  Advances in manipulating the structure of optical beams enable the study of
interaction between structured light and low-dimensional semiconductor systems.
We explore the photocurrents in two-dimensional systems excited by such
inhomogeneous radiation with structured field. Besides the contribition
associated with the intensity gradient, the photocurrent contains contributions
driven by the gradients of the Stokes polarization parameters and the phase of
the electromagnetic field. We develop a microscopic theory of the photocurrents
induced by structured light and derive analytical expressions for all the
photocurrent contributions at intraband transport of electrons. The theory is
applied to analyze the radial and azimuthal photocurrents excited by twisted
light beams carrying orbital angular momentum, and possible experiments to
detect the photocurrents are discussed.
