Transition between Electron Localization and Antilocalization in Graphene

We show that quantum interference in graphene can result in antilocalization of charge carriers—an increase of the conductance, which is detected by a negative magnetoconductance. We demonstrate that depending on experimental conditions one can observe either weak localization or antilocalization of carriers in graphene. A transition from localization to antilocalization occurs when the carrier density is decreased and the temperature is increased. We show that quantum interference in graphene can survive at high temperatures, up to $T\sim 200\mathrm{K}$, due to weak electron-phonon scattering.

Figure 1

(a) The trajectories of an electron scattered by impurities that give rise to a quantum correction to the conductance. (b) A diagram of the scattering times related to quantum interference in graphene. The solid curve separates the regions of electron localization and antilocalization. Points are experimental values found from the analysis of the magnetoconductance using Eq. (1), for three regions of electron density.

Figure 2

(a) Resistivity as a function of the carrier density, with the three regions where the magnetoconductance is studied indicated by bars. Insets: a diagram of the sample and the results of the quantum Hall effect measurement. (b),(c),(d) Evolution of the magnetoconductance with decreasing electron density, at three temperatures. Solid curves are fits to Eq. (1).

Figure 3

(a),(b),(c) Evolution of the magnetoconductance with increasing temperature in the three studied regions, showing a transition from positive to negative low-field magnetoconductance. Bottom panels show the results at high temperatures. Solid curves are fits to Eq. (1).

Figure 4

Temperature dependence of the dephasing rate for the three regions. Solid curves are fits to the electron-electron scattering rates found as a sum of Eq. (3, 5): (a) $\alpha =1.5$, $\beta =0$; (b) $\alpha =1.5$, $\beta =2.5$; (c) $\alpha =0$, $\beta =2.5$. Dotted lines are electron-phonon rates calculated using Eq. (4).