  We study the conductance of graphene nanoribbons with long-range disorder.
Due to the absence of intervalley scattering from the disorder potential,
time-reversal symmetry (TRS) can be effectively broken even without a magnetic
field, depending on the type of ribbon edge. Even though armchair edges
generally mix valleys, we show that metallic armchair nanoribbons possess a
hidden pseudovalley structure and effectively broken TRS. In contrast,
semiconducting armchair nanoribbons inevitably mix valleys and restore TRS. As
a result, in strong disorder metallic armchair ribbons exhibit a perfectly
conducting channel, but semiconducting armchair ribbons ordinary localization.
TRS is also effectively broken in zigzag nanoribbons in the absence of valley
mixing. However, we show that intervalley scattering in zigzag ribbons is
significantly enhanced and TRS is restored even for smooth disorder, if the
Fermi energy is smaller than the potential amplitude. The symmetry properties
of disordered nanoribbons are also reflected in their conductance in the
diffusive regime. In particular, we find suppression of weak localization and
an enhancement of conductance fluctuations in metallic armchair and zigzag
ribbons without valley mixing. In contrast, semiconducting armchair and zigzag
ribbons with valley mixing exhibit weak localization behavior.
