  According to Bliokh et al., allowing free propagation along the direction of
a uniform magnetic field, the familiar Landau electron state can be regarded as
a non-diffracting version of the helical electron beam propagating along the
magnetic field. Based on this observation, they argued that, while propagating
along the magnetic field, the Landau electrons receive characteristic rotation
with three different angular velocities, depending on the eigen-value $m$ of
the canonical OAM operator, which is generally gauge-variant, and this
splitting was in fact experimentally confirmed. Through complete analyses of
highly mysterious $m$-dependent rotational dynamics of the quantum Landau
states, we try to make clear how and why their observation does not contradict
the widely-believed gauge principle.
