We demonstrate that dislocations in the graphene lattice give rise to electron Berry phases equivalent to quantized values $\left\{0,\pm \frac{1}{3}\right\}$ in units of the flux quantum but with an opposite sign for the two valleys. An elementary scale consideration of a graphene Aharonov-Bohm ring equipped with valley filters on both terminals, encircling a dislocation, says that in the regime where the intervalley mean-free path is large compared to the intravalley phase coherence length, such that the valley quantum numbers can be regarded as conserved on the relevant scale, the coherent valley-polarized currents sensitive to the topological phases have to traverse the device many times before both valleys contribute, and this is not possible at intermediate temperatures where the latter length becomes of the order of the device size, thus leading to an apparent violation of the basic law of linear transport that magnetoconductance is even in the applied flux. We discuss this discrepancy in the Feynman path picture of dephasing when addressing the transition from quantum to classical dissipative transport. We also investigate this device in the scattering matrix formalism, accounting for the effects of decoherence by the Büttiker dephasing voltage probe type model which conserves the valleys, where the magnetoconductance remains even in the flux, also when different decoherence times are allowed for the individual, time-reversal connected, valleys.

• Received 13 November 2008

DOI:https://doi.org/10.1103/PhysRevB.79.155111