  We theoretically investigate the interband transitions and quantum kinetics
induced by light carrying orbital angular momentum, or twisted light, in bulk
semiconductors. We pose the problem in terms of the Heisenberg equations of
motion of the electron populations, and inter- and intra-band coherences. Our
theory extends the free-carrier Semiconductor Bloch Equations to the case of
photo-excitation by twisted light. The theory is formulated using cylindrical
coordinates, which are better suited to describe the interaction with twisted
light than the usual cartesian coordinates used to study regular optical
excitation. We solve the equations of motion in the low excitation regime, and
obtain analytical expressions for the coherences and populations; with these,
we calculate the orbital angular momentum transferred from the light to the
electrons and the paramagnetic and diamagnetic electric current densities.
