Figure 1

(Color online) (a) Sample geometry and measurement configuration. The boundary of our graphene sheet is denoted by a white line. (b) Upper set: time-reversal closed paths contributing to WL in a normal electronic system with an isotropic scattering probability (shown on the right). Lower set: similar time-reversal closed paths in graphene with an anisotropic scattering probability (shown on the right). (c) A cone-shape energy dispersion relation of graphene. There are two different $K$ points (valleys) with different chiralities (denoted by $\pm$). The dotted and solid arrows represent the intravalley and the intervalley scatterings, respectively.Reuse & Permissions

Figure 2

(Color online) (a) The back-gate-voltage dependence of the longitudinal sample resistance. The mobility $\left(\mu \right)$ of the sample is $\sim 4000{\text{cm}}^2/\text{V}\text{s}$ outside the Dirac region. Inset: the half-integer quantum Hall effect measured in 9 T and at 120 mK confirms that our graphene sheet is single layered. (b) Correction of the magnetoconductivity for various gate voltages $\left(G_Q=e^2/h\right)$. The carrier density can be estimated with a relation $n\left(\text{in}{\text{cm}}^{-2}\right)=7\times {10}^{10}\left[V_{bg}\left(\text{in}\text{V}\right)-32\right]$ with the positive (negative) value for electrons (holes). Dots and lines represent experimental data and best fits, respectively.Reuse & Permissions

Figure 3

(Color online) (a) Best-fit values of the characteristic lengths as a function of gate voltage at the base temperature of 120 mK. As denoted by arrows, the lower bounds of the error bars of $L_{\ast }$ for a few $V_{bg}$ go as low as $\sim 1\text{nm}$, which are not physical and are considered to arise from the uncertainty involved in fitting to the particular functional form of Eq. (1) as discussed in Ref. 3. (b) Inelastic scattering rate as a function of conductance $g$ at the base temperature, 120 mK. The line is a best fit to the first term in Eq. (2). (c) Temperature dependence of the characteristic lengths at a dense-electron region $\left(V_{bg}\sim 60\text{V}\right)$. Dotted lines are guides to the eyes. (d) Inelastic scattering rates at different gate voltages as a function of temperature. The values of ${\tau }_{\varphi }^{-1}$ for $V_{bg}=60\text{V}$ $\left(-35\text{V}\right)$ is multiplied by a factor of three (ten) for clarity of the temperature dependence. Lines are best fits to Eq. (2). Inset: Temperature dependence of $L_{\varphi }$. Dotted lines are guide to the eyes and the arrows indicate the saturation temperature $\left(T_{\text{sat}}\right)$.Reuse & Permissions