The paper overviews experimental and theoretical studies of photocurrents induced in various Dirac fermions systems by polarized electromagnetic radiation. We consider second order opto-electronic phenomena [1,2] excited by terahertz radiation in topological insulators (TIs). In focus of our discussion are two- (2D) and three- (3D) dimensional HgTe-based topological TIs [3,4]. We present the state-of-the-art of the experiments, discuss the phenomenological and microscopic theory, and show that nonlinear transport excited by laser radiation opens up new opportunities for the probing of Dirac electrons. A particular attention is paid to the helicity sensitive edge photogalvanic currents in 2D TIs [5] and cyclotron resonance assisted spin polarized currents in 3D TIs [6] and HgTe/HgCdTe quantum wells of a critical thickness [7,8]. We demonstrate that cyclotron resonance induced photocurrents in the surface states of 3D TIs provides a sensitive method to probe the cyclotron masses of Dirac fermions, which can be applied even for micrometer sized structures, to measure Fermi velocity, and to study tiny details of the spin orientation in TIs, in particular, to explore the role of bulk and structure inversion asymmetry in the band structure.

[1] S.D. Ganichev and W. Prettl, Intense Terahertz Excitation of Semiconductors, Oxford University Press (2006)

[2] M.M. Glazov and S.D. Ganichev, Physics Reports 535 101-138 (2014)

[3] B.A. Bernevig, et al., Science 314, 1757 (2006)

[4] M.S. König, et al., Science 318, 766 (2007)

[5] Z.D. Kvon, et al., JETP Letters 99, 290-294 (2014)

[6] K.-M. Dantscher, et al., Phys. Rev. B 92, 165314 (2015)

[7] P. Olbrich, et al., Phys. Rev. B 87, 235439 (2013)

[8] C. Zoth, et al., Phys. Rev. B 90, 205415 (2014)