Sliding electron crystals develop a transverse Hall velocity set by Galilean non-invariance as well as parent-band Berry curvature, so the net Hall conductance is generally unquantized.
Remarkably, the dc transport data are consistent with a pinning-depinning transition, and the Hall conductance in the depinned regime is indeed unquantized
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Berry Phase Dynamics of Sliding Electron Crystals
Sliding electron crystals develop a transverse Hall velocity set by Galilean non-invariance as well as parent-band Berry curvature, so the net Hall conductance is generally unquantized.