Quantum geometry is a well-established framework for understanding transport and optical responses in quantum materials. In this work, I study the photon drag effect in Dirac electrons using the quantum geometric interpretation of nonvertical optical transitions. Due to the particle-hole symmetry inherent in Dirac electrons, the shift photon-drag photocurrent is dominated by dissipationless Fermi surface contributions, connected to the dipole of quantum metric tensor. I find that this dipole is significantly enhanced by a small band gap in massive Dirac electrons and remains robust in the massless limit. I demonstrate the existence of a circular shift photon-drag current in the effective Hamiltonian at the $L$ point of bismuth, where the bands exhibit trivial topology, highlighting the ubiquity of the circular photon-drag effect in centrosymmetric materials.

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• Photocurrent
• Photogalvanic effect
• Dirac semimetal
• Approximation methods for many-body systems
• Many-body techniques
• Perturbation theory