  We demonstrate that dislocations in the graphene lattice give rise to
electron Berry phases equivalent to quantized values {0,1/3,-1/3} 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 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 Buttiker 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.
