We develop a phenomenological theory describing the interaction of superconducting condensate with a Bessel beam of twisted light characterized by a nonzero angular momentum $m$. Starting from the time-dependent Ginzburg-Landau model with the complex relaxation time, we calculate the spatial profiles of dc photoinduced currents and magnetic fields as well as the second harmonic response. The photocurrents and magnetic fields are shown to be determined both by the helicity of light and its orbital momentum $m$. Analyzing the half-space and thin film geometries, we discuss possible experimental tests aimed to probe the superconducting photocurrents and magnetic fields.

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• Photocurrent
• Structured light
• Superconductivity
• Time-dependent Ginzburg-Landau theory