  Laser-driven electron transport across a sample has garnered enormous
attentions over several decades, because it potentially allows one to control
spin transports in spintronics. But light is a transverse electromagnetic wave,
how an electron acquires a longitudinal velocity has been very puzzling. In
this paper, we show a general mechanism is working. It is the magnetic field
{\bf B} that steers the electron moving along the light propagation direction,
while its strong transverse motion leads to local excitation. We employ the
formalism put forth by Varga and Toroke to show that if we only include {\bf
E}, the electron only moves transversely with a large velocity. Including both
{\bf B} and {\bf E} and using real experimental laser parameters, we are able
to demonstrate that a laser pulse can drive the electron along the axial
direction by 20 to 262 $\rm \AA$, consistent with the experiments. The key
insight is that {\bf B} changes the direction of the electron and allows the
electron to move along the Poynting vector of light. Our finding has an
important consequence. Because a nonzero {\bf B} means a spatially dependent
vector potential ${\bf A} (\br,t)$, ${\bf B}=\nabla \times {\bf A}(\br,t)$,
this points out that the Coulomb gauge, that is, replacing ${\bf A}(\br,t)$ by
a spatial independent ${\bf A}(t)$, is unable to describe electron and spin
transport under laser excitation. Our finding is expected to have a potential
impact on the ongoing investigation of laser-driven spin transport.
