$). The particular device was $1\mu \mathrm{m}$ wide, and $T=50\mathrm{K}$ was chosen to be high enough to suppress universal conductance fluctuations, still visible on the curves.

Figure 2

Electron transport in graphene below 300 K can be described by the empirical expression $\rho (V_g,T)={\rho }_L(V_g)+{\rho }_S(T)$ where ${\rho }_S$ is independent of $V_g$ but varies with $T$. After subtracting ${\rho }_S$ that for this sample changed from $\approx 40\Omega$ at low $T$ to $\approx 70\Omega$ at 260 K, the resulting curves ${\sigma }_L(V_g)=1/{\rho }_L(V_g)$ became indistinguishable (the cluster marked $1/{\rho }_L$ consists of 5 such curves). The experiments were carried out in a field of 0.5 T to ensure that weak localization corrections (rather small [1, 22] but still noticeable) do not contribute into the reported $T$ dependences.

Figure 3

$T$-dependent part of resistivity for 4 SLG samples (symbols). The accuracy of measuring $\Delta {\rho }_S$ was limited by mesoscopic fluctuations at low $T$ and by gate hysteresis above 300 K. The hysteresis appeared when $V_g$ was swept by more than 20 V. To find $\Delta {\rho }_S$ at higher $T$, we recorded $\rho$ as a function of $n$ (found from simultaneous Hall measurements). The solid curve is the best fit by using a combination of $T$ and $T^5$ functions, which serves here as a guide to the eye. One of the samples (green circles) was made on the top 200 nm of ${\mathrm{SiO}}_2$ covered by further 100 nm of polymethylmethacrylate (PMMA) and exhibited $\mu \approx 7000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$. The same values of $\mu$ for ${\mathrm{SiO}}_2$ and PMMA substrates probably rule out charged impurities in ${\mathrm{SiO}}_2$ as the dominant scattering mechanism for graphene. The inset shows $T$ dependence of maximum resistivity ${\rho }_{\mathrm{NP}}$ (at the neutrality point) for SLG and BLG (circles and squares, respectively). Note a decrease in ${\rho }_{\mathrm{NP}}$ with decreasing $T$ below 150 K for SLG, which is a generic feature seen in many samples.

Figure 4

$T$ dependence in bilayer graphene. At the neutrality point, $\sigma$ rapidly increases with $T$ but, away from it, no changes are seen. $\sigma (V_g)$ exhibits a small sublinear contribution that can also be interpreted in terms of a constant ${\rho }_S$. The inset plots nominal values of $\mu$ found from linear fits of ${\sigma }_L$($V_g$) at $V_g>20\mathrm{V}$ away from NP and using ${\rho }_S\approx 50\Omega$. Here, $\mu$ does not change within $\approx 2\%$ and, if anything, shows a slight increase at higher $T$. The measurements were carried out at $B=0.5\mathrm{T}$ to suppress a small contribution of weak localization.