Intervalley Scattering, Long-Range Disorder, and Effective Time-Reversal Symmetry Breaking in Graphene

We discuss the effect of certain types of static disorder, like that induced by curvature or topological defects, on the quantum correction to the conductivity in graphene. We find that when the intervalley scattering time is long or comparable to ${\tau }_{\varphi }$, these defects can induce an effective time-reversal symmetry breaking of the Hamiltonian associated to each one of the two valleys in graphene. The phenomenon suppresses the magnitude of the quantum correction to the conductivity and may result in the complete absence of a low-field magnetoresistance, as recently found experimentally. Our work shows that a quantitative description of weak localization in graphene must include the analysis of new regimes, not present in conventional two-dimensional electron gases.

Figure 1

Geometry of the scattering process analyzed in the text. An impurity potential is placed at the center of a spherical bump in a flat sheet.

Figure 2

Wave functions within the spherical cap shown in Fig. 1 for $\updownarrow =20$. These two solutions, in flat space, are related by the effective time-reversal symmetry defined in each valley.