  Twisted bilayer graphene (TBG) aligned with hexagonal boron nitride (h-BN)
substrate can exhibit an anomalous Hall effect at 3/4 filling due to the
spontaneous valley polarization in valley resolved moir\'e bands with opposite
Chern number [Science 367, 900 (2020), Science 365, 605 (2019)]. It was
observed that a small DC current is able to switch the valley polarization and
reverse the sign of the Hall conductance [Science 367, 900 (2020), Science 365,
605 (2019)]. Here, we discuss the mechanism of the current switching of valley
polarization near the transition temperature, where bulk dissipative transport
dominates. We show that for a sample with rotational symmetry breaking, a DC
current may generate an electron density difference between the two valleys
(valley density difference). The current induced valley density difference in
turn induces a first order transition in the valley polarization. We emphasize
that the inter-valley scattering plays a central role since it is the channel
for exchanging electrons between the two valleys. We further estimate the
valley density difference in the TBG/h-BN system with a microscopic model, and
find a significant enhancement of the effect in the magic angle regime.
